Lebanese University Faculty of Engineering II. Final year project. Mechanical Engineering Degree. Samer Salloum

Lebanese University Faculty of Engineering II Final year project Submitted in fulfilment of the requirements for the Mechanical Engineering Degree by Samer Salloum Exoskeleton for human performance augmentation Project supervisor: Dr. Rany Rizk 2012

Acknowledgments First, I would like to express my sincere appreciation to my supervisor, Dr. Rany Rizk, for his guidance, encouragement, and support throughout my working period. I am especially grateful to my colleague in the Faculty of Engineering, Ali Krayyim, Ali Abou Hasan, Rouba Loutfi, for their tremendous help in writing my report. In addition, I want to thank the responsible of the Mechanical Department in the faculty of Engineering Dr.Khalil El Khoury whose assistance during the past few years has been of great value to my educational progress. II

Abstract The human's ability to perform a variety of physical tasks is limited not by his intelligence, but by his physical strength. A robot manipulator can easily perform some tasks human cannot do due to their physical limits. However robots artificial control algorithms miss flexibility. It seems therefore that, if we can more closely integrate the mechanical power of a machine with the human body under the supervisory control of the human's intellect, we will then have a system which is superior to a loosely integrated combination of a human and his fully automated robot, as in the present day robotic systems. Exoskeletons are such systems based on this principle. The human provides control signals for the exoskeleton. The exoskeleton actuators provide most of the power necessary for performing the task. Exoskeletons for human performance enhancement are controlled and wearable devices and machines. They can increase the speed, strength, and endurance of the operator. These systems have the capacity to combine decision making capabilities with machine dexterity and power, to greatly augment a person s physical abilities. In fact exoskeletons promise to allow people to run farther, jump higher, and bear larger loads while expending less energy. They have the ability to traverse non paved terrain accessing locations where wheeled vehicles cannot. Thus exoskeletons can turn ordinary people into "super soldiers". They give the ability to carry far more weight faster, farther, and for longer periods of time than is possible for humans alone. These "wearable robots" can also help rescue workers more effectively dig people out from under rubble after earthquakes or carry them from burning buildings while protecting the rescuers from falling debris and collapsing structures. Exoskeletons can help nurses to move patients and protect industrial and construction workers from back injuries while lifting heavy loads. Exoskeleton architecture and control scheme: We choose a pseudo anthropomorphic architecture with similar kinematics to a human for our exoskeleton. Each exoskeleton leg has three DOF at the hip, one DOF at the knee, and three DOF at the ankle. Only the flexion extension DOF at the hip, knee and ankle are actuated. Hip and ankle flexion extension DOF are also equipped with passive impedances. The exoskeleton is rigidly attached to the operator at the feet and at the torso. The exoskeleton legs can therefore follow the human. But they are not required to match exactly since there are only two rigid attachments. The control algorithm ensures that the exoskeleton moves in concert with the pilot with minimal interaction force between the two. The input to the exoskeleton is derived from the set of contact forces between the exoskeleton and the human. The contact force is estimated, based on measurements from the exoskeleton only, appropriately modified (in the sense of control theory to satisfy performance and stability criteria), and used as an input to the exoskeleton control, in addition to being used for actual manoeuvring. Therefore, the human wearing the exoskeleton exchanges both power and information signals with the exoskeleton. Such a control scheme ensures that the exoskeleton bears the bulk of the weight by itself, while transferring a scaled down value of the load s actual weight to the user as a natural feedback. In this fashion, the worker can still sense the load s weight and judge his/her motions accordingly. However the force he/she feels is greatly reduced. The effectiveness of the lower extremity exoskeleton is a direct result of the control system s ability to leverage the human intellect to provide balance, navigation, and path planning while ensuring that the exoskeleton actuators provide most of the strength necessary for supporting payload and walking. III

Table of Contents Cover Page I Acknowledgments II Abstract III Table of Contents IV 1 State of The Art 1 1.1 History and Background 1 1.1.1 Early Exoskeletons: 1 1.1.2 DARPA Program Exoskeletons 2 1.1.3 Other Lower Limb Exoskeletons 3 1.2 Anatomical Terminology 4 1.2.1 Relative positions 4 1.2.2 Anatomical reference planes 4 1.2.3 Joint motion 5 1.3 Human Gait 6 1.3.1 Introduction 6 1.3.2 Muscle activity during the gait cycle 6 1.3.3 Ground reaction forces during gait cycle 7 1.4 Metabolic effect of forces applied to the human during walking 8 1.5 Introduction of passive elements 9 1.5.1 Introduction 9 1.5.2 Hip Kinematics and Kinetics 9 1.5.3 Knee Kinematics and Kinetics 10 1.5.4 Ankle Kinematics and Kinetics 11 1.5.5 Conclusion: 11 2 Dynamic Models 12 2.1 Introduction 12 2.2 The Human Machine Interface Model 12 2.3 Frames and notations 13 2.4 Jump (Double Swing) Model 14 2.5 Single Support Model 16 2.6 Double support model: 19 2.7 Double Support with One Redundancy 21 2.8 Double support double redundancy model: 23 2.9 Conclusion: 24 3 Evaluation of Contending Control Strategies 25 3.1 Introduction 25 3.2 Myosignal based Systems 25 3.3 Master slave control 25 IV

3.4 Direct Force Feedback 26 3.5 Virtual Generalized Force Control 27 3.6 Virtual Joint Torque Control 27 3.7 Conclusion 28 4 Virtual torque control stability and performance analysis 29 4.1 Introduction 29 4.2 Simple One Degree of Freedom (DOF) 30 4.2.1 Introduction 30 4.2.2 Closed loop analysis 31 4.2.3 Frequency response 33 4.2.4 Stability 37 4.3 Nonlinear Systems 38 4.4 Stability of a Multi D.O.F. Nonlinear System with Feedback Linearization 39 4.5 Conclusion 40 5 General conclusion 41 6 References 43 7 Appendix : Derivation of mathematical equations 1 7.1 Jump (double swing) dynamic model: 1 7.2 Single support dynamic model: 8 7.3 Double support: one redundant leg 17 7.4 Double support: foot flat 21 V

1 State of The Art 1.1 History and Background In this section, we describe the research done in developing exoskeletons primarily intended to allow healthy individuals to perform difficult tasks more easily or enable them to perform tasks that are otherwise impossible using purely human strength or skill. 1..1.1 Early Exoskeletons: The earliest mention of a device resembling an exoskeleton is granted to Yagn in 1890. His invention consisted of long bow/leaf springs operating in parallel to the legs. It was intended to augment running and jumping. The bow spring stores energy developed by the body weight and by the act of walking, running, or jumping. This machine effectively transfers the body s weight to the ground to reduce the forces borne by the stance leg. The device was never built or successfully demonstrated. In the late 1960s, General Electric constructed a full body powered exoskeleton prototype, dubbed Hardiman (from the Human Augmentation Research and Development Investigation ). The exoskeleton was an enormous hydraulically powered machine (680 kg, 30 DOFs).It includes components for amplifying the strength of the arms and legs of the wearer. The intention of the Hardiman project was to drastically increase the strength capabilities of the wearer (approximately 25:1). This man amplifier was designed as a master slave system. The master portion was the inner exoskeleton which followed all the motions of the human operator. The outer exoskeleton consisted of a hydraulically actuated slave which followed all the motions of the master. This system was too large and heavy with severe stability problems. Difficulties in human sensing, stability of the servomechanisms, safety, power requirements and system complexity kept it from walking. Fig1.1: Yagn exoskeleton Fig1. 2: Hardiman exoskeleton 1

1.1.2 DARPA Program Exoskeletons 1) Berkeley Exoskeleton (BLEEX): Its developers claim it as the first load bearing and energetically autonomous exoskeleton. It has seven degrees of freedom per leg. Four are powered by linear hydraulic actuators. This system allows its wearer to carry significant loads with minimal effort over rough, unstructured, and uncertain terrains. The control system utilizes the information from 8 encoders and 16 linear accelerometers to determine angle, angular velocity, and angular acceleration for each of the eight actuated joints. A foot switch, and load distribution sensor per foot determines ground contact and force distribution between the feet during double stance. Eight single axis force sensors are used in force control of each of the actuators. An inclinometer determines the orientation of the backpack with respect to gravity. The control strategy allowed the human to provide the intelligent control while the actuators provided the necessary strength for locomotion. In terms of performance, users wearing BLEEX can reportedly support a load of up to 75 kg while walking at 0.9 m/s, and can walk at speeds of up to 1.3 m/s without the load. 2) Sarcos Exoskeleton: Full body Wearable Energetically Autonomous Robot (WEAR). The system permits walking and running and can react to disturbance inputs, e.g. stumbling. It employs rotary hydraulic actuators located directly on the powered joints of the device. The Sarcos exoskeleton has reportedly been successful in demonstrating a number of impressive feats: structure supporting entire load of 84 kg, wearer standing on one leg while carrying another person on their back, walking at 1.6 m/s while carrying 68 kg on the back and 23 kg on the arms, walking through 23 cm of mud, as well as twisting, squatting, and kneeling. 3) MIT Exoskeleton: The MIT exoskeleton employs a quasi passive design that does not use any actuators for adding power at the joints. Instead, the design relies completely on the controlled release of energy stored in springs during the (negative power) phases of the walking gait.the quasi passive elements in the exoskeleton (springs and variable damper) were chosen based on an analysis of the kinetics and kinematics of human walking. The 3 DOF hip employs a spring loaded joint in the flexion/ extension direction that stores energy during extension that is released during flexion. The knee of the MIT exoskeleton consists of a magnetorheological variable damper. It is controlled to dissipate energy at appropriate levels throughout the gait cycle. For the ankle, separate springs for dorsi and plantar flexion are implemented in order to capture the different behaviours during these two stages of motion. Without a payload, the exoskeleton weighs 11.7 kg and requires only 2W of electrical power during loaded walking. This power is used mainly to control the variable damper at the knee. Fig1.3: DARPA exoskeleton a) Bleex exoskeleton b) Sarcos exoskeleton c) MIT exoskeleton 2

1.1.3 Other Lower Limb Exoskeletons 1) Hybrid Assistive Leg: In 2002, Tsukuba University in Japan developed an exoskeleton called the Hybrid Assistive Leg. Using EMG sensors on the human s leg muscles and ground reaction force sensors, HAL controls its electric actuators at the knee, hip and elbow. In distinction to the load carrying BLEEX, Sarcos, and MIT exoskeletons, the HAL system does not transfer a load to the ground surface, but simply augments joint torques at the hip, knee, and ankle. HAL can provide assist torques for the user's hip and knee joints according to the user's intention by using EMG signal as the primary command signal. Reportedly, it takes two months to optimally calibrate the exoskeleton for a specific user. HAL 5 is currently in the process of being readied for commercialization. 2) Nurse Assisting Exoskeleton: In Japan, the Kanagawa Institute of Technology has developed a full body wearable power suit, powered by unique pneumatic actuators. The forces at their three actuators (knee, waist, and elbow) are controlled by measuring the hardness of the corresponding human muscles. The controller structure calculates the joint torques required to maintain a statically stable pose by computing the inverse of a rigid body model that takes into account the current joint angles and masses of the components of the exoskeleton and the weight of the patient. The weight of the patient is measured beforehand. User intent is determined via force sensing resistors (FSRs) attached to the surface of the skin above a muscle (the rectus femoris for the knees) via an elastic band. One of the interesting aspects of the mechanical design of the Kanagawa full bodied suit is that there is no mechanical component on the front of the wearer, allowing the nurse to have direct physical contact with the patient that he or she is carrying. 3) RoboKnee: RoboKnee is an exoskeleton developed by the company Yobotics. The device is supporting the knee motion with a series elastic actuator attached to the thigh and shank. The control system calculates the actuator force based on the knee torque necessary for maintaining a statically stable pose. This is performed by estimating the ground reaction forces under both feet with two load cells. From the actuator length the knee angle is derived. Through inverse computation of the dynamics of this model the knee joint torque is computed which is required to maintain a statically stable pose with the current angular configuration, even when the system is in motion. This knee torque is multiplied by a factor that defines the support ratio of the actuation, resulting in the amount of support the actuation is contributing to the motion. Fig1.4: Other Lower Limb Exoskeletons a) HAL exoskeleton b) nurse assisting exoskeleton c) RoboKnee exoskeleton 3

Talking about exoskeleton, one should never forget the work done by Miomir vukobratovic and his associates at the Mihailo Pupin Institute in Belgrade in the late 1960s and 1970s. Miomir devoted his work to the development of assistive technologies for physically challenged persons (active orthoses) to help them to walk. One of the most lasting contributions of the work with exoskeletons at Pupin Institute is in control methods for robotic bipeds. Indeed, Prof. Vukobratovic along with Devor Juricic is credited with developing the concept of the zero moment point and its crucial role in the control of bipedal locomotion. 1.2 Anatomical Terminology Due to its anthropomorphic nature, the motions, orientations, positions and geometry of the lower extremity exoskeleton will be described using the same vocabulary as the anatomical human. A quick review of the terminology used in the analysis of biomechanical systems follows. 1.2.1 Relative positions Anterior: to the back of the person Posterior: to the front of the person Distal: away from the trunk Proximal: towards the trunk Lateral: to the side of the person, away from the centreline. 1.2.2 Anatomical reference planes The anatomical position is often used for reference. It consists of an individual standing straight up with palms facing forward. From there, it is useful to define the anatomical planes. Spatial positions of various parts of the human body can be described referring to the three orthogonal reference planes shown in figure below The transverse plane passes through the hip bone and lies at a right angle to the long axis of the body, dividing it into superior and inferior sections. Any imaginary sectioning of the human body that is parallel to this plane is called a transverse section or cross section. The frontal plane is the plane that divides the body into anterior and posterior sections. It is also called the coronal plane. The sagittal plane is the front to back plane that cuts the human into two symmetric halves. The sagittal plane divides the body into left and right sections. It is the only plane of symmetry in the human body. Fig1.5: Reference planes of body in standard anatomic position (Inman et al., 1981). 4

1.2.3 Joint motion Anatomists have also introduced standard terminology to classify motion configurations of the various parts of the human body. Most movement modes require rotation of a body part around an axis that passes through the centre of a joint, and such movements are called angular movements. The common angular movements of this type are flexion, extension, adduction, and abduction. Flexion and extension are movements that occur parallel to the sagittal plane. Flexion is rotational motion that brings two adjoining long bones closer to each other, such as occurs in the flexion of the leg or the forearm. Extension denotes rotation in the opposite direction of flexion; for example, bending the head toward the chest is flexion and so is the motion of bending down to touch the foot. Flexion at the shoulder and the hip is defined as the movement of the limbs forward whereas extension means movement of the arms or legs backward. In other words, Extension is the rotation direction in which the joint straightens, and flexion is the direction in which the joint angle increases. Abduction and adduction are the movements of the limbs in the frontal plane. Abduction is movement away from the longitudinal axis of the body whereas adduction is moving the limb back. Swinging the arm to the side is an example of abduction. During a pull up exercise, an athlete pulls the arm toward the trunk of the body, and this movement constitutes adduction. Spreading the toes and fingers apart abducts them. The act of bringing them together constitutes adduction. Further, motion of the ankle in the coronal plane is referred to as eversion (away from the centre of the body) and inversion. Yet another example of angular motion is the rotation of a body part with respect to the long axis of the body or the body part. This angular motion is called rotation. The rotation of the head could be to the left or right. Similarly, the forearm and the hand can be rotated to a degree around the longitudinal axis of these body parts. There are other types of specialized movements such as the gliding motion of the head with respect to the shoulders or the twisting motion of the foot that turns the sole inward. Fig1.6: Joint motion Note: The sign convention that is used is that each joint angle is measured as the positive counter clockwise displacement of the distal link from the proximal link (zero in standing position). 5

1.3 Human Gait Fig1.7: The eight main phases of the walking cycle from heel strike to heel strike (Perry, 1992). 1.3.1 Introduction The locomotion mechanism changes its structure during a single walking cycle from an open to a closed kinematic chain. During walking, two different situations arise in sequence: the statically stable double support phase in which the mechanism is supported on both feet simultaneously, and statically unstable single support phase, when only one foot of the mechanism is in contact with the ground while the other is being transferred from the back to front positions. 1.3.2 Muscle activity during the gait cycle Muscles can contract concentrically, isometrically or eccentrically. Concentric contraction (Positive work) occurs when the muscle gains tension and shortens. Isometric contraction occurs when the muscle gains in tension but does not change length. Eccentric contraction (negative work) occurs when the muscle gains tension and lengthens. Many muscles responsible for walking contract isometrically to allow for maintenance of upright posture against gravity. Brief bursts of more energy expensive contraction of muscle are added when needed to provide power for forward motion (Inman et al., 1981). Much muscle activity in walking is isometric or eccentric. Negative work allows the limbs to absorb energy while resisting the pull of gravity, yet remain metabolically efficient. Positive work of muscles during walking allows acceleration of limbs and powers such activities as flexion of the hip during pre swing. The gait cycle is comprised of two distinct phases, the support phase and the swing phase, which require different motor strategies (Winter, 1983). During the support phase a net extensor moment generated by the hip, knee and ankle joints is required to prevent the collapse of the stance limb (Winter, 1983). In fact, during the stance phase, the muscles at the hip, knee and ankle generally act to decelerate and stabilize the body. The stance phase begins with heel contact, following a phase of controlled ankle plantar flexion. At the ankle, we see a small dorsiflexion moment shortly after contact. This moment prevents the foot from slapping down during initial contact with the ground. This is immediately followed by very rapid loading on the forward limb with shock absorption through controlled knee flexion and slowing of the body's 6

forward momentum. The quadriceps musculature eccentrically controls the rate of flexion, bringing the center of mass of the body to its lowest point. Then, the inertia of the trunk moving over the leg, helped by the quadriceps, returns the knee to full extension by the time of midstance, bringing the center of mass of the body to its maximum height. As the subject moves into the latter half of stance, a sizable plantarflexion moment is generated as a main contributor to the body s forward progression (forward acceleration of the trunk). This increase in plantarflexion moment is due to the gastrocnemius and soleus muscles contracting, essentially pushing the foot into the ground. Finally, during preswing, and while there is double limb support of the body weight, the knee eccentrically flexes, the hip flexes and the ankle plantarflexes to accelerate the leg forward into the swing phase. During the first half of the swing phase, the ankle dorsiflexes to ensure clearance of the ground by the toe (Mena et al., 1981; Winter, 1991) and the leg accelerates forward due to concentric hip flexion and the effect of gravity. The extension of the knee is controlled at this time by the eccentric contraction of the quadriceps. In the mid swing phase, the concentric contraction of the hip extensors and the inertia of the foot and the shank continue to extend the knee (Cavanagh & Gregor, 1975; Winter, 1991). An eccentric contraction of the hamstrings slowly decelerates the foot and shank until the knee is fully extended. During late swing, activation of the hamstrings group causes a flexion moment at the knee, and an extension moment at the hip, both of which contribute to the reduction of the anterior posterior (A P) velocity of the foot prior to heel contact (HC). Finally, with a plantarflexed ankle, the heel touches the ground. 1.3.3 Ground reaction forces during gait cycle The ground reaction forces for a subject walking at a natural cadence are illustrated in Fig8. The vertical component of the ground reaction force (GRF) is by far the largest, with the peak AP (anteroposterior) component of the GRF next largest in magnitude. Notice how the AP force component has both a negative phase and a positive phase corresponding to braking and propulsive phases during stance (62%). The first hump of the vertical component of the GRF corresponds to a deceleration of the whole body COM during weight acceptance (note how this corresponds with the AP braking force). The second hump in the vertical component of the GRF and the positive phase of the AP force component accelerate the body COM upward and forward as the subject prepares for push off at the end of stance. Fig1.8: Ground reaction forces during the stance phase of natural cadence walking (Winter 1991). The stance phase begins at foot strike and ends when the foot leaves the ground. 7

1.4 Metabolic effect of forces applied to the human during walking Walking metabolism is set by muscles that act to perform work on the centre of mass, swing the legs relative to the centre of mass, and support the body weight. Total metabolic energy expenditure during locomotion is composed of 10 33% for leg swing and 67 90% for body weight support and forward propulsion. A number of researchers have performed metabolic experiments where external loads were applied to the body in vertical and horizontal directions. The results of these experiments are summarized in Fig9. Fig1.9: Summary of results from metabolic studies while exerting external forces on the human (Figure courtesy of Daniel Paluska). One set of experiments recorded metabolic data while various levels of assistive and impeding external horizontal forces were applied to the waist of a subject walking on a treadmill (Gottschall and Kram, 2003). A 47% reduction in metabolic rate was found when an aiding horizontal force equal in magnitude to 10% body weight was applied to a person. Further, the study showed that the 10% value was optimal and that a larger assisting force increased metabolic demands. Researchers have also performed experiments to examine the effect of gravity on the metabolic rate of walking (Farley and McMahon, 1992). In this investigation, a series of steel springs were used to apply a nearly constant upward force to the body through a bicycle saddle. This reduced the force that the muscles had to generate to support the weight of the body. Simulated reduced gravity experiments have demonstrated that the metabolic cost of walking and running can be reduced by 33% and 75% respectively, if gravity is reduced by 75% [Jiping et al. (1991); Farley & McMahon (1992)]. These experiments have shown that if gravity is decreased by at least 50%, a person can run at a lower metabolic rate than he could have walked. These biomechanical experiments suggest that it may be possible to build a leg exoskeleton that reduce the metabolic cost of walking while carrying a load, by adding power throughout the gait cycle, to propel the wearer forward and to reduce the effects of exoskeleton mass. Furthermore, the exoskeleton greatly reduces the stress on the shoulders and back, by efficiently transferring the load forces to the ground. Conversely, without the exoskeleton, the entire payload force was transmitted through the human s shoulders, hips, and legs. This resulted in an experience of discomfort at the shoulder strap and waist belt interfaces. 8

1.5 Introduction of passive elements 1.5.1 Introduction Muscle tissue requires metabolic energy (i.e. fuel) to develop force. The total energy consumption depends on both the force and work performed during the contraction. Early studies showed that isolated muscle requires some energy during active lengthening contractions (negative work), a little more energy during isometric contractions (Force but no mechanical work) and the most energy during active shortening contractions (positive work). In other words, there is always metabolic cost associated with absorbing mechanical energy. However, the metabolic cost of absorbing power is 0.3 to 0.5 times that of producing power [De Looze et al. (1994)]. With the introduction of passive elements (springs and dampers) to the exoskeleton joints, the human muscles would absorb less negative power and produce less positive power, thus providing metabolic advantages. In fact, springs as energy storage elements can be implemented at joints that have a period of negative power followed by a period of positive power. The spring could store energy during the negative power period and release it during the positive power period. The human muscles would then absorb less negative power and produce less positive power, thus providing metabolic advantages. Dampers can be implemented for joints that mainly dissipate energy. These dissipative joints have a negative average joint power. The human muscles would then absorb less negative power, thus providing metabolic advantages. However, the spring and damper elements may or may not lower the metabolic cost for walking. Each passive element added to the exoskeleton leg is an additional distal mass. Added distal mass increases leg swing costs due to added inertia and collision costs due to foot ground impact [Royer et al. (2005)]. Thus to attain a metabolic reduction, the benefits of the passive elements must outweigh the disadvantages of the additional distal mass needed to implement the passive element [Royer et al. (2005)]. In the remainder of this chapter, biomechanics data of the hip, knee, and ankle joints will be analyzed to appropriately implement such passive elements and to find the desired spring and damper values. These kinematic data from Natick Army Labs are based on a participant walking normally and carrying a 47kg backpack [Harman (2000)]. 1.5.2 Hip Kinematics and Kinetics During normal walking, the human hip joint follows an approximate sinusoidal pattern. The thigh is flexed forward on heel strike and then the hip moves through extension during stance as the body is pivoted over the stance leg in a pendulum like motion. At heel strike there is a sharp increase in hip torque as the leg accepts the weight of body to begin the stance phase. A peak negative hip torque is experienced as the leg accepts load. A maximum positive torque occurs during the swing phase as the hip muscles provide energy to swing the leg forward. From the power profile at the hip, shown in Figure 10, three distinct regions are identified. H1 is a small region of positive power, not always present, which corresponds to concentric hip extensor activity during loading response. H2 is a region of negative power, corresponding to eccentric hip flexor activity during mid stance. Lastly, H3 is a region of positive power, corresponding to concentric activity in the hip flexors during pre swing and initial swing. 9

Fig1.10: Hip power profile and hip angle, 47 kg backpack (Harman data set from the Natick Army Labs). We conclude that that a spring placed at the hip joint could absorb the negative energy in H2 and release it during H3 to assist in swinging the leg forward. Plotting hip torque vs. hip angle, an approximate linear relationship can be seen between the hip torque and angle during the stance phase of the walking cycle. The spring constant for such an extension spring could be found, but its value depend heavily on the human exoskeleton mass. 1.5.3 Knee Kinematics and Kinetics In early stance there is initial flexion extension of the knee to help maintain a near horizontal trajectory of the body s centre of mass. After the initial flexion extension the knee remains locked for the remainder of the stance phase. The knee then undergoes flexion to allow for foot clearance during the swing phase. On heel strike, the knee bends slightly while exerting a maximum negative torque as the leg accepts the weight of the human. This is followed by a large positive extension torque that keeps the knee from buckling during early stance and also assists in straightening the leg. Figure 11 outlines the power of the knee as a function of gait cycle. At heel strike there is a region of negative power followed by a period of positive power as the knee goes through stance flexion extension. This quick flexion and extension motion is undesirable for the exoskeleton since it is preferred that the exoskeleton leg remain straight during this period. When the exoskeleton leg is completely straight, it acts as a column and all the downward vertical forces from the payload get transmitted through the exoskeleton leg. Thus the exoskeleton would not benefit from a torsional spring placed at the knee. Also this figure show that for a large part of the swing phase the leg has a pendulum like motion with the knee varying the damping to control the swing leg duration. Fig1.11: knee power profile and knee angle, 47 kg backpack (Harman data set from the Natick Army Labs). From the gait data it appears that a variable damper is a perfect candidate for the knee joint (since the power profile is largely negative). During the swing phase, the variable damper would be engaged to control the swinging of the leg. However, due to his distal mass, the variable damper mechanism is 10

proven to be inefficient. Furthermore, in other task such as squatting and climbing stairs, the knee power profile becomes largely positive. 1.5.4 Ankle Kinematics and Kinetics The ankle joint experiences a range of motion of approximately 15 degrees in both directions during normal human walking. During the mid and late stance phases of walking the ankle eccentric plantarflexor activity creates negative joint torque as the ankle controls the forward movement of the centre of mass. From the power profile at the ankle, Fig 12, two distinct regions are identified. A1 is a region of negative power, corresponding to eccentric plantarflexor activity at the ankle during midstance and terminal stance. A2 is a region of positive power, corresponding to the concentric burst of propulsive plantarflexor activity during pre swing. Fig1.12: Ankle power profile and ankle angle, 47 kg backpack (Harman data set from the Natick Army Labs). We conclude that that a spring placed at the ankle of the exoskeleton could absorb the negative energy in A1, during controlled dorsiflexion, and later release it during A2 to assist in swinging the leg forward. 1.5.5 Conclusion: Biomechanical experiments suggest that it may be possible to build a leg exoskeleton that reduce the metabolic cost of walking while carrying a load, by adding power throughout the gait cycle, to propel the wearer forward and to reduce the effects of exoskeleton mass. A passive spring at the hip store energy through hip extension in the stance phase that is later released to assist in powered hip flexion through the swing phase. A passive spring at the ankle engages in controlled dorsiflexion to store energy that is later released to assist in powered plantarflexion. A damper at the knee would be engaged during the swing phase to control the swinging of the leg. However, due to his distal mass, the variable damper mechanism is proven to be inefficient. Although for slow walking speeds these passive elements could greatly reduce metabolic cost, at faster walking speeds the positive power becomes increases, and in this case a hybrid actuation approach may be beneficial where a small motor is used in conjunction with the spring. In this thesis, we will adopt this approach. 11

2 Dynamic Models 2.1 Introduction The locomotion mechanism changes its structure during a single walking cycle from an open to a closed kinematic chain. A different dynamic model is used depending on the configuration of the machine during the various states which occur during walking and running: jump (double swing), single stance, double stance, double stance with one redundant leg, double stance with two redundant legs. Along the bottom of the foot, switches detect which parts of the foot are in contact with the ground, and therefore identify the foot s configuration on the ground. This information is used by the controller to determine in which phase the exoskeleton is operating and which of the five dynamic models (listed above) apply. A load distribution sensor, (rubber pressure tube filled with hydraulic oil and sandwiched) is implemented between the human s foot and the main exoskeleton foot structure. Only the weight of the human (not the exoskeleton) is transferred onto the pressure tube and measured by the sensor. This sensor is used by the control algorithm to detect how much weight the human places on their left leg versus their right leg. This chapter is concerned with developing the dynamics models of a lower extremity exoskeleton worn by a human. The dynamic equations are derived using iterative Newton Euler dynamic formulation. 2.2 The Human Machine Interface Model The human is rigidly connected at the feet and the torso and compliantly attached along the shank and thigh. The force imposed by the human on the machine is the result of a non ideal source. It depends on a deviation between the positions of the human and the exoskeleton. It depends also on the force command input from the central nervous system. As described by Kazerooni, the human machine interface is compliant. The force generated by this impedance is the product of a diagonal positive definite impedance matrix and the positioning error between each degree of freedom of the human and of the machine. The operational torque imposed by the human, at some operational position q on the machine, can be modeled as: _) The determination of KH depends on factors relating to specific users and how well they fit to the machine. An exact quantification of KH is hence unreasonable for a multidimensional system. Nonetheless, the controller should be designed for the case in which there is no damping between the human and the machine. The impedance KH mimics a spring in tension and compression. This scenario is the most vulnerable to Instability. 12

2.3 Frames and notations Reference Frames Reference coordinate systems for the lower extremity exoskeleton are shown in Fig2.1, except for the inertia reference frame, frame 0, which depends on the system state. Frame 1: Fixed to the stance foot (foot 1) at the ankle with pointing toward the ground joint. Frame 2: Fixed to the stance shank (shank 1) at the knee with pointing toward the stance ankle (ankle 1). Frame 3: Fixed to the stance thigh (thigh 1) at the hip with pointing toward the stance knee (knee 1). Frame 4: Fixed to upper body at the hip with pointing toward the head. Frame 5: Fixed to the swing thigh (thigh 2) at the hip with pointing toward the swing knee (knee 2). Frame 6: Fixed to the swing shank (shank2) at knee2 with pointing toward the swing ankle (ankle 2). Frame 7: Fixed to the swing foot (foot 2) at ankle 2 with pointing toward the toe of foot2. Generalized Coordinates : Angle of foot l with ground : Ankle 1 extension (plantarflexion) : knee 1 flexion : Thigh l hip extension : Thigh 2 hip flexion : Knee 2 extension : Ankle 2 flexion (dorsiflexion) Body Segment properties Fig2.1: coordinate frame Denotes the segment's mass, Ii denotes the segment's inertia about its center of gravity (CG), L denotes the segment's length, LG denotes the distance between a segment's distal joint (furthest from the upper body), and its CG in the direction. The exception to this rule is the foot, where denotes the distance between the ankle and the foot CG. 13

The body properties of the leg are as follows: Foot: Shank: Thigh: Upper body: m,i,l,h,l m,i,l,h,l m,i,l,h,l m,i,h,l Fig2.2: segment dimension 2.4 Jump (Double Swing) Model This situation arises when neither leg of the exoskeleton is in contact with the ground. In this model the inertia frame is chosen as the upper body. Each leg is assumed to be an independent 3 segment manipulator (thigh, shank, and foot) pinned to the upper body at the hip. Given the selection of the Global frame, each leg is assumed to be completely dynamically independent from the other leg. It will be analyzed as a separate entity. Each joint is actuated. The human interaction with the machine is modeled as an external torque on each link. Global Reference Frame Frame 0 is fixed to the torso at the hip joint with pointing vertically upwards, aligned with gravity as shown in Fig15 Fig2.3: Jump model 14

Equation of motion: The human applies external torques on the exoskeleton. Using the Newton Euler formulation, the human machine equivalent torque vector could be derived, for each leg, by computing the following expressions:,, :,,,, The 3 equations of motion obtained for each leg (Left and Right) can be grouped into a vector equation:,,,,,, Where,, are 3 1 joint input torque vectors,,, are 3 1 the humanmachine joint torque vectors, are the joint angle vectors(for left and right leg), is the 3 3 kinetic energy matrix, is a 3 1 vector comprising the centrifugal and Coriolis acceleration terms, and is 3 1 joint vector induced by gravity. 15

Thus the net joint torques caused by the human on the machine can be expressed as:,,,,,, 2.5 Single Support Model In the single support model the stance leg is supporting the body and the other leg is free to swing. The machine is described as a serial chain of 7 segments in which the bottom segment is pinned to the ground. Fig2.4: single support model (Racine 2003) Three situations occur in single stance: the stance leg is only in contact with the ground at the toe (Fig.2.4.A), the stance foot is only in contact with the ground at the heel (Fig.2.4.B), or the stance foot is flat on the ground (Fig.2.4.C).(Racine 2003). In situations A and B the external torques are due to the human. In situation C the ground exerts a net torque on the foot segment and the human exerts a torque on all the other segments. A single set of equations can be used as long as proper care is taken in differentiating external torques due to the ground reaction force and external torques due to the human. The foot segment represents: 1 the ankle toe segment if the toe is in contact with the ground (Fig.16.A) 2 the ankle heel segment if the heel is in contact with the ground (Fig.16.B) 3 either segment if both the heel and toe are in contact with the ground (Fig.16.C). In this case the foot is flat on the ground and is static. The foot link does not contribute to the humanmachine dynamics and can be chosen arbitrarily to represent the ankle toe segment. Global Reference Frame: Frame 0: Global frame fixed to ground at the ground joint with pointing vertically upwards. (Fig2.1) Equation of motion: The human applies external torques on the exoskeleton. Using the Newton Euler formulation, the human machine equivalent torque vector could be derived by computing the following expressions: 16

,,,,,, : 17

,,,,,,, The 7 equations of motion obtained for (i = 1, 2, 3, 4, 5, 6 and 7), can be grouped into a vector equation:, Where,,,,,, is the joint input torque,,,,,,, is the human machine joint torque vector,,,,,,, is the joint angle vector, is the 7 7 kinetic energy matrix, b is a 7 1 vector comprising the centrifugal and Coriolis acceleration terms, and p is 7 1 joint vector induced by gravity. The equation for i = 1 is slightly different. In effect, there is no actuation at the toe, associated with joint angle q (T 0). Thus the net joint torques caused by the human on the machine can be expressed as:, 18

2.6 Double support model: System Partitioning In the double support state, both feet are flat on the ground. The system is modeled as two planar 3 degree of freedom manipulators in parallel and rigidly connected along their upper segments. The degrees of freedom include the ankle, the knee and the hip. The approach used to establish the dynamic equations of this system will be to partition the device through the sagittal plane and conduct a separate dynamic analysis for each of the two 3 degree offreedom serial manipulators (Kazerooni 2001). The bottom segment of each leg is pinned to the ground. Fig2.5: system partitioning, Zero Redundancy (Kazerooni, Bleex project) Global Reference Frames Frame 0: Global frame fixed to ground at the heel with y pointing vertically upwards. Equation of motion: Fig2.6: double support, foot flat model The human applies external torques on the exoskeleton. Using the Newton Euler formulation, the human machine equivalent torque vector could be derived, for this 3 linear DOF manipulator, by computing the following expressions: 19

,, :,,,, The 3 equations of motion obtained for each leg can be grouped into a vector equation:,,,,,,,,,,,,,,,,,, Where,, are 3 1 joint input torque vectors,,, are 3 1 human machine joint torque vectors, are 3 1 joint angle vectors(for left and right leg),,, are the 3 3 kinetic energy matrix,,, are a 3 1 vectors comprising the centrifugal and Coriolis acceleration terms, and,, are 3 1 joint vectors induced by gravity. And are effective torso masses supported by each leg and is the total torso mass such that: 20

The contributions of on each leg are chosen as functions of the location of the torso center of mass relative to the locations of the ankles (Kazerooni, On the Control of the Berkeley Lower Extremity Exoskeleton) such that: Where, x,is the horizontal distance between the torso center of mass and the left ankle, and x is the horizontal distance between the torso center of mass and the right ankle. Needless to say, this equation is valid only for quasi static conditions, where the accelerations and velocities are small. This is in fact the case. In the double support phase, both legs are on the ground and angular acceleration and velocities are quite small. Thus the net joint torques caused by the human on the machine can be expressed as:,,,,,,,,,,,, Note: The contributions of on each leg could be otherwise found by using a load distribution sensor. It is implemented between the human s foot and the main exoskeleton foot structure. This sensor is used by the control algorithm to detect how much weight the human places on their left leg versus their right leg. 2.7 Double Support with One Redundancy In the double support single redundancy state, one foot is flat on the ground (Non redundant leg). The other leg is in contact with the ground only through its toe or heel (redundant leg).the system is modeled as a 3 degree of freedom serial manipulator (the flat foot leg) in parallel with a 4 degree of freedom manipulator. Each serial link supports a portion of the torso weight. Fig2.7: system partitioning, one Redundancy (Kazerooni, Bleex project) The two bodies are rigidly connected along their upper segments. Depending on the physical model, the bottom link of the 4 dof manipulator can be used to represent either the ankle heel segment or the ankle toe segment. 21

Global Reference Frames Frame 0: Global frame fixed to ground at the heel with y pointing vertically upwards. Equation of motion: Fig2.8: double support, redundant leg model The human applies external torques on the exoskeleton. The equations of motion, for the 3 DOF serial manipulator (the flat foot leg), have already been established in the previous section,,,,,, is the effective torso masse supported by the Non redundant leg. Using the Newton Euler formulation, the human machine equivalent torque vector could be derived, for the 4 DOF serial manipulator (redundant leg), by computing the following expressions:,,, : 22

,,,, The 4 equations of motion (i=1, 2, 3, and 4), obtained for the redundant leg, can be grouped into a vector equation:,,,,,, Where, is 4 1 joint input torque vectors (for the redundant leg) with the first term set to zero because there is no actuation at the toe,, is 4 1 human machine joint torque vectors, is 4 1 joint angle vectors, is the 4 4 kinetic energy matrix, is a 4 1 vectors comprising the centrifugal and Coriolis acceleration terms, and is 4 1 joint vectors induced by gravity. is the effective torso masse supported by the redundant leg. Thus the net joint torques caused by the human on the machine can be expressed as:,,,,,,,,,,,, 2.8 Double support double redundancy model: In this model, the system is modeled as two 4 degree of freedom serial manipulators, each of them representing a leg and a portion of the upper body. Both legs are pinned to the ground. The segment connected to the ground can be used to represent either the ankle heel segment or the ankle toe segment. 23

Fig2.9: system partitioning, two Redundancy (Kazerooni, Bleex project) The equations of motion, for the 4 DOF serial manipulator (the flat foot leg), have already been established in the previous section,,,,,,,,,,,, And are effective torso masses supported by each leg (left and right leg). 2.9 Conclusion: For simplicity in control we consider our exoskeleton to have five distinct phases: jump (double swing), single stance, double stance, double stance with one redundant leg, double stance with two redundant legs. In each phase a different dynamic model is derived to command the actuator input in such a way the exoskeleton will follow human motion with minimal interaction force. Along the bottom of the foot, switches detect which parts of the foot are in contact with the ground, and therefore identify the foot s configuration on the ground. This information is used by the controller to determine in which phase the exoskeleton is operating and which of the five dynamic models (listed above) apply. 24

3 Evaluation of Contending Control Strategies 3.1 Introduction In the human performance enhancing exoskeleton, the human and the machine are integrated and in physical contact. This not only couples the dynamics of the human closely to that of the machine but places size and geometry restriction on the hardware involved in the control architecture. There are multiple aspects of the lower extremity exoskeleton that may place limitations on the successful application of the control laws used in similar systems. The selection process of an appropriate control law involves a detailed survey of some existing strategies and an evaluation of how they might satisfy the exoskeleton requirements, which can be summarized below: Adaptability to different operators Ability to conduct different activities Controller robustness: influence of system model uncertainties Ergonomics: comfort of the interface between the human and the machine. Non obtrusive: the exoskeleton does not impede human movement Low human sensors Low computational requirements 3.2 Myosignal based Systems By measuring neuromuscular electrical activity through either surface or internal electrodes, electromyograrns (EMGs) can determine when muscles are active (i.e. generating tension).it also gives an approximation of the intensity of the muscle activity. This measured muscle intensity is used to control the exoskeleton actuators. Complications with EMG: It is not possible to obtain a one to one relationship between a joint torque and the EMG signal of a particular muscle.this partly occurs because muscles usually act in conjunction with other muscles: synergistic muscles work simultaneously, and antagonistic muscles work in opposite sense. A more accurate estimate of the joint torque would hence have to utilize EMGs captured for all of the major muscles acting across a joint. Assuming a predictable relationship can be obtained between EMGs and muscle activity, muscle moment arms (which vary with joint angle) also need to be determined in order to establish a relationship between muscle force and joint torque. Thus controller based on EMGs would have to be personalized to the operator since both muscle moment arms and the correlation between EMG signal intensity and muscle force vary between individuals Furthermore, a mechanical model of the muscle is needed. Without invasive internal electrodes it is not possible to access every muscle involved in the joint motion. That generates an additional complication. Finally EMG signals are extremely noisy and necessitate extensive signal conditioning. 3.3 Master slave control Master slave control has traditionally been used in telerobotics systems. The objective is to mimic the movements of a human operator. There must be two exoskeletons; a master exoskeleton worn by the human to record joint angles or body segment positions and orientations, and a powered slave exoskeleton which mimics the motion of the human. 25

In a master slave control scheme the human must be able to move to a desired position to initiate a resulting machine movement, without being obstructed by the machine. Thus a control law based on a master slave will result in a system in which space must be allocated between the machine and the human. This allows to insert the appropriate instrumentation and to enable the human to move inside the machine. When applied in joint space, this method aims to match the machine joint angles one to one with the corresponding human joint angles through feedback control. This control scheme allows not only the control of the position and orientation of the end effector but of the entire posture of the manipulator. The geometry of the human and the machine must be matched in order to avoid interference between the two. The tracking properties of the controller would hence be compromised by the fact that hip abduction and rotation angles may be difficult to measure without obstructive instrumentation worn by the operator. 3.4 Direct Force Feedback In robotic force control systems the force between the manipulator and its environment is maintained at a predetermined level through force sensor feedback. In the case of an exoskeleton system, the force between the operator and the machine should be controlled such that the operator does not feel the machine. Since there is actual physical contact between the exoskeleton and the human, this method allows transfer of mechanical power in addition to information signals via force sensors. In contrast to masterslave control, where the operator has no physical feedback from the machine, the human feels a scaled version of the load that the exoskeleton is carrying. In force feedback control all interaction forces are measured and there is no other contact point between the human and the machine than through the force sensor. Although it is theoretically possible to build such control law, it would be quite difficult to implement the hardware associated with it. All ergonomic interfaces between the human and the machine would need to be fitted with force sensors. Any contact point not fitted with sensors would render the control efforts of the machine inadequate. Large forces appearing at such contact points would be ignored by the controller. One approach to solving this problem would be to minimize the number of contact points between the human and the machine. Sensing interface points along the shank or thigh of the operator would be undesirable. People have very low tolerance for any prolonged rubbing or contact forces over those parts of their body. Furthermore the absence of flat or rigid surfaces renders the leg segments unattractive for a machine interface. Another complication arises from the fact that different people have different limb shapes and sizes. Most likely any leg segment interface would have to be custom fitted to a particular operator. More natural contact points for the machine would be at locations through which humans are accustomed to feeling contact forces like the soles of the feet and the back. If 3 independent forces are measured at both the feet and the back there will be sufficient input signals to implement a controller for the machine. Of course, any forces resulting from human machine contacts at any point other than the feet and the back would persist, since the control law would ignore them. Whereas the backpack may provide the space and flexibility to design a sensing interface, the shoe interface would be more difficult to construct. In effect, there is very limited space available under the feet to embed a tri axial force sensor capable of sustaining the several human body weights of force that occur at heel strike. In the current state of technology for instrumented foot sole sensors, only normal forces are measured. 26

3.5 Virtual Generalized Force Control Force feedback control method presents drawbacks based on the inability to properly sense humanmachine interaction forces in the system. If the human is in contact with the machine at points not accessible by the force sensors, it will not be clear whether the measurements will be reflective of the net human machine interaction forces. The virtual generalized force control method is based on estimating interaction forces that cannot be measured, through a mathematical model. This information is used to create a force feedback control law. Thus, instead of having a real sensor interface at predetermined locations along the machine's segments, this methodology aims to replace these interfaces with virtual sensors (which are nothing more than mathematical models of the machine dynamics). Instead of using data related to the human, the mathematical models only require information inherent to the design of the machine and the current state of the kinematic and actuation data that instantaneously characterizes the exoskeleton system. The jacobian of the generalized force vector is needed to compute the human machine force. This implies that the exact position of the human machine force is needed. Note that this control law must be extended to include multiple contact points since it is required for the machine to be in contact with the human at the feet and along the torso. This is theoretically possible. However designing single point interfaces between the human and the machine may not be realizable without compromising the comfort, rigidity or size of the machine. 3.6 Virtual Joint Torque Control It is possible to circumvent the limitations of the above controller by selecting a generalized force vector. The control law is constructed in the machine's joint space rather than a set of forces and torques applied at a point on the upper body. Such control architecture is based on the net external joint torque imposed by the human on the machine. The net machine human torque is due to forces and torques induced by human machine impedance. It is a function of differences in position of the human and the machine at the different contact points, and of the differences in orientation between the machine and the various human segments in contact with the machine. As mentioned before, the net machine human torque is written as a product of the difference between the angular positions of some equivalent machine and the human. K _q) For a multiple degree of freedom system the estimated net machine human joint torque becomes, As opposed to the control law in the generalized force space, a control law in the joint torque space does not require any knowledge of the point of action of human forces and torques acting on the system. This offers considerable freedom for the design of the exoskeleton hardware. The ergonomic aspect of the architecture need not be compromised for the benefit of the control law. Points of attachment to the human can be placed where they are the most practical and offer the most comfort. It is also worth noting that the control law does not make use of any information about the operator or of any of the mechanical characteristics of the human machine interface, thus making the control law suitable for different machines and human operators. The main disadvantage of this control law over master slave and feedback force control is that the mass properties of the exoskeleton must be known in order to 27

obtain a good estimate of the human machine torque. This additional uncertainty introduced in the control law must be measured against the potential unreliability of the force measurements that would appear under the feedback force control method. 3.7 Conclusion Virtual joint torque control is the appropriate control law which most satisfies the exoskeleton requirements. In fact, no sensors need to be mounted on the operator and thus no need to be fined tuned to a specific human. In addition, the virtual torque method does not make any assumptions on the activities performed by the operator. Furthermore, both the geometry of the machine and any hardware involved in the human machine interface can be designed with operator comfort as a priority because this control law does not require any knowledge of the point of action of human forces and torques acting on the system. Also the virtual torque method is highly Non obtrusive because of the lack of human sensors and the flexibility of designing the human machine attachments where they are the least obtrusive from a mechanical standpoint. 28

4 Virtual torque control stability and performance analysis 4.1 Introduction Lower extremity exoskeletons seek to supplement the intelligence and sensory systems of a human with the significant strength and endurance of a pair of wearable robotic legs that support a payload. The device bears the bulk of the weight while transferring a scaled down load to the pilot. In this fashion, the pilot can still sense the load s weight and judge his/her movements accordingly, but the force he/she feels is greatly reduced. The basic principle for the control law of such device rests on the notion that the exoskeleton needs to shadow the wearer s voluntary and involuntary movements quickly, and without delay. The controller estimates, based on measurements from the exoskeleton only, how to move so that the pilot feels very little force. Thus the controller objective is to minimize human machine interaction force without any direct measurements from the pilot or the human machine interface (e.g. no force sensors between the two); this requires a high level of sensitivity in response to all forces and torques on the exoskeleton, particularly the forces imposed by the pilot. Addressing this need involves a direct conflict with control science s goal of minimizing system sensitivity in the design of a closed loop feedback system. In classical and modern control theory, every effort is made to minimize the sensitivity function of a system to external forces and torques. But for exoskeleton control, one requires a totally opposite goal: maximize the sensitivity of the closed loop system to forces and torques. In classical servo problems, negative feedback loops with large gains generally lead to small sensitivity within a bandwidth, which means that they reject forces and torques (usually called disturbances). Clearly this opposes our objective. To achieve a large sensitivity function, we can use the inverse of the exoskeleton dynamics as a positive feedback controller so that the loop gain for the exoskeleton approaches unity This control law discussed here has 4 major drawbacks: The first is that an exoskeleton with high sensitivity to external forces and torques would respond to other external forces not initiated by its pilot. The second is that maximizing system sensitivity to external forces and torques leads to a loss of robustness in the system, and therefore the precision of the system performance will be proportional to the precision of the exoskeleton dynamic model. The third is that obtaining a good model of torso is nontrivial because the torso includes a variable payload. The mass and COG of the torso must be well known. The fourth is that this method is computationally very expensive. In the single stance phase, the controller must calculate the full inverse dynamics of a 7 DOF serial chain of links every time through the control loop. Thus the torque equation must be simplified as possible. 29

4.2 Simple One Degree of Freedom (DOF) 4.2.1 Introduction The control of the exoskeleton is motivated here through the simple 1 DOF shown below This figure schematically depicts a human leg attached or interacting with a 1 DOF exoskeleton leg in a swing configuration (no interaction with the ground). Fig4.1: Simple 1 DOF exoskeleton leg interacting with the pilot leg. The exoskeleton leg has an actuator that produces a torque T about the pivot point A. The total equivalent torque associated with all forces and torques from the pilot on the exoskeleton is represented by T. In the absence of gravity, this simplified system would be linear. The open loop block diagram is depicted in Fig4.2 Where: Fig4.2: open loop block diagram K is the impedance between the human and the machine. T is the joint torque applied by the human on the machine. G is the system transfer function. q is the machine's position. q is the human's position. is the joint torque applied by the actuator. T The sensitivity transfer function S, represents how the equivalent human torque affects the exoskeleton angular velocity. S maps the equivalent pilot torque,t, onto the exoskeleton position q. Thus:. 30

The objective is to increase exoskeleton sensitivity to pilot forces and torques through feedback but without measuring T. Any negative feedback from the exoskeleton, leads to a smaller sensitivity transfer function. Thus to increase exoskeleton sensitivity, one has to use positive feedback loop from the exoskeleton variables only. 4.2.2 Closed loop analysis In the absence of nonlinearities, a straightforward proportional derivative controller can be used to analyze the virtual torque control law. Since T K q q), the tracking objective of 0 is identical to the tracking objective of The block diagram of the 1 DOF closed loop system is shown below Fig4.3: closed loop block diagram Where G is an estimate of the machine forward dynamics such that, if the model is perfect, G*G =1 (4.2) And the gain function is The virtual torque control law is.. Using Laplace presentation.... 31

The open loop system equation is: Thus. Assuming perfect knowledge of the model, G*G =1 and then we will have. If the loop gain 1 machine. 1 and it follows that 0 and the human never feels the In the absence of gravity, and assuming damping and kinetic friction torque, which is function only of the joint angular velocity, and then by applying dynamics equations, we will have: Thus. Then. Substituting C for its value. A good physical interpretation of this equation can be obtained by expressing it in the time domain.. The left hand side of this equation is that of a standard second order mechanical system. The right hand side represents the external forces on that system. When the controller gains are set to zero, equation 4.14 becomes: Thus the net effect of the proportional gain of the controller K is hence to amplify the human machine impedance and making the system more sensitive to the motion of the human. The derivative gain K introduces mimics viscous damping between the human and the machine which acts to dampen the response and stabilize the system. 32

4.2.3 Frequency response Equation 4.13 can be written The steady state sinusoidal frequency response of a circuit is described by the phasor transfer function. If q q sin ωt, then at the steady state, and for stable system, sin With q Thus, the system can be thought of a second order system of natural frequency And a high pass filter with a cut off frequency ω. If we pose 2, is the damping factor, then G(s) can be written. Fig4.4: Bode plots of a second order system and a high pass filter From this bode plots it can be seen that for low frequencies below ω the system is close to a unity gain with negligible phase lag. This indicates that at low frequencies the machine will track the human. Above ω an increasing phase lag is introduced and the system becomes less responsive to the motion of the human. Because ω depends on K, the responsiveness of the system will be a function of the physical human machine interface impedance. This indicates that the controller performance will benefit from a stiffer human machine attachment. The high pass filter portion adds phase to the system thereby providing a faster response and enhanced stability. The added phase, as we can see from figure above, depends on the value of. 33

The values of K and K are chosen in such a way the exoskeleton leg will always follow the human leg for all 0, In other word, 1 0 for all 0, In the following, we will try to give insight of how the value of K and K affect the system response and how to choose this parameters to have a good tracking performance. In doing so, we will take specific values for J, B, and K. 1;10; 200 Then 2001 ω 2 200 10 Each value of (K,K lead to a unique and speciic value of,ω Now we will try to study the frequency response of this system while changing the value of relative to. Case1: Or Then For low frequency, 34

For then Thus will decrease sharply and eventually it will become 0(slope= 1) Above ω an increasing phase lag and magnitude ratio is introduced and the system becomes less responsive to the motion of the human. Conclusion: For ω ω, K, the system has excellent tracking performance as long as ω Fig4.5: Bode diagram using mathlab /,. /,. Case2: : For, ω ω can be neglected thus 0 1 35

And 0 As increases, a slightly positive magnitude ratio is introduced, and it will attain its maximum for 1 2 (Overshoot) Meanwhile a slightly negative phase angle is introduced, but remains small for. For the magnitude ratio begin to decrease sharply and so does the phase angle. For, 0 ω ω can be neglected thus 0 1 And 0 As increases, a slightly negative magnitude ratio and negative phase angle are introduced, but remains small for. For the magnitude ratio begin to decrease sharply and so does the phase angle. For, 0 Conclusion: For ω ω, the system has good tracking performance as long as ω Fig4.6: Bode diagram using mathlab /, /,. Case3: For 0ω the high pass filter will have no effect on the steady state performance and the system can be thought only of a second order system of natural frequency. Thus as increases, a negative magnitude ratio is introduced, and it will attain its maximum (Resonant Peak) for 1 2. For, will have a relatively high value since. Meanwhile a slightly negative phase angle is introduced, but remains small for since. Conclusion: For ω ω the system will have a very bad tracking performance. 36

Fig4.7: Bode diagram using mathlab /, /,. 4.2.4 Stability The system is stable if and only if the poles have a negative real part. This will be true if the polynomial coefficients of the system's characteristic equation (the denominator) are all positive. The root locus of for : OLP: ; (start point for 0) OLZ: 0 (end point for ) N m=1 then there is 1 asymptote Break in: 0 1 37

Fig4.8: root locus of as varies from 0 to When increases, relative stability of increases, as the Break in point is moving away from the origin in the left hand plane. The system response became faster. For, The system is marginally stable for 0. For 01 stiffness dominates, and oscillatory behaviour results (2 complex root in the LHP). This response is called under damped. As the damping factor increases from 0 to 1 the velocity of system response increases also. For 1, friction and stiffness are "balanced," yielding the fastest possible nonoscillatory response. This system is critically damped. For 1 friction dominates, and sluggish behaviour results (2 real negative roots). The system is overdamped. As the damping factor increases, the system becomes slower. Note that for all value of 0, the roots of the characteristic equation are all in the LHP, and stability is achieved for all Conclusion: The system is stable for all K and K 0. Also system velocity and relative stability increases as K increases. For K cte, increasing the derivative gain K will dampen the system response and reduce the overshoot as long as 0 1 4.3 Nonlinear Systems In the presence of gravity, the equation of the 1 d.o.f system becomes 38

Where m is the system's mass, L is the distance from the joint centre to the COG of the system. The inclusion of gravity renders this system nonlinear and a selection of controller gains for optimal performance becomes difficult. One approach to solve this problem is to include a model of the system nonlinearities in the control law such as to make the overall closed loop system appear linear. In this method, the controller will be partitioned into a model based portion, to cancel the nonlinearities, and a servo portion. Since the model based portion of the control law will have the effect of making the system appear linear, the design of the servo portion will be quite simple. In this case, the linearizing torque is equal to the torque necessary to counteract gravity: The closed loop dynamic equation can be written: This is now a linear equation. The servo portion of the input torque can be chosen as The closed loop equation becomes _ This is identical to the closed loop equation obtained when gravity was ignored. 4.4 Stability of a Multi D.O.F. Nonlinear System with Feedback Linearization The dynamic equations of a multi dimensional system can be expressed as, The same feedback linearization concept can be applied to a multidimensional system so that the control input becomes Where the human machine force is estimated using, And and are diagonal controller gain matrices. 39

Using the control equations yields the following closed loop system equation, If the human is at rest, 0 and defining this equation becomes Consider the candidate Lyapunov function, The function is always positive or zero because the mass matrix A and the amplified impedance matrix are positive definite matrices. Differentiating, Which is non positive since are positive definite. In taking the last step, we have made use of the interesting identity:, This can be shown by investigating of the structure of Lagrange s equation of motion. To prove asymptotic stability the system must be studied at the point where 0 This implies that 0 Using this equilibrium value in the dynamic equation yields 0 which means that the solution asymptotically converges towards a zero steady state error and the feedback linearization law can successfully be implemented on a multi DOF system. 4.5 Conclusion The human machine contact force is estimated. This estimated force is appropriately modified by adding a PD controller and then used as an input to the exoskeleton actuators. The control of the exoskeleton is first motivated through the simple 1 DOF joint (gravity is ignored). The system is stable for all K and K 0. Also system velocity and relative stability increases as K increases. For K cte, increasing the derivative gain K will dampen the system response and reduce the overshoot as long as 0 1 The system has excellent tracking performance especially when.the exoskeleton will rapidly follow human movement without any delay and with minimal interaction force. Finally the multi DOF system is shown to be always stable by using Lyapunov method. 40

5 General conclusion The exoskeleton is worn by the human for the purpose of direct transfer of mechanical power. Consequently, there is actual physical contact between the exoskeleton and the human, allowing transfer of mechanical power in addition to information signals (commands). In fact the human becomes a part of the exoskeleton, and "feels" some scaled down version of the load that the exoskeleton is carrying. In this fashion, the human can still sense the load s weight and judge his/her movements accordingly, but the force he/she feels is much smaller than what he/she would feel without the device. In other word, the human provides an intelligent control system to the exoskeleton, while the actuators ensure most of the necessary strength to perform the task. A pseudo anthropomorphic architecture with similar kinematics to a human was chosen for our exoskeleton. Each exoskeleton leg has three DOF at the hip, one DOF at the knee, and three DOF at the ankle. This exoskeleton is only activated in the sagittal plane. A broad objective of many lower extremity exoskeletons is to allow the wearer to expend less of their own energy for locomotion. Passive elements were implemented in the exoskeleton to either store or dissipate energy throughout the walking cycle thus reducing the metabolic load on the human. In fact, springs as energy storage elements can be implemented at joints that have a period of negative power followed by a period of positive power. The spring could store energy during the negative power period and release it during the positive power period. The human muscles would then absorb less negative power and produce less positive power, thus providing metabolic advantages. Dampers can be implemented for joints that mainly dissipate energy. These dissipative joints have a negative average joint power. The power profiles for the hip, knee and ankle in the sagittal plane were analysed for a participant walking normally and carrying a 47kg backpack at a speed of 1.33 m/s [Harman (2000)]. From these power profiles, it could be concluded that: A passive spring at the hip stores energy through hip extension in the stance phase that is later released to assist in powered hip flexion through the swing phase. A passive spring at the ankle engages in controlled dorsiflexion to store energy that is later released to assist in powered plantarflexion. A damper at the knee would be engaged during the swing phase to control the swinging of the leg. However, due to his distal mass, the variable damper mechanism is proven to be inefficient. Although for slow walking speeds these passive elements could greatly reduce metabolic cost, at faster walking speeds the positive power becomes increasing large and in this case, hybrid actuation approach may be beneficial where a small motor is used in conjunction with the spring. In this thesis, we have adopted this approach. The dynamic behavior of an open loop exoskeleton (without any control feedback) is derived by a set of nonlinear differential equations using the Newton Euler formulation. However, the rigid body dynamics are not sufficient for modeling due to model uncertainties; therefore a PD controller is used to ensure stability while maintaining robustness against approximation of desired target impedances over bounded frequency ranges. 41

Five different dynamic models were derived for each of the five phases that occurs during walking: jump (double swing), single stance, double stance, double stance with one redundant leg, double stance with two redundant legs. These dynamic models are used to estimate the human machine force. This force is appropriately modified (in the sense of control theory to satisfy performance and stability criteria)and then used as an input to the exoskeleton actuators in such a way the exoskeleton will follow human motion with minimal interaction force. In fact the controller objective is to minimize human machine interaction force without any direct measurements from the pilot or the human machine interface (e.g. no force sensors between the two). Along the bottom of the foot, switches detect which parts of the foot are in contact with the ground, and therefore identify the foot s configuration on the ground. This information is used by the controller to determine in which phase the exoskeleton is operating and which of the five dynamic models (listed above) apply. This control scheme will greatly increases the closed loop system sensitivity in response to all forces and torques on the exoskeleton, particularly the forces imposed by the pilot. However this control law is based on disturbance observer and it will be affected by modelling errors. Thus it has little robustness to parameter variations and therefore requires a relatively good dynamic model of the system. This is tradeoffs between having sensors to measure human variables and the lack of robustness to parameter variation. The control of the exoskeleton is first motivated through the simple 1 DOF joint (gravity is ignored). The system is stable for all K and K 0. Also system velocity and relative stability increases as K increases. For K cte, increasing the derivative gain K will dampen the system response and reduce the overshoot as long as 0 1 The system has excellent tracking performance especially when. The exoskeleton will rapidly follow human movement without any delay and with minimal interaction force. Finally the multi DOF system is shown to be always stable by using Lyapunov method. 42

6 References [1] Vukobratovic M., When Where Active Exoskeletons Actually Born, International Journal of Humanoid Robotics, Vol. 4, No. 3. pp 459 487, 2007. [2] Miomir Vukobratovic, ACTIVE EXOSKELETAL SYSTEMS AND BEGINNING OF THE DEVELOPEMENT OF HUMANOID ROBOTICS 2008, Vol. 2, pp.329 348. [3] Miomir Vukobratovic, BELGRADE SCHOOL OF ROBOTICS The scientific journal FACTA UNIVERSITATIS Series: Mechanics, Automatic Control and Robotics Vol.2, No 10, 2000 pp. 1349 1376. [4] Aaron M. Dollar, Member, IEEE, and Hugh Herr, Member, IEEE, Lower Extremity Exoskeletons and Active Orthoses: Challenges and State of the Art IEEE TRANSACTIONS ON ROBOTICS, VOL. 24, NO. 1, FEBRUARY 2008. [5] Daniel P. Ferris, Gregory S. Sawicki and Monica A. Daley, A physiologist s perspective on robotic exoskeletons for human locomotion, International journal of humanoid robotics vol. 4, no. 3 (2007) 507 528. [6] Vukobratovic M., Borovac B., Zero Moment Point Thirty five years of its Life, Int. Journal of Humanoid Robotics, Vol 1, No 1, pp 157 173, 2004. [7] Farley, C.T. & Ferris, D.P. (1998) Biomechanics of Walking and Running: from Center of Mass Movement to Muscle Action, Exercise and Sport Sciences Reviews, pp. 26:253 285. [8] De Looze, M.P., Toussaint, H. M., & Commissaris, D.A. (1994), Relationships Between Energy Expenditure and Positive and Negative Mechanical Work in Repetitive Lifting and Lowering, Journal Applied Physiology pp. 77:420 426. [9] Gottschall, J.S. & Kram, R. (2003) Energy cost and muscular activity required propulsion during walking, Journal Applied Physiology, pp. 94: 1766 1772, 2003. [10] Farley, C. & McMahon, T. (1992) Energetics of walking and running: insights from simulated reduced gravity experiments, The American Physiological Society, pp. 2709 2712. [11] Griffen, T. M., Roberts, T. J., Kram, R. (2003) Metabolic cost of generating muscular force in human walking: insights from load carrying and speed experiments, Journal of Applied Physiology, 95: 172 183, 2003. [12] Bastien, G.J, Willems, P.A., Schepens, B., Heglund, N.C. (2005) Effect of load and speed on the energetic cost of human walking, European Journal of Applied Physiology, 94: 76 83 43

[13] Griffin, T.M., Tolani, N.A., & Kram, R. (1999), Walking in simulated reduced gravity: mechanical energy fluctuations and exchange, Journal Applied Physiology pp. 383 390. [14] Harman, E., Han, K., Frykman, P., Pandorf, C. (2000), The Effects of Backpack Weight on the Biomechanics of Load Carriage, USARIEM Technical Report pp. T100 17,Natick, Massachusetts. [15] Gregory Stephen Sawicki, Mechanics and energetics of walking with powered exoskeletons Ph.D. dissertation, University of Michigan 2007 [16] Conor James Walsh (2003), Biomimetic Design of an Under Actuated Leg Exoskeleton For Load Carrying Augmentation, Master s thesis, Dept. Mech. Eng., Massachusetts Inst. Technol., Cambridge, Feb. 2006. [17] Valiente, Design of a quasi passive parallel leg exoskeleton to augment load carrying for walking, Master s thesis, Dept. Mech. Eng., Massachusetts Inst. Technol., Cambridge, Aug. 2005. [18] Elie NAJEM, Rami TARABAY, PASSIVE LOWER LIMB ORTHOSIS, Master s thesis, Dept. Mech. Eng., LEBANESE UNIVERSITY FACULTY OF ENGINEERING II 2010. [19] Aaron M. Dollar, Member, IEEE, and Hugh Herr, Member, IEEE, Design of a Quasi Passive Knee Exoskeleton to Assist Running International Conference on Intelligent Robots and Systems, Acropolis Convention Center, Nice, France, Sept, 22 26, 2008 [20] James A. Norris, Anthony P. Marsh, Kevin P. Granata, Shane D. Ross, POSITIVE FEEDBACK IN POWERED EXOSKELETONS: IMPROVED METABOLIC EFFICIENCY AT THE COST OF REDUCED STABILITY? Proceedings of the ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, September 2007, Las Vegas, Nevada, USA [21] John J. Craig, introduction to robotics, chapter 9, 10, pp.300 364 [22] Sylvie Pommier, Dynamique des systèmes de Solides 2005 2006 [23] Aydın Tözeren, human body dynamics. [24] Vorgelegt von, Christian Fleischer, Controlling Exoskeletons with EMG signals and a Biomechanical Body Model, Master s thesis, Technische Universität Berlin,2007 [25] Sébastien Bédard, MODELISATION ET SIMULATION DYNAMIQUE D'UN BIPÈDE PLAN À 9 DDL, Master s thesis, Dept. Mech. Eng., Laval university, 2006. [26] Ahmed Chemori, Quelques contributions à la commande non linéaire des robots marcheurs bipèdes sous actionnés Ph.D. dissertation, INSTITUT NATIONAL POLYTECHNIQUE DE GRENOBLE,2005 44

[27] Christopher L Vaughan Brian L Davis, Jeremy C O Connor, Dynamics of human gait Kiboho Publishers, Cape Town, South Africa [28] Kazerooni, H. and Guo, J. 1993 Human Extenders, ASME Journal of Dynamic Systems, Measurements, and Control 115(2B):281 289 [29] Kazerooni, H. "The extender technology at the University of California, Berkeley, Journal of the Society of Instrument and Control Engineers in Japan, Vol. 34, 1995, pp. 291 298. [30] Kazerooni, H., The Human Power Amplifier Technology at the University of California, Berkeley, Journal of Robotics and Autonomous Systems, Elsevier, Volume 19, 1996, pp. 179 187. [31] Kazerooni, H., "Human Robot Interaction via the Transfer of Power and Information Signals," IEEE Trans. on Systems and Cybernetics, V. 20, No. 2, Mar. 1990. [32] Kazerooni, H, Issues on the control of robotic systems worn by the human American Control Conference Boston, Massachusetts, June 1991 [33] H. Kazerooni, "Stability and Performance of Robotic Systems Worn by Humans", IEEE. International Conference on Robotics and Automation, Cincinnati, Ohio, May 1990. [34] Kazerooni, H., Guo, H., "Dynamics and Control of Human Robot Interaction", American Control Conference, San Francisco, California, June 1993, pp. 2398 2402. [35] H. Kazerooni, and S. Mahoney, "Dynamics and Control of Robotic Systems Worn By Humans," ASME Journal of Dynamic Systems, Measurements, and Control, V113, No. 3, pp. 379 387, September 1991. [36] H. Kazerooni and R. Steger, The Berkeley Lower Extremity Exoskeleton, Trans. ASME, J. Dyn. Syst., Meas., Control, vol. 128, pp. 14 25, Mar. 2006 [37] Kazerooni, H., Racine, J. L., Huang, L., Steger, R., On the Control of the Berkeley Lower Extremity Exoskeleton (BLEEX), IEEE Int. Conf. on Robotics and Automation, April 2005, Barcelona. [38] Zoss, A. and Kazerooni, H. 2005 On the Mechanical Design of the Berkeley Lower Extremity Exoskeleton. IEEE Int. Conf. on Intelligent Robots and Systems, Edmonton, Canada. [39] Chu, A., Kazerooni, H., Zoss, A On the Biomimetic Design of the Berkeley Lower Extremity Exoskeleton (BLEEX), IEEE Int. Conf. on Robotics and Automation, April 2005, Barcelona. pp. 4356 4363. [40] J. L. Racine, Control of a lower extremity exoskeleton for human performance amplification, Ph.D. dissertation, University of California, Berkeley, 2003. 45

[41] H. Kazerooni, A. Chu and R. Steger, That which does not stabilize, will only make us stronger, Int. J. Robotics Research 26 (2007) 75 89. [42] Justin Ghan and H. Kazerooni, System Identification for the Berkeley Lower Extremity Exoskeleton (BLEEX) Proceedings of the 2006 IEEE International Conference on Robotics and Automation Orlando, Florida May 2006 [43] H. Kazerooni Ryan Steger Lihua Huang, Hybrid Control of the Berkeley Lower Extremity Exoskeleton (BLEEX) The International Journal of Robotics Research 2006; 25; 561 [44] Kawamoto, H. and Sankai,Y. 2002. Power Assist System HAL 3 for gait Disorder Person. International Conf. on Computers Helping People with Special Needs, Austria. [45] K. Yamamoto, K. Hyodo, M. Ishii, T. Matsuo, "Development of Power Assisting Suit for Assisting Nurse Labor." JSME International Journal Series C., vol. 45, no. 3, Sept. 2002. [46] J. E. Pratt, B. T. Krupp, C. J. Morse, and S. H. Collins, The RoboKnee: An exoskeleton for enhancing strength and endurance during walking, in Proc. IEEE Int. Conf. Robot. Autom, New Orleans, LA, 2004, pp. 2430 2435. [47] Xiaopeng Liu, K.H.Low, Hao Yong Yu, Development of a Lower Extremity Exoskeleton for Human Performance Enhancement in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS), Sendai, Japan, 2004, pp. 3889 3894. 46

7 Appendix : Derivation of mathematical equations List of notation: force exerted on link i by link i 1 =Torque exerted on link i by link i 1 angular velocity of joint i relative to inertial frame angular acceleration of joint i relative to inertial frame X,Y,J : Constant parameter (depend on geometric and mass configuration) 7.1 Jump (double swing) dynamic model: There are no forces acting on the end effector, and so we have: 1

The base of the robot is not rotating, and hence we have: To include gravity forces we will use: Outward iterations: And The vectors which locate the centre of mass for each link are: Thus,, : 2

Inward iterations: Link 7: /..... 3

Link 6: Or: ] ] 4

/ Link 5: 5

] ] ] Or: / 6

Conclusion: 7

7.2 Single support dynamic model: There are no forces acting on the end effector, and so we have: The base of the robot is not rotating, and hence we have: To include gravity forces we will use: Outward iterations:,,,,,, 8

The vectors which locate the centre of mass for each link are: 9

,,,,,, : Thus 10

Inward iterations: 11

] 12

13

14

Conclusion: 15

16

7.3 Double support: one redundant leg The base of the robot is not rotating, and hence we have: To include gravity forces we will use: Outward iterations:,,, 17

The vectors which locate the centre of mass for each link are: Thus,,, : Inward iteration 18

] 19

Conclusion: 20

7.4 Double support: foot flat The base of the robot is not rotating, and hence we have: To include gravity forces we will use: Outward iterations:,, 21

The vectors which locate the centre of mass for each link are: Thus,, : Inward iteration 22

23

Conclusion: 24