LIMITATIONS in current robot compliance controls motivated

Transcription

1 586 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 5, NO. 6, NOVEMBER 1997 Analysis and Implementation of a Neuromuscular-Like Control for Robotic Compliance Chi-haur Wu, Senior Member, IEEE, Kao-Shing Hwang, Member, IEEE, and Shih-Lang Chang Abstract In comparison with robot manipulators, primate limbs excel robots in facile movements requiring compliance control. Based on this fact, this paper will extend our findings in modeling the muscle-reflex mechanism of primate limbs to robotic control. After some salient properties of the neuromuscular system were identified, a neuromuscular-like model that can accurately emulate different involuntary and voluntary movements was developed. To link the findings from the biological system to robotic control, the developed neuromuscularlike controller was implemented on a PUMA 560 robot. The experimental results demonstrated that the emulated spindlereflex model in the neuromuscular-like controller acts as an impedance to any changing displacement and will comply and enhance the needed compliant forces or torques for the changing motion. Due to this force-enhancement property, no external force sensor is required for sensing force feedback in this control. The capability in performing various free and constrained movements demonstrated that a neuromuscular-like control is very useful for robotic applications requiring adaptation. Index Terms Biological control systems, biological system modeling, control systems, force control, man machine systems, nonlinear systems, robots, system analysis and design. I. INTRODUCTION LIMITATIONS in current robot compliance controls motivated the study of this paper. In robot motion maneuvers, there are two types of motion, unconstrained and constrained. Unconstrained motion requires only position control, which is the motion that most of industrial robots are allowed. The constrained motion, such as assembling parts, requires compliance control that combines both position control and force control [1], [2]. In recognizing the importance of compliance control for advanced robotic applications, many approaches were proposed. One approach selected free joints for the motion and controled these free joints with forces and other joints with positions [3]. Another approach controled both positions and contact forces generated at the robot wrist to provide compliance [4]. Other approaches have used force feedback strategies, such as accommodation force control [5] and active stiffness control [6]. Advancing the concept of stiffness control to the control of mechanical impedance about the limb joint by coactivation of antagonist muscles, an impedance control was also proposed for robot compliance [7]. Manuscript received January 2, 1996; revised March 4, Recommened by Associate Editor, B. Espiau. C. Wu and S.-L. Chang are with the Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL USA. K.-S. Hwang is with the Department of Electrical Engineering, National Chung-Cheng University, Chia-Yi, Taiwan. Publisher Item Identifier S (97) Although many approaches were proposed, the performance of industrial robots is still crude in providing compliance. This deficiency remains one of the major problems limiting the scope of robotic applications. It is widely recognized that the primate limb has much superior performance for delicate, skillful maneuvers, especially in adaptation to different loads and capability to execute compliant tasks. It seems that a good compliance control for robotic applications should emulate the compliant capability of the neuromuscular system. However, only few developed schemes for robotic compliance control take advantage of findings in biological limb research. Hogan s impedance control relates to the spring-like interface between limb and environment. Modeling the spring-like behavior of the neuromuscular system, while the limb is in contact with the environment, allows successful impedance control to provide compliance for a robot. The concept of flexion and extension in muscular system was also adopted by Jacobsen et al. to control manipulator links with two tendon-driven actuators [8]. Their control algorithms in position and force control showed good results, experimentally. The success of these efforts indicates that a better design of robotic compliance control may benefit from modeling the mechanisms of biological limbs. According to an extensive body of experimental evidence [9] [11], a nonlinear property extracted from force-velocity data shows that force response is proportional to a low fractional power, 0.17, of muscle s velocity. From our initial study, we found that this unusual nonlinear damping property acts as a control function to regulate different limb movements [12]. Intrigued by this property, we further studied the characteristics of the neuromuscular system. Although the nonlinear dynamics of the muscle-reflex system have been studied previously [13] [16], the neurophysiological models are too complicated to be simulated or to be used for robotic control. To develop a neuromuscular-like control model for practical applications, the mechanisms of the muscle-reflex system were studied. According to the biological model, the muscle-reflex mechanisms form a feedback system called the motor servo [9], [15], consisting of a muscle, its spindle receptors, and the corresponding reflex pathways back to the muscle. This neuromuscular system mediates the stretch and unloading reflex of the muscle by the feedback. To replicate the musclereflex system, Gielen and Houk proposed a model of the motor servo that incorporated a nonlinear description of the behavior of muscle spindle receptors, a delay in the reflex loop via the spinal cord, and a nonlinear model describing muscle /97$ IEEE

2 WU et al.: NEUROMUSCULAR-LIKE CONTROL FOR ROBOTIC COMPLIANCE 587 Fig. 1. Muscle-reflex model. mechanical properties [15]. To simplify the biological model proposed by Gielen and Houk [15] for practical applications, a muscle-reflex model shown in Fig. 1, consists of a spindlelike model and a simple muscle stiffness mechanism was developed first to emulate various involuntary movements [17]. The parameters in the model were optimized through fitting the experimental data. This model will be explained in Section II. After further fitting the experimental data of various voluntary movements. a neuromuscular-like model was developed for emulating limb movements [18], [19]. A very important property was found that the control based on the neuromuscular-like model can provide the needed reflex and compliance for moving the limb. The emulated spindlelike model in the neuromuscular-like model will react reflexly to any changing displacement. In other words, when it senses a small change in limb position, it will reflexly enhance the muscle force to move the limb. Due to this property, the neuromuscular-like model can emulate various voluntary movements (free movements) through motor commands and adapt to the transition from voluntary movements to involuntary movements (constrained movements) without using a force sensor. This capability is essential in designing a compliance control for robots. Current industrial robots are poor in compliant control and adaptability, a neuromuscularlike control seems to be a reasonable approach to improve that. In this paper, the practicality of modeling the muscle-reflex system for actual robotic applications will be demonstrated with experiments on a PUMA 560 robot. II. A MODEL OF NEUROMUSCULAR-LIKE CONTROL The proposed neuromuscular-like control is modeled from the physiological properties of the primate muscle-reflex mechanisms. After studying the properties of the muscle-reflex mechanisms, a muscle-reflex model shown in Fig. 1. was developed first [17]. This muscle-reflex model can emulate the response of extensor or flexor for the involuntary movement. However, to emulate voluntary movements, a more complete model is required for performing the operations of both extensor and flexor. In other words, voluntary movements require torques in two directions (flexion and extension), and therefore two separate muscles. Involuntary movements are driven by external forces, but voluntary movements are dictated by the CNS (central nervous system) through motor commands as well as by external forces. Based on these basic distinctions between voluntary and involuntary movements, a neuromuscular-like model, depicted in Fig. 2, consists of a pair of agonist and antagonist muscles for flexion and extension was proposed [18], [19]. The proposed neuromuscular-like model was originally modeled from two muscles producing opposing torques on a hand. The hand rotates about the wrist with a single degree of freedom (DOF). In Fig. 2 and this paper, the subscripts ago and ant represent agonist and antagonist, respectively. The neuromuscular-like model proposed in Fig. 2 has two muscles. Each muscle is emulated by a muscle-reflex model that consists of two major parts: spindle-like mechanism emulating the reflex property of the biological muscular system for absorbing impacting forces, and muscle-stiffness mechanism emulating muscle stiffness for tracking various movements. The analogy of this muscle-reflex model is depicted in Fig. 1. The model has two possible inputs, motor command and external disturbing force. The load movement is represented as. Whenever there is a load movement, the muscle length will vary with load position [9]. This equilibrium movement at the muscle is represented as, where is the initial position of the load sensed at the muscle. The reflex signal from the spindle-like model, scaled through a reflex gain coefficient, is combined with the motor command to produce a reflex-induced command for generating muscle force. However, to simulate the smoothing of commands by motor neuron pools such that a bell-shaped velocity profile for limb movements can be induced, a lowpass filter (LPF) must also be included in the model. Based on the experimental data, a time constant of 30 ms is extracted for this filter effect [15]. The linear feedback gain coefficient shown in Figs. 1 and Fig. 2, represents the effect of muscle length-tension, which represents any spring-like behavior in the muscle-reflex system [9]. This effect describes that any change in muscle length will produce a muscle force through muscle stiffness. In sum, both spindle and muscle stiffness mechanisms will induce muscle forces. The resultant muscle force combined with the disturbing force at the load will then move the load at the hand with a movement and cause an equilibrium movement of at the muscle. If the hand is modeled by an inertial load with a damping constant, the dynamic system under the neuromuscular-like

3 588 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 5, NO. 6, NOVEMBER 1997 Fig. 2. Neuromuscular-like two muscle model. control can be represented as where and represent the load velocity and acceleration, respectively. The muscle force is then produced by two muscle-reflex models shown in Fig. 2, representing an agonist and an antagonist. Each muscle-reflex model consists of a simple muscle stiffness mechanism, driven by the sum of a voluntary command and a reflex signal produced by a spindlelike model. Muscle-stiffness mechanism is assumed to be spring-like, with a spring constant. With this stiffness, muscle force is generated as follows: In the above equation, and represent the length-tension effect of the agonist and antagonist to the muscle force, respectively; and and represent the equilibrium movements sensed at agonist and antagonist, respectively. The equilibrium movement at each muscle is obtained from the difference between its initial position, or, and the sensed load movement as depicted in Fig. 2. As for and, they represent lumped neural inputs to the agonist and antagonist muscle, respectively. These two lumped inputs are the outputs of two LPF s represented in Fig. 2. The purpose of these LPF s is to induce the bellshaped velocity profile for the voluntary movement. (It might represent smoothing of motor commands by motor neuron pools.) This effect is represented as follows: (1) (2) LPF (3) LPF (4) where and are the neural signals before filtering, and LPF represents a LPF with a time constant, which is about s based on the experimental data [15]. In (3) and (4), each is the sum of voluntary motor command and reflex signal generated from the spindle-like model. This relationship at the agonist and antagonist can be represented, respectively, as (5) (6) where and are the reflex signals generated from the spindle-like models of the agonist and antagonist, respectively; and is the reflex gain coefficient. In order to model the spindle-like mechanism in Fig. 2, physiological properties of the spindle mechanism have to be known. The physiological studies indicated that the motor servo of neuromuscular system has two salient nonlinear dynamic features, a stiffness enhancement at small signals and a fractional velocity-dependent viscosity [13] [16]. The stiffness of the neuromuscular system, which is not constant over the stretching range, has more effect on the initial elastic force response, a property which is referred to as the short-range enhancement. The velocity-dependent viscous force response, however, shows a nonlinear viscosity property that has been postulated to damp limb movements when variable loads are involved. In sum, spindle receptors of the muscle-reflex system will sense both muscle length and the rate of change of muscle length and produce a firing rate reflecting both measurements. Therefore, the simulated spindle-like model in our model must capture the physiological properties of the described nonlinear damping effect multi-

4 WU et al.: NEUROMUSCULAR-LIKE CONTROL FOR ROBOTIC COMPLIANCE 589 plied by the short-range elasticity enhancement. After fitting recorded experimental data in our previous research [17], a spindle-like model was developed for each muscle as follows: where and are the internal position, velocity, and bias position of the spindle-like model for the agonist (the antagonist counterparts are with a subscript of ant ) and is the reflex stiffness and is a scaled damping coefficient for each spindle-like model. In this spindle-like model, the short-range elasticity enhancement for moving either direction (positive or negative) was fitted through experimental data and modeled as for the agonist muscle; similar effect was also modeled for the antagonist. According to (7) and (8), any change of load position will cause an equilibrium movement at each muscle, represented as and. Then these changes will induce reflex signals and at the corresponding muscles by the spindle-like model. And these reflex signals scaled by a reflex gain will then produce muscle forces to respond to the change. With property of the nonlinear damping effect multiplied by the short-range elasticity enhancement, this spindle-like model will provide a property of force enhancement and acts as a control function regulating the limb motion in such a manner that the neuromuscular-like system will enhance the limb motion when high velocity is needed; conversely, it will also help stop limb motion promptly when velocity decreases to the low-velocity range. In other words, the spindle-like mechanism is capable of making automatic corrections in muscle forces to respond to external disturbance forces, rapidly. Therefore, it has the capability in absorbing any impacting force that causes load displacements by complying muscle forces or torques to the motion. To identify the parameters of the neuromuscular-like model, different sets of experimental data collected from different involuntary and voluntary movements were used as the templets for fitting the proposed model. These experimental data were provided by the Laboratory of Professor J. Houk, Department of Physiology, Northwestern University, Evanston, IL. In our simulated limb wrist model, was set to one so that represents the muscle mechanical stiffness describing the linear effect of muscle length-tension. As the involuntary movements involve no motor commands, and were both set to zero. After minimizing the mean-square errors between the simulated results and the experimental data, a set of parameters were obtained as follows: m/n, N/m, N/m, N/m (s/m) m, and RC s. The initial study of involuntary movements demonstrated that the neuromuscular-like model has appealing features for controlling constrained movements [17]. Then, the study of voluntary movements further proved that the proposed model can perform both free and constrained movements as required by robotic compliance control [19]. For the purpose of enhancing the capability of robots in compliance, these (7) (8) encouraging results from our initial studies prompt the research done in this paper. III. IMPLEMENTATION OF THE NEUROMUSCULAR-LIKE CONTROL ON ROBOT In the research of limb control, limb movements are usually assumed to be under the equilibrium trajectory control [7], [24]. Under such a hypothesis, the brain sends equilibrium trajectory to the limb without worrying about the low-level control problems. This theory makes maximum use of viscoelastic properties of the muscle-reflex system and treats both free movements and constrained movements coherently. In other words, a lot of complicated computations can be avoided if the low-level control system can adapt to different task conditions. From this hypothesis, the neuromuscular-like control seems to be a good choice for low-level control. Therefore, the main goal of this paper is to link our findings in modeling the biological muscle-reflex system to the development of a control method that can aid the performance of an industrial robot. The developed controller will be implemented on a PUMA 560 robot. A. Motor Commands Patterns Under the hypothesis of equilibrium trajectory control, limb movements can be partly modeled by velocity profile and force profile. According to a bell-shape velocity profile, minimum-jerk criterion was proposed to emulate human arm movements as straight lines [21]. Based on minimum-jerk criterion, a movement trajectory can be described by a fifthorder polynomial. In contrast with minimum-jerk planning, Uno et al. proposed a minimum-torque method, which can emulate certain limb movements that are not straight lines. To relate planning with dynamics, Hollerbach and Atkeson pointed out that there is a fundamental, time-scaling relationship between manipulator s velocity and its dynamics that allows trajectory planning and inverse dynamics to be coupled exactly and efficiently [22]. To move a multijoint limb, Flash also modeled the arm movement based on the equilibrium trajectory control [23], in which each equilibrium point is generated by a spring-like elastic energy function [24] with the directional position-dependence stiffness and viscosity. To determine a set of motor commands for a multiplejoint robot, we must decide the domain for planning these commands. In investigating whether planning variables of human arm movements are at the Cartesian domain or joint domain, a staggered joint interpolation was proposed [22], in which a time delay is introduced to one joint to slow down that joint. This method could approximate straight lines in the Cartesian space. They concluded that this planning may best describe human movements. In our applications, we will adopt their concept of staggered planning to plan motor commands representing position commands. Given a starting position and a final position, motor commands for this movement will be mathematically planned by the following equation: (9)

5 590 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 5, NO. 6, NOVEMBER 1997 Fig. 3. One-muscle implementation on joint i of a PUMA 560 robot. where represents a time delay if the staggered planning is used. This formulation has the advantage of representing most of command types we are going to investigate. For example, if is a constant, then the command type is step; however, if is a first-order function, then it is ramp. If a minimum-jerk planning is required, then will be a fifth-order function of time. The minimum-jerk planning has been used successfully in emulating straight-line human movements for a two-joint limb by other researchers [21], [25]. To provide a smooth planning for an industrial robot such as PUMA 560, the planning of minimum-jerk in (9) will be adopted for our experiments. The concept of staggering strategy will also be applied in our planning if the geometrical shape of a path needs to be maintained. Based on those patterns, motor commands representing positions will be planned by (9) and sent to the neuromuscular-like controller. B. Neuromuscular-Like Control for Robot Joints A six-joint PUMA 560 robot in our laboratory is used to implement the proposed neuromuscular-like controller. The ideal neuromuscular-like model, shown in Fig. 2, consists of two muscles producing opposing forces on a joint. However, to implement this controller on PUMA 560 robot, two-muscle implementation is not feasible because there is only one motor at each joint. To accommodate this model for the PUMA robot, the single-muscle model shown in Fig. 1 is implemented as Fig. 3 to drive each joint of PUMA robot. Since this implementation has only one muscle, there are no coactivation of two muscles in this model. The mechanisms of this singlemuscle model acting on a joint will be explained in the following. In general, the dynamic system of an degree-of-freedom robot is represented by the following equation: (10) where and represent joint positions, velocities, and accelerations of all joints, respectively; and represent the inertia matrix, the Coriolis and centripetal force vector, and the gravity force vector, respectively; and represents applied joint torque/force vector. In our earlier study, we found that a system controlled by the nonlinear damping in the neuromuscular-like model can adapt to different inertial loads [12]. Based on this property, the neuromuscular-like control seems to be a good candidate for controlling a robot with changing configurations. To utilize the neuromuscular-like controller for controlling this nonlinear robot, the controller will generate the required muscle force and apply it to each joint. In other words, the applied torque/force will be equivalent to the muscle force computed from the neuromuscular-like controller for all joints. To design a neuromuscular-like controller for each robot joint, we will model the dynamic system of joint of a robot as (11) In this equation, and represent velocity and acceleration of joint, respectively. represents the joint inertial load varied with the changing robot configurations,, and is the damping constant of the actuator at joint. represents all the external forces and disturbance forces coupled from other joints motion. As for, it represents the muscle force computed from the neuromuscular-like control and applied to the actuator at joint. Assuming that joint has its initial joint position at, the muscle force generated by the neuromuscular-like controller can be rewritten from (2) to the following equation: (12) where represents the equilibrium position that muscle moves, and represents an input to the muscle after an LPF and can be represented as follows: LPF (13) In the above equation, is computed as (14) where is a positional motor command generated for joint from the planning, and is a reflex signal generated by the spindle-like model. In order to provide equilibrium position commands, is generated by the following equation: (15)

6 WU et al.: NEUROMUSCULAR-LIKE CONTROL FOR ROBOTIC COMPLIANCE 591 Fig. 4. Joint 1 involuntary movement (Km =781 N-m, H =2:065 rad/n-m). where is the planned desired joint position. As for the reflex signal, it is generated from the spindle-like model [(7) and (8)] at joint as follows: (16) where and are the internal position, velocity, and bias position of the spindle-like model at joint, is the reflex stiffness, and is a scaled damping coefficient for the spindle-like model. The properties of these parameters were discussed in the previous section. Biologically, the spindle-like model in the neuromuscularlike model emulates the function of spindle receptors [17]. This mechanism is capable of making automatic corrections in muscle toning to respond to external disturbance forces. It serves as a reflex sensor on the muscle force. When the muscle force rises past a threshold level, the spindle receptors will inhibit the motor unit, and turn the muscle activity off to prevent muscle from over-lengthening [26]. Meanwhile, it also regulates the muscle stiffness in voluntary movements. Based on this physiological phenomenon, the operation of the neuromuscular-like control has two modes, voluntary and involuntary, for free and constrained movements. In the voluntary mode for free movements, the motor commands defining the equilibrium joint positions can be computed from (15) based on the desired joint trajectory according to a planned path. If a voluntary movement is imposed by an external force, to adapt to the constraint, the transient equilibrium position will be shifted to comply the disturbance force. However, when the disturbance force dissipates, the equilibrium position will return to the desired target defined by motor commands. As for the involuntary mode, it is a pure force-following mode that has no positional motor commands from the planning. To emulate the effect of external force on muscle movement of this one-muscle model, the equivalent muscle movement,, in (12) and (16) needs to be remodeled as. After reversing the sign of the equivalent muscle movement, the reflex signal, generated by the spindle-like model in (16), will comply to the external disturbance force that changes. Then, the reflex signal will stimulate muscle mechanism and generate the muscle force at the joint actuator. As a result, the joint will move freely with the external force. Therefore, to have this involuntary model for force-following motion, an artificial Fig. 5. Joint 1 force enhancement in involuntary movement (Km = 781 N-m, H = 2:065 rad/n-m). control switch is needed for reversing the sign of equivalent muscle movement. By examining the neuromuscular-like control model carefully, it is noted that the spindle-reflex mechanism will generate the needed compliance for any motion, scaled through the reflex gain, in the muscle system. Without this nonlinear spindle-reflex mechanism, the muscle mechanism is simply a positional control mechanism. In summary, the internal spindle-reflex mechanism behaves as an impedance to comply to a changing displacement from the environment and then enhance the muscle force and provide the compliance for the motion. IV. EXPERIMENTS OF NEUROMUSCULAR-LIKE CONTROLLER ON PUMA 560 ROBOT In order to implement this neuromuscular-like control on each robot joint successfully, we will first simplify the number of changing parameters in the controller. Since the proposed spindle-reflex mechanism was experimentally modeled from the study of limb movements [17], we will assume that the spindle-reflex mechanism will be the same for all joints. In other words, the values of and in the model will be the same at all joints for any reflex motion. The parameter representing the length-tension effect will be kept to be one as in the original model to represent a linear feedback of joint position. The nonlinear effect of this length-tension gain will be explored in our future works. Particularly, the implementation of the neuromuscular-like control for each robot joint is simplified to adjust two parameters, the reflex gain and the muscle stiffness. The reflex gain will be adjusted for scaling different reflex forces represented by the discharge rate,. The muscle stiffness will be adjusted for different stiffnesses in needs of different joint muscles. In other words, these two parameters will be adjusted for controlling different free and constrained movements. A. Setup of PUMA 560 Robot System To implement the neuromuscular-like control on a PUMA 560 robot in our laboratory, we modified the original PUMA VAL controller. The modified system consists of a PC 486, a custom-made interface board, and a PUMA 560 arm. The custom-made interface board can switch the arm control from

7 592 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 5, NO. 6, NOVEMBER 1997 Fig. 6. Joint 1 voluntary movement (Km = 781 N-m, H = 2:065 rad/n-m). Fig. 8. Joint 1 position errors of voluntary movement (Km = N-m, H =0:118 rad/n-m). Fig. 7. Joint 1 voluntary movement with disturbance force (Km = 781 N-m,H = 2:065 rad/n-m). the VAL controller to PC. The encoder information fed back from each PUMA joint is read through this interface board. The torque output computed from each neuromuscular-like joint controller implemented on PC is also sent through this board to each joint. The command planning strategies and robot forward and inverse kinematics of PUMA 560 robot are implemented in C language and running on our PC. At every sampling time, six neuromuscular-like joint controller will receive the motor command generated from our planning system and send joint muscle torques through the interface board to drive six PUMA joints. In order to drive individual joint, PUMA joints can also be locked through software control in PC so that any desired joint can be selected to move without interference from the other joints. Under this setup, the performance of neuromuscular-like controller will be examined with different gains for different free and constrained movements. B. Experiments on PUMA Joint 1 In this part of experiments, we try to identify a set of feasible gains for parameters in the neuromuscular-like control and their effectiveness to robotic control. To start our initial setup for gains, we converted the values of parameters in the neuromuscular-like model described in Section II to the rotating motion of PUMA robot. According to the kinematic and dynamic data of the robot and the dynamic data of the experiment setup for collecting movements [11], the following set of values are used in our model for starting up our initial experiments: rad/n-m, N-m/rad, N-m/rad, N-m/rad (s/rad) rad, and s. As discussed in the previous section, we will assume a fixed spindle-reflex mechanism for the controller and adjust the reflex gain and muscle-stiffness gain for generating various movements. To test the capability of a neuromuscular-like control on an industrial robot, we performed some experiments with joint 1 of PUMA 560 robot. The setup for testing involuntary movements on PUMA joint 1 was that we pulled or pushed joint 1 after all other five joints were locked. By pulling or pushing joint 1 alone, we could determine whether the joint torque is generated and enhanced by the neuromuscular-like control. If it is, the joint will follow the applied motion freely. The force-enhancement to observe is the property of the nonlinear damping effect multiplied by the short-range elasticity enhancement in the spindle-like model. This experiment tests the force-following capability of the neuromuscular-like controller without a force sensor because the spindle-like model will act as a reflex sensor. The servo sampling rate for the neuromuscular-like controller is about 1.5 ms measured by the PC486 clock. At each sampling time, the neuromuscularlike controller implemented on PC486 sends the computed torques through the interface board to PUMA controller that drives joint 1. After some experiments by adjusting the value of to rad/n-m and to 781 N-m/rad, the response of PUMA s joint 1 was amazingly good and smooth. The result in Fig. 4 shows the involuntary movement of joint 1 followed by an external force applied to the arm. Fig. 5 depicts the enhanced muscle forces versus the positional changes of joint 1. Since this experiment had no input motor commands, the internal spindle-reflex mechanism will comply to the changes in joint position and generated the muscle force to provide the compliance for the involuntary motion. As demonstrated in Fig. 5, the muscle force was generated and enhanced by the spindle-like model to move the joint to follow the external force. The force enhancement with a big jump can be observed at the beginning of the movement (from 90 to 87 ). Conversely, when the external force diminished gradually from

8 WU et al.: NEUROMUSCULAR-LIKE CONTROL FOR ROBOTIC COMPLIANCE 593 (a) (b) (c) Fig. 9. PUMA 560 is commanded to insert a peg into the outlet tube of a funnel. (a) Projection of tip position on X-Z plane. (b) Projection of tip position on Y -Z plane. (c) The trajectory of tip in Cartesian space. 60 to 29, the muscle force should diminish accordingly. Therefore, the limb motion should stop rapidly (reversibly enhanced) at the end of the motion as demonstrated in the figure. Due to this force enhancement property provided by the spindle-like model, no extra force sensor for designing a force control is required for the neuromuscular-like control to have force-following capability. And more significantly, it demonstrated that a compliance control can be designed for a robot without using any force sensor. To generate voluntary movements, we used the same gain set as in testing the involuntary movement. The desired motor commands for the intermediate joint positions at joint 1 were generated by (9) based on the planning strategy of minimumjerk. The experimental result of moving 100 is plotted in Fig. 6. In this case the maximum position error is about 2 in the middle of the movement. The error at the end is about 0.9. To test the compliant capability of the control, we did another experiment. With the same voluntary movement, during the joint motion, we could stop the joint with our hand, easily. Then, after we released the joint for holding it about 3 s, an amazing result was that the joint moved to its destination without any problem. In other words, the developed controller attempts to make up the lost time by following the original trajectory. This experiment further demonstrated that a robot joint controlled by the neuromuscular-like model can be compliant and adapt to its environment. To further improve the accuracy of voluntary movements, we also performed another experiment by increasing the gain to N-m/rad and decreasing the gain of to rad/n-m. The position errors along the same movement are plotted in Fig. 8. The maximum positional error is less than 0.1 and the settling error in position is less than However, for such a strong stiffness, the joint motion could not be stopped during the movement as we demonstrated in the previous experiment. This experiment showed that a precise positional control for free voluntary movements can also be designed with the neuromuscular-like controller in addition to the compliant capability of force-following. In summary, our experiments with joint 1 of PUMA 560 robot demonstrated that the neuromuscular-like controller can have different stiffness for free voluntary movements, constrained involuntary movements and compliant movements (partially constrained) by adjusting the reflex gain and the muscle-stiffness gain. The product of these two parameters within the control loop provides certain degree of force enhancement for muscle force. With the same degree of force enhancement, the higher the reflex gain is, the more compliant the system will be. On the other hand, the higher the stiffness

9 594 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 5, NO. 6, NOVEMBER 1997 (a) (b) (c) Fig. 10. Robot arm is led by hand to trace a circle drawn on a table. (a) Projection of tip position on X-Y plane. (b) Projection of tip position on Y -Z plane. (c) The trajectory of tip in Cartesian space. gain is, the stiffer the system will be. These experimental results strongly proved that the neuromuscular-like control has the advantage in providing compliance for the constrained tasks. In addition, the spindle-like model in the neuromuscularlike control will generate the needed compliant force from changes in position. This reflex force will then generate the muscle force through the product of reflex gain and muscle stiffness gain. As a result, an expensive force sensor is not required for providing the force feedback in the system. This is a great cost saving in designing a compliance control. In the next section, we will explore this property further for improving robotic control in compliance. C. Experiments of Compliance on Six Joints of PUMA 560 Robot During our experiments with PUMA joint 1, we found that different parameters of the neuromuscular-like controller control different functions. The reflex gain will affect the capability of the system in adaptation. The muscle stiffness gain will affect the errors in position tracking. These two parameters have opposite effects on the system. One will increase the compliant capability of the system and the other will increase the stiffness of the system for a better position control. As for the spindle-like mechanism, it simply performs an amazing task of converting changing positions to compliant forces. Because of its capability, no force sensor is needed in the system. To set up the parameters of the neuromuscular-like controller for all joints, the same approach and experiments as we did for joint 1 were also applied to the other five joints of PUMA robot. To have all six neuromuscular-like controllers running on the PC486 for a Cartesian task, the sampling time for sending joint torques requires 2.4 ms to finish all computations needed for planning, gravity compensation, control, and data transfer. Although the 2.4-ms servo sampling time is longer than we desired for controlling our robot, the performance is acceptable. The servo sampling time can be tremendously shortened if a Pentium PC is used. By adjusting the reflex and muscle-stiffness gains for all six joint controllers, the following three experiments with different constrained tasks were performed by the PUMA robot. To demonstrate the compliance control for a constrained motion, three plots in Fig. 9 show the results of an experiment that PUMA robot inserted a peg into the outlet tube of a funnel and the neuromuscular-like controllers adjusted the tip path for insertion. The result demonstrated that robot s

10 WU et al.: NEUROMUSCULAR-LIKE CONTROL FOR ROBOTIC COMPLIANCE 595 (a) (b) (c) (d) (e) (f) Fig. 11. Robot is pulled away by a disturbance force while it is approaching to the target point. (a) Joint 1 trajectory. (b) Joint 2 trajectory. (c) Joint 3 trajectory. (d) Joint 4 trajectory. (e) Joint 5 trajectory. (f) Joint 6 trajectory. tip was compliant to the constraint caused by the contacting surface. To prove the capability of a pure force-following for constrained tasks, three plots in Fig. 10 show the results of an experiment that robot was hand-led to roughly trace a circular object. To further verify the compliant capability of the controller, six plots in Fig. 11 illustrate the responses of six joints of the PUMA 560 robot when the robot adapted to a stopping force during a voluntary movement and then reached its target position after the constrained force was removed. This experiment further substantiated that a robot controlled by six neuromuscular-like joint controllers can comply and adapt to its environment. V. CONCLUSION Limitations in current robot compliance controls motivates the study of the neuromuscular system and limb movements. Based on the properties and mechanisms of the musclereflex system, a neuromuscular-like model was formulated

11 596 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 5, NO. 6, NOVEMBER 1997 for control. A very important property of the developed neuromuscular-like control is that it provides the needed compliance for various movements. The capability in performing free and constrained movements demonstrated that a neuromuscular-like control is very useful for robotic applications requiring adaptation. To confirm our findings from the biological muscle-reflex system, we use a PUMA 560 robot to demonstrate the proposed controller. The experimental results showed that the same neuromuscular-like controller can generate free voluntary movements, constrained involuntary movements, and partially constrained compliant movements by adjusting the values of two parameters, the reflex gain and the musclestiffness gain. The product of these two parameters within the control loop provides certain degree of force enhancement for muscle force. With the same degree of force enhancement, the higher the reflex gain is, the more compliant the system will be. On the other hand, the higher the stiffness gain is, the stiffer the system will be. These experimental results strongly proved that the proposed controller has the advantage in providing compliance for the constrained tasks. Another important property of the neuromuscular-like control is that the emulated spindle-reflex mechanism will comply to the sensed changes in position. This reflex force will then generate the muscle force through the product of reflex gain and muscle stiffness gain. As a result, no expensive force sensor is required for providing the force feedback in the system. This is a great cost saving in designing a compliance control. Due to the capability of current industrial robots, applications of robots have been limited. Although many approaches were proposed to solve the problem, the mechanism of primate limb seems to be the best solution. Therefore, we believe that the success of this research in linking the findings in the biological muscle system to current robotic control will advance robotic applications to the next level requiring adaptation. [10] C. C. A. M. Gielen, J. C. Houk, S. L. Marcus, and L. E. Miller, Viscoelastic properties of the wrist motor servo in man, Ann. Biomed. Eng., vol. 12, pp , [11] L. E. Miller, Reflex stiffness of the human wrist, M.S. thesis, Dept. Physiology, Northwestern Univ., Evanston, IL, [12] C. H. Wu, J. C. Houk, K. Y. Young, and L. E. Miller, Nonlinear damping of limb motion, in Multiple Muscle Systems: Biomechanics and Movement Organization, J. M. Winters and S. L.-Y. Woo, Eds. New York: Springer-Verlag, 1990, pp [13] G. I. Zahalak, A Distribution Moment approximation for kinetic theories of muscular contraction, Math. Biosci., vol. 55, pp , [14] A. F. Huxley, Muscle structure and theories of constraction, Prog. Biophys. Chem., vol. 7, pp , [15] C. C. A. M. Gielen and J. C. 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Neurosci., vol. 5, pp , [22] J. M. Hollerbach and C. G. Atkeson, Deducing planning variables from experimental arm trajectories: Pitfalls and possibilities, Biol. Cybern., vol. 56, pp , [23] T. Flash, The control of hand equilibrium trajectories in multijoint arm movements, Biol. Cybern., vol. 57, pp , [24] N. Hogan, The mechanics of multijoint posture and movement control, Biol. Cybern., vol. 52, pp , [25] Y. Uno, M. Kawato, and R. Suzuki, Formation and control of optimal trajectory in human multijoint arm movement, Biol. Cybern., vol. 61, pp , [26] A. T. McMahon, Muscles, Reflexes, and Locomotion. Princeton, NJ: Princeton Univ. Press, REFERENCES [1] C. H. Wu, Compliance control of robot manipulators based on joint torque servo, Int. J. Robot. Res., vol. 4, pp , [2] C. H. Wu, Compliance, in International Encyclopedia of Robotics: Application and Automation, vol. 1. New York: Wiley, 1988, pp [3] P. R. Paul and B. Simano, Compliance and control, in Proc Joint Automat. Contr. 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Physiological Soc., 1981, pp Chi-haur Wu (S 79 M 80 SM 91) received the B.S. degree in electrical engineering from National Taiwan University, Taiwan, in 1973, the M.S. degree in electrical engineering from Virginia Polytechnic Institute and State University, Blacksburg, in 1977, and the Ph.D. degree in electrical engineering from Purdue University, West Lafayette, IN, in He joined Unimation Inc., Danbury, CT, as a Senior Engineer. His job involved in designing robot motion control algorithms and digital servo systems for PUMA robots and hydraulic-servo Unimate robots. Since September 1983, he has been an Associate Professor of Electrical and Computer Engineering at Northwestern University, Evanston, IL. His areas of interest are robotics, limb control and compliance control, rehabilitation robot, part assembly strategy, computer graphics and CAD/CAM industrial automation, computer-assisted surgical robot system, medical instrumentation and automation, layered manufacturing, control of smart structures, vibration and noise control, and active suspension control. During 1985, Dr. Wu was honored with the Outstanding Young Manufacturing Engineer Award from the Society of Manufacturing Engineers. He was a member of the Organized Committee of the 1992 IEEE International Conference on Systems, Man, and Cybernetics and the 1993 IEEE International Symposium on Intelligent Control. He was also a member of the Program Committee of the 1993 IEEE International Conference on Robotics and Automation, the 1995 IEEE International Conference on Decision and Control and the 1996 IEEE International Conference on Robotics and Automation.

12 WU et al.: NEUROMUSCULAR-LIKE CONTROL FOR ROBOTIC COMPLIANCE 597 Kao-Shing Hwang (S 92 M 92) received the B.S. Degree in Industrial Design from National Cheng Kung University, Taiwan, in 1981, and the M.M.E. and Ph.D. degrees in electrical engineering and computer science from Northwestern University, Evanston, I.L., in 1989 and 1993, respectively. He was a Design Engineer at the SANYO Electric Co., Taipei, Taiwan during Between 1987 and 1988, he joined the C & D Microsystem Co., Plastow, NH, as a System Programmer. His job involved designing PC drivers, and graphic animation. Since August 1993, he has been with National Chung Cheng University, Taiwan, where he is an Associate Professor. He is also the Director of the Information Management Division at the university computer center. His interests include neural networks and learning control, robotic compliance, and collision avoidance. Shih-Lang Chang received the B.S. degree in mechanical engineering from National Chiao Tung University, Hsinchu, Taiwan, in 1989, and the M.S. degree from Northwestern University, Evanston, IL, in He is currently a Ph.D. candidate of mechanical engineering in Northwestern University. During , he was an Ordinance Lieutenant in the Taiwan military while performing his obligatory service. Since 1995, he has been a Research Assistant in the Rehabilitation Institute of Chicago, where he is engaged in research of human limb dynamics. His research interests include learning control, flexible manufacturing systems, and compliance control. Mr. Chang is a member of ASME and SAE.