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

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1 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

2 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

3 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

4 Table of Contents Cover Page I Acknowledgments II Abstract III Table of Contents IV 1 State of The Art History and Background Early Exoskeletons: DARPA Program Exoskeletons Other Lower Limb Exoskeletons Anatomical Terminology Relative positions Anatomical reference planes Joint motion Human Gait Introduction Muscle activity during the gait cycle Ground reaction forces during gait cycle Metabolic effect of forces applied to the human during walking Introduction of passive elements Introduction Hip Kinematics and Kinetics Knee Kinematics and Kinetics Ankle Kinematics and Kinetics Conclusion: 11 2 Dynamic Models Introduction The Human Machine Interface Model Frames and notations Jump (Double Swing) Model Single Support Model Double support model: Double Support with One Redundancy Double support double redundancy model: Conclusion: 24 3 Evaluation of Contending Control Strategies Introduction Myosignal based Systems Master slave control 25 IV

5 3.4 Direct Force Feedback Virtual Generalized Force Control Virtual Joint Torque Control Conclusion 28 4 Virtual torque control stability and performance analysis Introduction Simple One Degree of Freedom (DOF) Introduction Closed loop analysis Frequency response Stability Nonlinear Systems Stability of a Multi D.O.F. Nonlinear System with Feedback Linearization Conclusion 40 5 General conclusion 41 6 References 43 7 Appendix : Derivation of mathematical equations Jump (double swing) dynamic model: Single support dynamic model: Double support: one redundant leg Double support: foot flat 21 V

6 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 Early Exoskeletons: The earliest mention of a device resembling an exoskeleton is granted to Yagn in 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

7 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

8 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

9 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 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 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

10 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

11 1.3 Human Gait Fig1.7: The eight main phases of the walking cycle from heel strike to heel strike (Perry, 1992) 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 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

12 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 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

13 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

14 1.5 Introduction of passive elements 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)] 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

15 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 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

16 proven to be inefficient. Furthermore, in other task such as squatting and climbing stairs, the knee power profile becomes largely positive 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 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

17 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

18 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

19 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

20 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

21 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

22 ,,,,,, : 17

23 ,,,,,,, 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

24 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

25 ,, :,,,, 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

26 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

27 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

28 ,,,, 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

29 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

30 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