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Recent experiments suggest a simple relationship between posture and movement. Posture appears to result from the CNS setting the activity levels of agonist and antagonist muscles around the joint, resulting in an equilibrium force, the ratios of which are different for different positions. Control of movement is accomplished by changing the set of opposing length/tension curves. However, the experimental evidence also indicates that during movement there is active control of the trajectory, in addition to control of final position. A simple strategy of choosing a new posture via the length/tension curves and letting a limb move until equilibrium is established is not the control algorithm used by the vertebrate motor system.

Manipulation fundamentally requires the manipulator to be mechanically coupled to the object being manipulated; the manipulator may not be treated as an isolated system. This three-part paper presents an approach to the control of dynamic interaction between a manipulator and its environment. In Part I this approach is developed by considering the mechanics of interaction between physical systems. Control of position or force alone is inadequate; control of dynamic behavior is also required. It is shown that as manipulation is a fundamentally nonlinear problem, the distinction between impedance and admittance is essential, and given the environment contains inertial objects, the manipulator must be an impedance. A generalization of a Norton equivalent network is defined for a broad class of nonlinear manipulators which separates the control of motion from the control of impedance while preserving the superposition properties of the Norton network. It is shown that components of the manipulator impedance may be combined by superposition even when they are nonlinear.

The dependence of muscle force on muscle length gives rise to a "spring-like" behavior which has been shown to play a role in the execution of single-joint posture and movement. This paper extends this concept and considers the influence of the apparent mechanical behavior of the neural, muscular and skeletal system on the control and coordination of multiple degree of freedom posture and movement. A rigorous definition of "spring-like" behavior is presented. From it a numerically quantifiable, experimental test of spring-like behavior is formulated. It is shown that if the steady-state force-displacement behavior of a limb is not spring-like, this can only be due to the action of inter-muscular feedback, and can not be due to intrinsic muscle properties. The directional character of the spring-like behavior of a multiple degree of freedom system is described. The unique way in which synergistic coactivation of polyarticular muscles may modulate the directional properties of the spring-like behavior of a multiple degree of freedom system is explained. Dynamic aspects of postural behavior are also considered. The concept of mechanical impedance is presented as a rigorous dynamic generalisation of the postural stiffness of the limb. The inertial behavior of the system is characterised by its mobility. As with the stiffness or impedance, in the multiple degree of freedom case it has a directional property. The way in which the apparent kinematic redundancy of the musculo-skeletal system may be used to modify its dynamic behavior is explained. Whereas the inertial behavior of a single limb segment is not modifiable, it is shown that the apparent inertial behavior of a multiple degree of freedom system may be modulated by repositioning the joints. A unified description of the posture and movement of a multi-joint system is presented by defining a "virtual trajectory" of equilibrium positions for the limb which may be specified by the neuro-muscular system. The way in which this approach may lead to a simplification of some the apparent computational difficulties associated with the control of multi-joint motion is discussed.

Dynamic interaction with the environment is fundamental to the process of manipulation. This paper describes an approach to the design of ‘interaction controllers’ and contrasts this with an approa...

This paper (Part II of two) presents an experimental demonstration of the performance achieved by implementing the mathematically derived optimal myoprocessor described in Part I. Almost an order-of-magnitude improvement over the common myoprocessor is obtained. Excellent agreement of the experimental results with the analytical predictions verifies the mathematical analysis. The relative contributions of each stage of the optimal myoprocessor are examined. A discussion and comparison of several existing and proposed techniques for myoprocessor improvement are presented.

Cybernetic aspects of assistive devices are discussed. Some of the neuro-physiological basis of natural motion control is outlined. Analytical and experimental results are presented which highlight the role of the inherent mechanical and kinematic properties of the musculo-skelete1 system in the parameter-adaptive control of motion. An explanation of antagonist co-activation and the importance of polyarticular muscles is presented.

One hypothesis for the generation of spatially oriented arm movements by the central nervous system is that a desired joint position is determined by the ratio of the tensions of agonist and antagonist muscles. According to this hypothesis, the transition between equilibrium states should be solely a function of the contraction time of the motor units and the mechanical properties of the arm. We tested this hypothesis in intact and deafferented rhesus monkeys by holding the forearm and measuring the accelerative transient after release of the forearm and by directly measuring the time course of the increase in torque during the movement. Both methods indicated an average time of 400 msec for attaining peak torque in a movement with a duration of 700 msec. In addition, by displacing the arm from its normal trajectory during the movement, we observed that the arm returned neither to the initial nor to the final equilibrium positions, but to points intermediate between them. We conclude that the processes underlying trajectory formation must be more complex than a simple switch between one equilibrium position and another.

Even simple movements require the coordination of a bewildering number of muscles. How does the brain cope with this task? How can we begin to understand this extraordinarily complex behavior? One effective way is to formulate a quantitative, mathematical theory of movement control. A theory simplifies matters because complex, detailed and experimentally testable predictions can be derived from basic concepts. This article will briefly review some attempts to develop a quantitative theory of motor coordination.

An efficient algorithm is presented for solving time-optimal control for a restricted class of manipulators: balanced, decoupled manipulators. It is shown how the dynamics of such manipulators are sufficiently simple that optimal control solutions for point-to-point moves can be found analytically. A change of coordinates is proposed in which the more difficult problem of time-optimal interception of moving targets can be solved efficiently. A fast algorithm is described for computing and updating optimal interception solutions on line.

This three-part paper presents an approach to the control of dynamic interaction between a manipulator and its environment. Part I presented the theoretical reasoning behind impedance control. In Part II the implementation of impedance control is considered. A feedback control algorithm for imposing a desired cartesian impedance on the end-point of a nonlinear manipulator is presented. This algorithm completely eliminates the need to solve the “inverse kinematics problem” in robot motion control. The modulation of end-point impedance without using feedback control is also considered, and it is shown that apparently “redundant” actuators and degrees of freedom such as exist in the primate musculoskeletal system may be used to modulate end-point impedance and may play an essential functional role in the control of dynamic interaction.

A myoelectric signal processing technique has been digitally implemented to provide realtime proportional control of a prosthetic elbow. This technique, previously implemented in analog circuitry, produced a five-fold improvement in the signal-to-noise ratio over the usual process of rectifying the signal from a single electrode pair and then smoothing it. This technique, which processes signals from four electrode pairs, applies a prewhitening transformation to the input signals in order to take advantage of the different information content of each signal. The prewhitening transformation matrix, which weights the signals with respect to each other, is calculated from the covariance matrix which characterizes the “cross talk” between signals and is different for each electrode set up. A major advantage of digital implementation is that this calibration is performed automatically. This adaptive, self-calibrating myoprocessor is an unique experimental facility. Its capabilities include the ability to maintain calibration under conditions of fatigue.

Interaction with the environment is an essential feature of manipulation. Interaction imposes constraints upon the behavior of a manipulator (e.g. robotic, prosthetic, or human arm) which are not imposed by the stability and performance of the isolated manipulator alone. These constraints must be understood and treated as part of the hardware and controller design process if suitable interactive behavior is to be achieved.

When the hand is displaced from an equilibrium posture by an external disturbance, a force is generated to restore the original position. We developed a new experimental method to measure and represent the field of elastic forces associated with posture of the hand in the horizontal plane. While subjects maintained a given posture, small displacements of the hand along different directions were delivered by torque motors. The hand was held in the displaced positions and, at that time, we measured the corresponding restoring forces before the onset of any voluntary reaction. The stiffness in the vicinity of the hand equilibrium position was estimated by analyzing the force and displacement vectors. We chose to represent the stiffness both numerically, as a matrix, and graphically, as an ellipse characterized by three parameters: magnitude (the area), shape (the ratio of axis) and orientation (direction of the major axis). The latter representation captures the main geometrical features of the elastic force field associated with posture. We also evaluated the conservative and nonconservative components of this elastic force field. We found that the former were much larger than the latter and concluded that the behavior of the neuromuscular system of the multiarticular arm is predominantly spring-like. Our data indicated that the shape and orientation of the stiffness were invariant over subjects and over time. We also investigated the ability of our subjects to produce voluntary and adaptive changes in the stiffness. Our findings indicated that, when a disturbance acting along a fixed and predictable direction was imposed, the magnitude of the stiffness was increased but only minor changes in shape and orientation occurred. Taken together, all of these experiments represent a step toward the understanding of the interactions between geometrical and neural factors involved in maintaining hand posture and its interactions with the environment.

The formation of forearm trajectories of moderate velocities (0.3–1.3 rad/s) was studied in monkeys performing a simple visuomotor task. The experiments were designed to test the hypothesis that the transition from one position to another is subserved by a rapid shift to a final equilibrium of forces in agonist and antagonist muscles. This idea is attractive because it suggests the possibility that in simple movements the trajectory is determined by the inherent inertial and viscoelastic properties of the limb and muscles around a joint. The results indicate that these moderate speed movements are controlled by a gradual, and not a step-like, shift to the final equilibrium position.

A practical technique for the design and evaluation of elbow prostheses has been developed for use in a laboratory environment where resources and manpower are limited. Prospective designs are emulated with a combination of hardware and software as opposed to constructing actual prototypes. The emulator system consists of a high-performance, electrically powered elbow prosthesis worn by an amputee and interfaced to a digital computer. Design changes may be examined simply by reprogramming the dynamic behavior of the emulator rather than by reconstructing hardware. Changing the inherent emulator dynamics to desired dynamics is achieved with a digitally supervised, analog control circuit that is more robust than a purely digital controller. The system can emulate existing powered elbow prostheses and some important characteristics of the intact elbow.

Recent neurophysiological research has demonstrated that an important aspect of movement control is the variability of mechanical parameters of the musculo-skeletal system. By co-activation of antagonist muscles such as the biceps and triceps, the individual can adjust the damping and the stiffness about the joint. The design of a myoelectrically controlled upper arm prosthesis with a high fidelity feedforward control path is presented. As with the natural arm, this device gives the user capability of tuning the mechanical impedance about the elbow joint to the task at hand. Variation of the stiffness and damping is accomplished through the variation of the gains in feedback loops within the arm itself. Parasitic impedances in the drive train (i.e. energy storages and non-linearities) are minimized so as to enhance the controllability of the prosthesis.

This paper reviews some recent studies related to the generation of simple multijoint arm movements. Two principal issues are considered. The first concern is how movements are represented internally by the central nervous system. There are many possible sets of coordinates that could be used to represent arm movements. Two of the possibilities are reviewed: representation in terms of joint angular motions versus representation in terms of motions of the hand in external space coordinates. A second concern is the transformation from intention to action: how is an internal representation of motion expressed by the neuromuscular system? The computational complexity of this problem is reviewed. A way in which the mechanics of the neuromuscular system could be exploited to simplify this problem is discussed.

A simple model representing the quasistatic behavior of skeletal muscle is presented in which the force produced by the muscle is a bilinear function of the muscle length and the neural activation of the muscle. Using two such muscles to represent the biceps and triceps, a biomechanical model of the elbow and forearm is developed. For maintenance of static posture of the elbow and forearm, this model predicts paradoxical patterns of muscular activation. An explanation of these counterintuitive patterns of muscular activation is presented and the competence of this model is assessed on the basis of preliminary experiments. >

Studies of the mechanical properties of the musculoskeletal apparatus have been found to be useful in gaining insights into the “rules” of the neural controller. This approach is based on the assumption that the neural control system must not only control but also take advantage of the musculoskeletal apparatus.

Cybernetic aspects of assistive devices are discussed. Some of the neuro-physiological basis of natural motion control is outlined. Analytical and experimental results are presented which highlight the role of the inherent mechanical and kinematic properties of the musculo-skeletel system in the parameter-adaptive control of motion. An explanation of antagonist co-activation and the importance of polyarticular muscles is presented.

Recent findings related to the control strategies underlying voluntary arm trajectory formation in monkeys will be presented. The respective roles of central preprogramming of movements and feedback modulation from peripheral sensory organs will be discussed. A computer simulation based on mathematical modelling and dynamic optimization of the motion will be presented which predicts observed behaviour within experimental error. The same analysis also predicts observed behaviour of monkeys and humans under widely varying task conditions. Applications to the control of prostheses and manipulators will be discussed.

Manipulation fundamentally requires a manipulator to be mechanically coupled to the object being manipulated. A consideration of the physical constraints imposed by dynamic interaction shows that control of a vector quantity such as position or force is inadequate and that control of the manipulator impedance is also necessary. Techniques for control of manipulator behaviour are presented which result in a unified approach to kinematically constrained motion, dynamic interaction, target acquisition and obstacle avoidance.

This paper presents a mathematical model which predicts both the major qualitative features and, within experimental error, the quantitative details of a class of perturbed and unperturbed large-amplitude, voluntary movements performed at intermediate speed by primates. A feature of the mathematical model is that a concise description of the behavioral organization of the movement has been formulated which is separate and distinct from the description of the dynamics of movement execution. Based on observations of voluntary movements in primates, the organization has been described as though the goal were to make the smoothest movement possible under the circumstances, i.e., to minimize the accelerative transients. This has been formalized by using dynamic optimization theory to determine the movement which minimizes the rate of change of acceleration (jerk) of the limb. Based on observations of muscle mechanics, the concept of a “virtual position” determined by the active states of the muscles is rigorously defined as one of the mechanical consequences of the neural commands to the muscles. This provides insight into the mechanics of perturbed and unperturbed movements and is a useful aid in the separation of the descriptions of movement organization and movement execution.

This paper considers some aspects of automatic deburring by robot. The strategy proposed is based on impedance control. Impedance control is a parameter-adaptive approach to manipulation aimed at modulating the effective dynamic behavior of a robot, rather than just its end-effector force or motion. To apply impedance control to robotic deburring, a simple model of the deburring process is developed. A target impedance for the robot is proposed which facilitates the identification of the parameters of the model of the deburring environment and leads to a straightforward parameter-adaptive control strategy for the robot. A method for selecting values for the parameters of an impedance appropriate for deburring is developed by describing the robot’s task as an optimization problem. This method yields simple expressions relating the target impedance parameters to tolerances on the interface forces between the tool and the workpiece and tolerances on the desired motion of the tool.

This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled mathematically by defining an objective function, a measure of performance for any possible movement. The unique trajectory which yields the best performance is determined using dynamic optimization theory. In the work presented here, the objective function is the square of the magnitude of jerk (rate of change of acceleration) of the hand integrated over the entire movement. This is equivalent to assuming that a major goal of motor coordination is the production of the smoothest possible movement of the hand. Experimental observations of human subjects performing voluntary unconstrained movements in a horizontal plane are presented. They confirm the following predictions of the mathematical model: unconstrained point-to-point motions are approximately straight with bell-shaped tangential velocity profiles; curved motions (through an intermediate point or around an obstacle) have portions of low curvature joined by portions of high curvature; at points of high curvature, the tangential velocity is reduced; the durations of the low-curvature portions are approximately equal. The theoretical analysis is based solely on the kinematics of movement independent of the dynamics of the musculoskeletal system and is successful only when formulated in terms of the motion of the hand in extracorporal space. The implications with respect to movement organization are discussed.

Time-optimal control of robot motion for dynamically decoupled manipulators is described in terms of potential functions. Avoidance of moving obstacles is incorporated via protective potential functions. An energy interpretation of the potential functions leads to rules for construction of avoidance functions and logical operations among them. Simple expressions for combining obstacle fields with an obstacle-free time-optimal solution result in the minimum safe influence of obstacles. Simulation results are given demonstrating high-speed target interception in the presence of obstacles.

Much can be learned about the central nervous system from a study of motor coordination, but its true richness and complexity become evident only in a multiarticular system. Despite the intrinsic complexity of multiarticular actions, they offer an unparalleled opportunity to learn about the central nervous system in a quantitative and experimentally testable way. For example, the observation that unconstrained, unperturbed arm movements are coordinated in terms of hand motion shows that motor control is organized in a hierarchy of increasing levels of abstraction. These arm motions are organized as though a disembodied hand could be moved in space; the details of how this is to be achieved must then be supplied by a different level in the hierarchy. The essence of human behavior is its adaptability. Just as the true complexity of coordination is evident only in multiarticular actions, the sophistication and subtlety of adaptive behavior are evident only in dynamic, interactive tasks. A study of movement alone is not sufficient to understand this behavior. The dynamic response of the limbs becomes the overriding concern and must be controlled by the central nervous system. The dynamic response of a limb is usually associated with its posture, rather than its movement, but in a functional task such as the use of a tool, the postural dynamics are an integral part of the action. This perspective on motor behavior leads to some useful insights. Coordination is not a problem for movement alone; in a multiarticular system, even posture requires coordination and control. Muscles do not merely act reciprocally to generate forces about the joints; the net mechanical impedance of the limb may be controlled by synergistic activation of all muscles, including antagonists. Controlling dynamic behavior is a far more demanding task than controlling motion. Consequently, features of the neuromusculoskeletal system that appear to be redundant or unnecessary for movement control can play a functional role in controlling dynamic behavior. Polyarticular muscles contribute to the mechanical impedance in a unique way. Skeletal redundancies have a profound influence on all aspects of dynamic behavior, including the apparent inertia of the limbs. Redundancies are commonly perceived as a complicating factor in the control of motion, a problem that must be solved by the central nervous system. Rather than presenting a problem requiring solution, they may present a solution to a problem. Posture is not merely the outcome of a motor act; it is one of the important preparatory stages in the production of motor behavior.