Investigating the Impedance Characteristic of Human Arm for Development of Robots to Cooperate with Human Operators.

Transcription

1 Investigating the Impedance Characteristic of Human Arm for Development of Robots to Cooperate with Human Operators. M. M. Rahman, R. Ikeura** and K. Mizutani Department of Mechanical Engineering, Mie University Kamihama-1515, Tsu, Mie, , Japan ABSTRACT In the near future many aspect of our life will be encompassed by tasks performed in co-operation with robots. Application of robots in home automation, agricultural production, medical operation etc. will be indispensable. As a result robots need to be made humanfriendly and to execute tasks in co-operation with human. Control systems for such robots should be designed to work imitating human characteristics. In this study, we have tried to achieve these types of goals by means of controlling a simple one degree-of-freedom robot. First, impedance characteristic of human arm in a co-operative task is investigated. Then, this characteristic is implemented in robot to perform co-operative task with human. It is observed that the proposed control method gave good characteristic to the robot for co-operating with human. 1. INTRODUCTION Progress in modern technologies as well as growing social demands require human-friendly robot, human characterised robot. Some robots need to execute the tasks in co-operation with human. As the co-operation task, we have considered a task of carrying an object by a robot and a human as shown in Figure 1 [l-4]. Control methods for multiple co-operative robots [7-lo] may be able to apply to the robots co-operating with human. Although many control method for the robots cooperating with human [l l-121 have been developed. However the control methods have been designed without considering human characteristic. To make robots humanfriendly, therefore, it is important to design the controller considering the human characteristics. Ikeura et.al. have investigated human characterised task in which two human co-operated with each other in carrying an object as shown in Figure 2 [l-3]. The human characteristics are approximated by a constant impedance model and showed that the damping factor is important for co-operation; mass and spring effects are almost ignored [2-31. Afterwards it has been observed that the damping factor varies with the operational speed and time. A model of one degree-of-freedom (DOF) horizontal motion of carrying out of an object by two operators has been constructed and fundamental idea of the variable damping control is introduced in co-operation task [l]. Some of the important points of their investigation are discussed in the section 2. In the present investigation, mass, stieess and damping factor for the variable impedance model has been considered. Where stiffhess and damping factor varies with the operational speed and time. The effectiveness of the model was verified in the experiment of human and robot co-operation task. Blind fold Human Robot Follower Leader Figure 1. Human-robot co-operation task. Figure 2. Human and human co-operation task. O O/99/$ IEEE II -676

2 2. CHARACTERISTIC OF HUMAN-HUMAN CO- OPERATION Model of one DOF task of carrying an object A model of one DOF (degree-of-freedom) task of carrying an object in the horizontal direction as shown in Figure 3 has been discussed [ 11. According to this report: Equation of motion for this task is: m.fi = f, + f2 (1) where m is mass, f, and f2 are the forces acts by the two bodies. By defining a (0 _< a I 1) as a distribution ratio a factor of the inertia load m_y, the forces fi and f2 are rewritten as, fi =czmz+ant (2) f* =(l-a)ti-ant (3) where, & is internal force. Generally, in the co-operation task by a human and a robot, the robot should not have a leadership role and must follow the motion of the human. On this assumption, the factor a can be equal to 1. Therefore the force acted by the human is fm =~+Ant (4) and by the robot is fr = -A, * (5) As shown in equation (4) and (5), the human controls both position and force and the robot controls only the internal force j& At the time of investigation of the impedance characteristic of human based on this theory is applied. Variable damping control In human-robot co-operation based on impedance control, if the damping factor is high the human can not operate quickly as in the case of co-operation between two humans. At low damping factor the human can perform the action quickly but the positioning operation is not stable. Therefore, the change of damping factor has been considered according to the speed of the operation [3-41. In the paper [3-41; the damping factor was changed from low level to the high level in a moment at a specified velocity. By the switching of the damping factors has been recognised as an important factor for obtaining the good operation. In paper [l], variable damping model approximated by an exponential function has been proposed. The damping factor was calculated by using the following equation. f(t) = c(t)xi(t) (6) In this model only damping factor was considered. But in the muscle-skeleton system, two opposite muscles drive the arm. Therefore, the human can not only accelerate an arm but also change the stiffness of the arm by activating both muscles [5-61. The muscle is mechanically analogous to a spring-damper system. So in this paper the human characteristics is investigated as a variable impedance model. Minimum jerk trajectory A time trajectory of position and velocity has been found during the experiment of co-operation between two human s [l]. The motion involving this type of feature is called the minimum jerk motion proposed by Flash and Hogan [ 131. They found that the human arm moves to minimize the following timction. J= (7) where, tf is the time duration of motion. The trajectory minimize the function J is derived as: +)=x0 +(xf -xo)(6r5-15~~ +10r3) (8) where Z = t / t,r, x0 and xf are the position at time to and TV respectively. The position and velocity for a 0.15 m movement is shown in Figure 4. In fact, the minimum jerk trajectory represents only the free arm motion of the human alone. Ikeura et. al. found the minimum jerk trajectory in the co-operation motion by two humans. This means that the follower human follows the motion of the leader so that he/she can move his/her arm along the minimum jerk trajectory. In the co-operation between a human and a robot, the robot should follow the motion of the human so that the human can move his/her arm along the minimum jerk trajectory. 0.16, / 0.4 h * m Carried object Figure 3. Model of the 1 DOF carrying task in horizontal direction. Figure 4. Time trajectory of position and velocity. II -677

3 3. EXPERIMENTS Experimental Set-up Figure 5 illustrates an experimental simple robot system. The one degree-of-freedom robot was constructed by a linear motor. A six axial force sensor is located in between the handle and the linear motor and its output is sent to the personal computer (PC) through the DSP board. A linear resolver senses the position of the motor and the data is pass to the computer through the counter board. All boards are implemented on an ISA bus of the PC. differentiation of position trajectory. Movement amplitude 0.11, 0.15 and 0.19 meters and the duration of the movements are from 0.4 second to 1.6 second, with the increment of two seconds, were considered as an input. Measuring the impedance characteristic of human arm Methods: Three subjects (human) considered in this present study. As shown in Figure 6, the robot and a subject move the object co-operatively. In the experiment we define a leader and a follower; the leader controls the position of the object and the follower tracks the motion of the object. Here, the robot is considered as a leader and moved the object in the forward and backward directions. According to the equation (4) and (5), the leader controls the position, so the role of the robot is the same as a human leader at this time. The reason of using the robot as leader was to investigate the impedance parameters at different conditions with defined operations. A human, who is blindfold, holds the handle and follows the movement of the linear motor. The arm movements, which have been considered, are in forward and backward direction of forearm is in the horizontal position. The elbow joint and the upper arm joint are assumed to have a constant centre of rotation and the forearm is treated as a rigid body. Desired position and velocity data was given in order to move. Figure 7, shows some of the time trajectories of the position data and the data of velocity. Position trajectories used in the experiments are minimum jerk trajectories. The velocity trajectory is the first order I 1 Human Robot(Linear Motor) Figure 6. Experimental co-operation task by the robot and the human. ~~~~~~~ Time (I) Tiie (s) Figure 7. Time trajectories of the position and the velocity. Data analysis: As the muscle is mechanically analogous to a spring-damper system, Figure 8, simple second-order equation is used as the model for the arm dynamics. In the model, mass, damping factor and stiffhess are considered. Figure 5. Experimental robot system Six Axial Force Sensor mjt+ci+kx=f (9) where m, c and k are the impedance parameters for the mass, for the damping factor and for the stiffness respectively and f is the force that acts on the arm. For the estimation of the impedance parameters, the System Identification Toolbox of Matlab (The MATH II -678

4 Works Inc) [14] was used. For calculation ARX (Auto Regressive exogenous) Model was used. To make similarity with the ARX model, position x(t) as an input and force f(t) as an output was considered. If T is the sampling time then, _q) = x(t) - x(t - 1) and jc(t) = x(t) - _?(t - 1) T T impedance parameters are shown in Figure 12 that derived from these types of results. This is the proposed model of the impedance characteristic of the human arm. Afterwards proposed model has been tested experimentally by using a robot system. SoI& Input velocity, Dashed: Output vebcity, 0.8 I.40 By using these values in the equation (9), the following was obtained, m+ct+k - (2m + CT) -w + x(t-1)+ Fx(t - 2) = f(t) (10) or, f(t) = a&) + a& - 1) + a&t - 2) (11) Figure 9. Time trajectory of the velocity and the force. where, m+ct-t-k u, = - (2m + CT),a2 = Equation (11) is a form of ARX model. Coefficients a,, a2 and a3 were estimated by using the different variants of the recursive least-squares method. Then, the impedance parameters m, c and k were calculated. (a) Movement amplitude 0.15 meter and duratbn of movement 0.6 sec. (b) Movement amplitude 0.15 meter and duration of movement 0.8 set Figure 10. Impedance parameters calculated from the experimental data. 0.8 Figure 8. Impedance model of the human arm. Results: Figure 9 shows a typical time trajectories of position, velocity and force measured during the experiments when the robot was the leader and the human acted as a the follower. This data was used for calculating the impedance parameters. Fifty-four replications were observed for the calculation of impedance parameters at different conditions among them four types of results are shown in Figures 10 and 11 as an example. An over all Time ($8 12 (a) Movement amplitude 0.15 meter and duration of movement 1.2 xc (b) Movement &pliide 0. I5 meter Time (E) and duration of movement 1.4 sec. Figure 11. Impedance parameters calculated from the experimental data. II -679

5 Implement the proposed impedance model in human robot co-operation Methods: Impedance control is implemented as shown in Figure 14. The desired position of the robot was calculated in real time by integrating the variable model as f(t) = ti(t) + c(t)a(t) + k(t)+) (12) The integration is executed by using the 4 order rungekutta method. The sampling time for the calculation and position control was 1 ms. The human moved the object over a distance of 0.15 m. There were four movements in each experiment. At first, he/she pulled the object to a distance about 0.15 m and after 1 to 2 seconds, he/she pushed it to the initial position. Then, he/she pushed it 0.15 m and kept it in the same position for 1 to 2 seconds and than brought it on the initial position. To confirm the appropriation of the proposed model, a constant model and an arbitrary model were used. In constant model, the lowest values of the proposed model were used i.e., the damping factor was 16 Ns/m and the stiffness was zero. The arbitrary model, Figure 13 was derived from the proposed model, where the parameters vary from high to the low within the period of 0.2 second. Results: Figure 16 shows the time trajectories of velocity by using three models. Convex shapes are for the pulling action and concave shapes are for the pushing action. The velocity of the minimum jerk trajectory is shown in bold line along with each figure. Figure (A-B), (C-D) and (E-F) represent the results of the proposed model, arbitrary model and constant model respectively. Comparison between the three models is shown in Figure (G-H). r - -- _~ I ti +cftkx=f Figure 14. Block diagram of the robot control system. i I I No oi lii2*m OS Figure 12: Impedance parameters for the proposed model. 1 c(r)=100 & k=o 1 Figure 15. Flow chart of the impedance control. 4. DISCUSSION o&-22w Tiie (5) Figure 13. Impedance parameters for the arbitrary model. It was observed from the Figure 10 and 11, that the mass effect was almost zero and damping factor was high at the starting position and was near to zero after 0.4 second. Stiffness has also similar characteristic as the damping factor. A number of subjects (human) were used to investigate the variation of the parameters. Even than the similar results were obtained. Finally, results were implemented to the robot and made the robot for the execution of the co-operative task with the human. As mentioned in section 2, that the robot characteristic would be imitated the human characteristic in this co-operative task, if it moves along the minimum II -680

6 jerk trajectory. Figure 16(C-D) shown that the velocity was slower at the time of arbitrary model. At the time of constant impedance control, Figure 16(E-F), with a damping factor 16Ns/m velocity was slower than the previous case. In the arbitrary model until certain time velocity run along the velocity of the minimum jerk trajectory while in constant model the velocity betrayed from the trajectory initially. From Figure 16(A-B), it is clear that in the proposed control method with the little variation almost all the lines of velocity follow the minimum jerk trajectory. This phenomena is realise from Figure 16(G-H). Where, bold line shows the velocity of the minimum jerk trajectory, dotted line shows the velocity of the proposed model, dashdot line shows the velocity of the arbitrary model and dashed line shows the velocity of the constant damping model. Arbiiary impedance model Tiie ( ) Constant impedance model Time (8) Figure 16. Time trajectories Comparison of models 5. CONCLUSION of the object velocity. The variable impedance control of a robot has been proposed in co-operation with human and has shown its effectiveness. Firstly, impedance characteristics of human arm in a co-operative task (push and pull an object) was analysed. The magnitudes of the impedance parameters were varied with the action. Both the damping factor and stiffness was high at the starting position and almost were zero after OA-second. A number of subjects were used and similar results were found. Finally, result is implemented to a simple one degree-of-freedom robot and made the robot for the execution of the co-operative task with the human. It was observed that the proposed control method showed promising characteristics to the robot in cooperation with human. 6. REFERENCES PI R. Ikeura, and Kazuki Mizutani, Control of Robot Cooperating with Human Motion, Proc. of IEEE International Workshop on Robotics and Human Communication, 1998 ~~ PI R. Ikeura, H. Monden and H. Inooka, Cooperative motion control of a robot and a human, Proc. of IEEE International Workshop on Robotics and Human Communication, 1994 pp R. Ikeura and H. Inooka, Variable impedance control of a robot for cooperation with a human, Proc.of IEEE international Conference on Robotics and Automation, 1995, pp [41 R. Ikeura, H. Inooka and K. Mizutani, A control method for a robot cooperating with a human in carrying an object, Proc. of the Japan-USA Symposium on Flexible Automation, 1996, pp H. Gomi, Y. Koike and M. Kawato, Human hand stiffness during discrete point-to-point multi-joint movement, Proc. of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1992, pp Fl T. Tsuji, K. Goto, M. Moritaui and M. Kaneko, Special characteristic of human hand impedance in multi-joint movements, Proc. of JSME Annual conference on Robotics and Mechatronics in Japan, 1994, pp [71 E. Nakano, S. Ozaki, T. Ishida and I. Kato, Co-operational Control of the Anthropomorphuos Manipulator MELARM, Proc. of 41h International Symposium on Industrial Robots, 1974, pp. 25 l-260. PI Y. F. Zheng and J. Y. S. Luh, Optimal Load Distribution for Two Industrial Robots Handling a Single Object, Proc. of 1988 IEEE International Conference on Robotics and Automation, 1988, pp [91 M. E. Pittelkau, Adaptive Load-Sharing Force Control for Two-Arm Manipulators, Proc. of IEEE International Conference on Robotics and Automation, 1988, pp [IO] C. D. Kopf and T. Yabuta, Experimental Comparison of Master/Slave and Hybrid Two Arm Position/Force Control, Proc. of 1988 IEEE International Conference on Robotics and Automation, 1988, pp [I l] 0. M. Al-Jan& and Y. F. Zheng, Ann-manipulator coordination for load sharing using variable compliance control, Proc. of I988 IEEE International Conference on Robotics and Automation, 1997, pp [12] K. Kosuge and N. Kazamura, Control of a robot handling an object in co-operation with a human, Proc. of IEEE International Workshop on Robot and Human Communication, 1997, pp [13] T. Flash and N. Hogan, The coordination of arm movements: An experimentally confirmed mathematical model, J. Neuro-science, 1985, pp l 703. [ 141 Lennart Ljung, System Identification Toolbox, User s Guide, The MathWorks, Inc., 1995, p and II -681