Control of Three- and Four-Joint Arm Movement: Strategies for a Manipulator With Redundant Degrees of Freedom

Behavioral Motor Performance

The human sensorimotor control system has exceptional abilities to perform skillful actions. We easily switch between strenuous tasks that involve brute force, such as lifting a heavy sewing machine, and delicate movements such as threading a needle in the same machine. Using a structure with different control architectures, the motor system is capable of updating its ability to perform through our daily interaction with the fluctuating environment. However, there are issues that make this a difficult computational problem for the brain to solve. The brain needs to control a nonlinear, nonstationary neuromuscular system, with redundant and occasionally undesired degrees of freedom, in an uncertain environment using a body in which information transmission is subject to delays and noise. To gain insight into the mechanisms of motor control, here we survey movement laws and invariances that shape our everyday motion. We then examine the major solutions to each of these problems in the three parts of the sensorimotor control system, sensing, planning, and acting. We focus on how the sensory system, the control architectures, and the structure and operation of the muscles serve as complementary mechanisms to overcome deviations and disturbances to motor behavior and give rise to skillful motor performance. We conclude with possible future research directions based on suggested links between the operation of the sensorimotor system across the movement stages. © 2024 American Physiological Society. Compr Physiol 14:5179-5224, 2024.

Bodily Communication of Emotion: Evidence for Extrafacial Behavioral Expressions and Available Coding Systems

Although scientists dating back to Darwin have noted the importance of the body in communicating emotion, current research on emotion communication tends to emphasize the face. In this article we review the evidence for bodily expressions of emotions—that is, the handful of emotions that are displayed and recognized from certain bodily behaviors (i.e., pride, joy, sadness, shame, embarrassment, anger, fear, and disgust). We also review the previously developed coding systems available for identifying emotions from bodily behaviors. Although no extant coding system provides an exhaustive list of bodily behaviors known to communicate a panoply of emotions, our review provides the foundation for developing such a system.

Anticipatory coarticulation in non-speeded arm movements can be motor-equivalent, carry-over coarticulation always is

In a sequence of arm movements, any given segment could be influenced by its predecessors (carry-over coarticulation) and by its successor (anticipatory coarticulation). To study the interdependence of movement segments, we asked participants to move an object from an initial position to a first and then on to a second target location. The task involved ten joint angles controlling the three-dimensional spatial path of the object and hand. We applied the principle of the uncontrolled manifold (UCM) to analyze the difference between joint trajectories that either affect (non-motor equivalent) or do not affect (motor equivalent) the hand's trajectory in space. We found evidence for anticipatory coarticulation that was distributed equally in the two directions in joint space. We also found strong carry-over coarticulation, which showed clear structure in joint space: More of the difference between joint configurations observed for different preceding movements lies in directions in joint space that leaves the hand's path in space invariant than in orthogonal directions in joint space that varies the hand's path in space. We argue that the findings are consistent with anticipatory coarticulation reflecting processes of movement planning that lie at the level of the hand's trajectory in space. Carry-over coarticulation may reflect primarily processes of motor control that are governed by the principle of the UCM, according to which changes that do not affect the hand's trajectory in space are not actively delimited. Two follow-up experiments zoomed in on anticipatory coarticulation. These experiments strengthened evidence for anticipatory coarticulation. Anticipatory coarticulation was motor-equivalent when visual information supported the steering of the object to its first target, but was not motor equivalent when that information was removed. The experiments showed that visual updating of the hand's path in space when the object approaches the first target only affected the component of the joint difference vector orthogonal to the UCM, consistent with the UCM principle.

Task Complexity Modulates Sleep-Related Offline Learning in Sequential Motor Skills

Recently, a number of authors have advocated the introduction of gross motor tasks into research on sleep-related motor offline learning. Such tasks are often designed to be more complex than traditional key-pressing tasks. However, until now, little effort has been undertaken to scrutinize the role of task complexity in any systematic way. Therefore, the effect of task complexity on the consolidation of gross motor sequence memory was examined by our group in a series of three experiments. Criterion tasks always required participants to produce unrestrained arm movement sequences by successively fitting a small peg into target holes on a pegboard. The sequences always followed a certain spatial pattern in the horizontal plane. The targets were visualized prior to each transport movement on a computer screen. The tasks differed with respect to sequence length and structural complexity. In each experiment, half of the participants initially learned the task in the morning and were retested 12 h later following a wake retention interval. The other half of the subjects underwent practice in the evening and was retested 12 h later following a night of sleep. The dependent variables were the error rate and total sequence execution time (inverse to the sequence execution speed). Performance generally improved during acquisition. The error rate was always low and remained stable during retention. The sequence execution time significantly decreased again following sleep but not after waking when the sequence length was long and structural complexity was high. However, sleep-related offline improvements were absent when the sequence length was short or when subjects performed a highly regular movement pattern. It is assumed that the occurrence of sleep-related offline performance improvements in sequential motor tasks is associated with a sufficient amount of motor task complexity.

Carry-over coarticulation in joint angles

Coarticulation indicates a dependence of a movement segment on a preceding segment (carry-over coarticulation) or on the segment that follows (anticipatory coarticulation). Here we study coarticulation in multidegrees of freedom human arm movements. We asked participants to transport a cylinder from a starting position to a center target and on to a final target. In this naturalistic setting, the human arm has ten degrees of freedom and is thus comfortably redundant for the task. We studied coarticulation by comparing movements between the same spatial locations that were either preceded by different end-effector paths (carry-over coarticulation) or followed by different end-effector paths (anticipatory coarticulation). We found no evidence for coarticulation at the level of the end-effector. We found very clear evidence, however, for carry-over, not for anticipatory coarticulation at the joint level. We used the concept of the uncontrolled manifold to systematically establish coarticulation as a form of motor equivalence, in which most of the difference between different movement contexts lies within the uncontrolled manifold that leaves the end-effector invariant. The findings are consistent with movement planning occurring at the level of the end-effector, and those movement plans being transformed to the joint level by a form of inverse kinematics. The observation of massive self-motion excludes an account that is solely based on a kinematic pseudo-inverse.

Reorganization of multi-muscle and joint withdrawal reflex during arm movements in post-stroke hemiparetic patients

OBJECTIVES

To investigate the behavior of the nociceptive withdrawal reflex (NWR) in the upper limb during reaching and grasping movements in post-stroke hemiparetic patients.

METHODS

Eight patients with chronic stroke and moderate motor deficits were included. An optoelectronic motion analysis system integrated with a surface EMG machine was used to record the kinematic and EMG data. The NWR was evoked through a painful electrical stimulation of the index finger during a movement which consisted of reaching out, picking up a cylinder, and returning it to the starting position.

RESULTS

We found that: (i) the NWR is extensively rearranged in hemiparetic patients, who were found to present different kinematic and EMG reflex patterns with respect to controls; (ii) patients partially lose the ability to modulate the reflex in the different movement phases; (iii) the impairment of the reflex modulation occurs at single-muscle, single-joint and multi-joint level.

CONCLUSIONS

Patients with chronic and mild-moderate post-stroke motor deficits lose the ability to modulate the NWR dynamically according to the movement variables at individual as well as at multi-muscle and joint levels.

SIGNIFICANCE

The central nervous system is unable to use the NWR substrate dynamically and flexibly in order to select the muscle synergies needed to govern the spatio-temporal interaction among joints.

Unpredictable elbow joint perturbation during reaching results in multijoint motor equivalence

Motor equivalence expresses the idea that movement components reorganize in the face of perturbations to preserve the value of important performance variables, such as the hand's position in reaching. A formal method is introduced to evaluate this concept quantitatively: changes in joint configuration due to unpredictable elbow perturbation lead to a smaller change in performance variables than expected given the magnitude of joint configuration change. This study investigated whether motor equivalence was present during the entire movement trajectory and how magnitude of motor equivalence was affected by constraints imposed by two different target types. Subjects pointed to spherical and cylindrical targets both with and without an elbow joint perturbation produced by a low- or high-stiffness elastic band. Subjects' view of their arm was blocked in the initial position, and the perturbation condition was randomized to avoid prediction of the perturbation or its magnitude. A modification of the uncontrolled manifold method variance analysis was used to investigate how changes in joint configuration on perturbed vs. nonperturbed trials (joint deviation vector) affected the hand's position or orientation. Evidence for motor equivalence induced by the perturbation was present from the reach onset and increased with the strength of the perturbation after 40% of the reach, becoming more prominent as the reach progressed. Hand orientation was stabilized more strongly by motor equivalent changes in joint configuration than was three-dimensional position regardless of the target condition. Results are consistent with a recent model of neural control that allows for flexible patterns of joint coordination while resisting joint configuration deviations in directions that affect salient performance variables. The observations also fit a general scheme of synergic control with referent configurations defined across different levels of the motor hierarchy.

Motor equivalence and self-motion induced by different movement speeds

This study investigated pointing movements in 3D asking two questions: (1) Is goal-directed reaching accompanied by self-motion, a component of the joint velocity vector that leaves the hand's movement unaffected? (2) Are differences in the terminal joint configurations among different speeds of reaching motor equivalent (i.e., terminal joint configurations differ more in directions of joint space that do not produce different pointer-tip positions than in directions that do) or non-motor equivalent (i.e., terminal joint configurations differ equally or more in directions of joint space that lead to different pointer-tip positions than in directions that do not affect the pointer-tip position). Subjects reached from an identical starting joint configuration and pointer-tip location to targets at slow, moderate, and fast speeds. Ten degrees of freedom of joint motion of the arm were recorded. The relationship between changes in the joint configuration and the three-dimensional pointer-tip position was expressed by a standard kinematic model, and the range- and null subspaces were computed from the associated Jacobian matrix. (1) The joint velocity vector and (2) the difference vector between terminal joint configurations from pairs of speed conditions were projected into the two subspaces. The relative length of the two components was used to quantify the amount of self-motion and the presence of motor equivalence, respectively. Results revealed that reaches were accompanied by a significant amount of self-motion at all reaching speeds. Self-motion scaled with movement speed. In addition, the difference in the terminal joint configuration between pairs of different reaching speeds revealed motor equivalence. The results are consistent with a control system that takes advantage of motor redundancy, allowing for flexibility in the face of perturbations, here induced by different movement speeds.

The role of intrinsic factors in control of arm movement direction: implications from directional preferences

The role of extrinsic and intrinsic factors in control of arm movement direction remains under debate. We addressed this question by investigating preferences in selection of movement direction and whether factors causing these preferences have extrinsic or intrinsic nature. An unconstrained free-stroke drawing task was used during which participants produced straight strokes on a horizontal table, choosing the direction and the beginning and end of each stroke arbitrarily. The variation of the initial arm postures across strokes provided a possibility to distinguish between the extrinsic and intrinsic origins of directional biases. Although participants were encouraged to produce strokes equally in all directions, each participant demonstrated preferences for some directions over the others. However, the preferred directions were not consistent across participants, suggesting no directional preferences in extrinsic space. Consistent biases toward certain directions were revealed in intrinsic space representing initial arm postures. Factors contributing to the revealed preferences were analyzed within the optimal control framework. The major bias was explained by a tendency predicted by the leading joint hypothesis (LJH) to minimize active interference with interaction torque generated by shoulder motion at the elbow. Some minor biases may represent movements of minimal inertial resistance or maximal kinematic manipulability. These results support a crucial role of intrinsic factors in control of the movement direction of the arm. Based on the LJH interpretation of the major bias, we hypothesize that the dominant tendency was to minimize neural effort for control of arm intersegmental dynamics. Possible organization of neural processes underlying optimal selection of movement direction is discussed.

Stabilizing unstable object by means of kinematic redundancy

The paper aims to investigate how humans deal with unstable objects under the possibility of choosing different strategy of interaction. The presented task consisted in balancing a 1 degree of freedom (DoF) elastic inverted pendulum by means of 2 DoF of the wrist (fexion/extension and pronation/supination). The pendulum was simulated using a virtual environment and the haptic feedback was generated by a robotic wrist device. The task is a redundant because the subject can choose how to use the 2 DoF in order to move and stabilize a 1 DoF simulated mechanical system: the inverted pendulum. Six subjects volunteered to participate and were tested in four different days performing the same task but experiencing different mechanical systems (pendulum) characterized by lower or higher dynamics due to the possibility to tune the stiffness of the pendulum. Subjects were asked to balance the inverted pendulum maintaining it in a vertical position for a required amount of time. It was found the adopted stabilization strategy was mainly characterized by using only one of the 2 available DoFs of their wrist when the pendulum was stiffer, while in case of lower stiffness of the pendulum (slower dynamic) wrist input redundancy was a more suitable strategy to perform the balancing task.

What does body configuration in microgravity tell us about the contribution of intra- and extrapersonal frames of reference for motor control?

The authors report that the reorganization of body configuration during weightlessness is based on an intrapersonal frame of reference such as the configuration of the support surface and the position of the body's center of gravity. These results stress the importance of “knowledge” of the state of internal geometric structures, which cannot be directly signalled by specific receptors responsible for direct dialogue with the physical external world.

Reciprocal and coactivation commands are not sufficient to describe muscle activation patterns

Recent results have shown that the relative activation of muscles is different for isometric contractions and for movements. These results exclude an explanation of muscle activation patterns by a combination ofreciprocal and coactivation commands. These results also indicate that joint stiffness is not uniquely determined and that it may be different for isometric contractions and movements.

Frames of reference interact and are task-dependent

The problem for the CNS in any particular movement task is to coordinate the various frames of reference appropriate to the task. Control variables are determined by this coordination. The coordination problem varies greatly from task to task, and so no single set of control variables is likely to account for a broad range of movement tasks.

Temporal representation in the control of movement

Theories of the representation of specific kinetic and spatiotem-poral features of movement range from the explicit assertion that temporal aspects of movement are not represented (Kugler et al. 1980) to the idea that they are represented and that they have neurophysiological correlates (Ivry & Corcos 1993; Ivry & Keele 1989). Jeannerod's thesis is that mental and visual images have common mechanisms and that there is a link between the image to move and the mechanisms involved with movement. The target article takes the position that certain parameters are coded in motor representations (sect. 4) but that the duration of an action is not one of them. This position is based on the work of Gottlieb et al. (1989b) and of Decety et al. (1989). Both these studies are worth considering in detail. In Note 1, Jeannerod suggests that: “in time-constrained tasks subjects control the amplitude parameter of force impulses, whereas in spatially constrained tasks the duration of the force impulse is affected by accuracy demands.” This is not exactly correct. Excitation pulse intensity (amplitude) is modulated both in tasks that require spatial and those that require temporal accuracy. Excitation pulse duration is modulated for changes in movement distance and inertial load. If subjects are required to be very accurate spatially, they will move at less than maximum speed for a given distance and this is achieved by lower levels of excitation intensity (Gottlieb et al. 1990).

The λ model for motor control: More than meets the eye

Understanding of the λ model has greatly increased in recent years as evidenced by most of the commentaries. Some commentators underscored the potential of the model to integrate aspects of different sensorimotor systems in the production of movement. Other commentators focused on not-yet-fully-developed parts of the model. A few persisted in misunderstanding some of its basic concepts, and on these grounds they reject it. In responding to commentaries we continue to elaborate on some fundamental points of the model, especially control variables, the idea of movement production by shifting the positional frame of reference and the hypothesis of biomechanical correspondence in motor control. We also continue to develop our ideas on the intrinsic generation of the frame of reference associated with external space and utilized for the control of arm movement and locomotion. The dynamic principles underlying the model are discussed in light of the dynamical systems approach.

Grip force adjustments during rapid hand movements suggest that detailed movement kinematics are predicted

The λ model suggests that detailed kinematics arise from changes in control variables and need not be explicitly planned. However, we have shown that when moving a grasped object, grip force is precisely modulated in phase with acceleration-dependent inertial load. This suggests that the motor system can predict detailed kinematics. This prediction may be based on a forward model of the dynamics of the loaded limb.

Let us accept a “controlled trade-off” model of motor control

The trade-off between force and length of muscle as adjusted by neural signals is a critical fact in the dynamics of motor control. Whether we call it “length-tension effect,” “feedback-like,” “invariant condition,” or “spring-like” is unimportant. We must not let semantics or details of representation obscure the basic physics of effects introduced by this trade-off in muscle.

Equilibrium-point control? Yes! Deterministic mechanisms of control? No!

The equilibrium-point hypothesis (the λ-model) is superior to all other models of single-joint control and provides deep insights into the mechanisms of control of multi-joint movements. Attempts at associating control variables with neurophysiological variables look confusing rather than promising. Probabilistic mechanisms may play an important role in movement generation in redundant systems.

The unobservability of central commands: Why testing hypotheses is so difficult

The experiments Feldman and Levin suggest do not definitively test their proposed solution to the problem of selecting muscle activations. Their test of the movement directions that elicit EMG activity can be interpreted without regard to the form of the central commands, and their fast elbow flexion test is based on a forward computation that obscures the insensitivity of the predicted trajectory to the details of the putative commands.

Biological variability and control of movements via δλ

Three issues related to Feldman and Levin's treatment of biological variability are discussed. We question the usefulness of the indirect component of δλ. We suggest that trade-offs between speed and accuracy in aimed movements support identification of δλ, rather than λ, as a control variable. We take issue with the authors' proposal for resolving redundancy in multi-joint movements, given recent data.

A few reasons why psychologlsts can adhere to Feldman and Levin's model

We emphasize the relevance to cognitive psychology of Feldman and Levin's theoretical position. Traditional views of motor control have failed to clearly separate “production control” at the level of motor command, based on task-independent CV (control variables), from intentional “product control” based on task-dependent parameters. Because F&L's approach concentrates on the first process (trajectory formation), it can distinguish the product control stage.

Levers to generate movement

The following questions are discussed: (1) Who determines the nature of “control variables”? (2) Is the “positional monopoly” healthy? (3) Does a descending command alter reflex threshold alone without eoncomitantly altering stiffness? (4) How does the CNS deal with history-dependent effects? (5) Should we abandon the idea that the CNS controls classical Newtonian variables such as muscle length?

Kinematic invariances and body schema

Generalizing the notion that muscles are positional frames of reference, a high-dimensional muscle space is defined for multi-muscle systems with an embedded low-dimensional motor manifold of functional articulators. A central representation of such a manifold is proposed as computational body schema. The example of the jaw-tongue system is presented, discussing the relation of functional articulators with kinematic invariances and control problems.

On the relation between motor imagery and visual imagery

Jeannerod's target article describes support, through empirical and neurological findings, for the intriguing idea of motor imagery, a form of representation hypothesized to have levels of functional equivalence with motor preparation, while being consciously accessible. Jeannerod suggests that the subjectively accessible content of motor imagery allows it to be distinguished from motor preparation, which is unconscious. Motor imagery is distinguished from visual imagery in terms of content. Motor images are kinesthetic in nature; they are parametrized by variables such as force and time and they are potentially governed by kinematic rules. Jeannerod acknowledges, however, that motor and visual imagery may not easily be separated, because actions take place in a spatial environment. I agree; in fact, I suggest here that visualization may generally be concomitant with, and may even subjectively dominate, motor imagery.

Tendon elasticity and positional control

The spring-like behaviour of a joint following a sudden change of torque is partly a result of the elastic properties of tendons. A large fall in a muscle with a long tendon may be accompanied by tendon recoil causing joint movements as large as 20°.

The representing brain: Neural correlates of motor intention and imagery

This paper concerns how motor actions are neurally represented and coded. Action planning and motor preparation can be studied using a specific type of representational activity, motor imagery. A close functional equivalence between motor imagery and motor preparation is suggested by the positive effects of imagining movements on motor learning, the similarity between the neural structures involved, and the similar physiological correlates observed in both imaging and preparing. The content of motor representations can be inferred from motor images at a macroscopic level, based on global aspects of the action (the duration and amount of effort involved) and the motor rules and constraints which predict the spatial path and kinematics of movements. A more microscopic neural account calls for a representation of object-oriented action. Object attributes are processed in different neural pathways depending on the kind of task the subject is performing. During object-oriented action, a pragmatic representation is activated in which object affordances are transformed into specific motor schemas (independently of other tasks such as object recognition). Animal as well as human clinical data implicate the posterior parietal and premotor cortical areas in schema instantiation. A mechanism is proposed that is able to encode the desired goal of the action and is applicable to different levels of representational organization.

Command invariants and the frame of reference for human movement

We describe a solution to the redundancy problem related to that proposed in Feldman & Levin's target article. We suggest that the system may use a fixed mapping between commands organized at the level of degrees of freedom and commands to individual muscles. This proposal eliminates the need to maintain an explicit representation of musculoskeletalgeometry in planning movements.

Frameworks on shifting sands

Feldman and Levin present a model for movement control in which the system is said to seek equilibrium points, active movement being produced by shifting frames of reference in space. It is argued that whatever merit this model might have is limited to an understanding of “the how” and not “the why” we move. In this way the authors seem to be forced into a dualistic position leaving the upper level of the proposed control hierarchy “floating.”

Conservative or nonconservative control schemes

The conservative strategy proposed by the authors suggests a solution of the degrees-of-freedom problem of the controller. However, several simple motor control tasks cannot be explained by this strategy. A nonconservative strategy, in which more parameters of the control signal vary, can account for these simple motor tasks. However, the simplicity that distinguishes the proposed model from many others is lost.