Outside the laboratory, human movement typically involves redundant effector systems. How the nervous system selects among the task-equivalent solutions may provide insights into how movement is controlled. We propose a process model of movement generation that accounts for the kinematics of goal-directed pointing movements performed with a redundant arm. The key element is a neuronal dynamics that generates a virtual joint trajectory. This dynamics receives input from a neuronal timer that paces end-effector motion along its path. Within this dynamics, virtual joint velocity vectors that move the end effector are dynamically decoupled from velocity vectors that do not. Moreover, the sensed real joint configuration is coupled back into this neuronal dynamics, updating the virtual trajectory so that it yields to task-equivalent deviations from the dynamic movement plan. Experimental data from participants who perform in the same task setting as the model are compared in detail to the model predictions. We discover that joint velocities contain a substantial amount of self-motion that does not move the end effector. This is caused by the low impedance of muscle joint systems and by coupling among muscle joint systems due to multiarticulatory muscles. Back-coupling amplifies the induced control errors. We establish a link between the amount of self-motion and how curved the end-effector path is. We show that models in which an inverse dynamics cancels interaction torques predict too little self-motion and too straight end-effector paths.

To claim that the center of mass (CM) of the body is a controlled variable of the postural system is difficult to verify experimentally. In this report, a new variant of the method of the uncontrolled manifold (UCM) hypothesis was used to evaluate CM control in response to an abrupt surface perturbation during stance. Subjects stood upright on a support surface that was displaced in the posterior direction. Support surface translations between 0.03 and 0.12 m, each lasting for 275 ms, were presented randomly. The UCM corresponding to all possible combinations of joints that are equivalent with respect to producing the average pre-perturbation anterior-posterior position of the center of mass (CM(AP)) were linearly estimated for each trial. At each point in time thereafter, the difference between the current joint configuration and the average pre-perturbation joint configuration was computed. This joint difference vector was then projected onto the pre-perturbation UCM as a measure of motor equivalence, and onto its complementary subspace, which represents joint combinations that lead to a different CM(AP) position. A similar analysis was performed related to control of the trunk's spatial orientation. The extent to which the joint velocity vector acted to stabilize the CM(AP) position was also examined. Excursions of the hip and ankle joints both increased linearly with perturbation magnitude. The configuration of joints at each instance during the perturbation differed from the mean configuration prior to the perturbation, as evidenced by the joint difference vector. Most of this joint difference vector was consistent, however, with the average pre-perturbation CM(AP) position rather than leading to a different CM(AP )position. This was not the case, however, when performing this analysis with respect to the UCM corresponding to the control of the pre-perturbation trunk orientation. The projection of the instantaneous joint velocity vector also was found to lie primarily in the UCM corresponding to the pre-perturbation CM(AP) position, indicating that joint motion was damped in directions leading to a change away from the pre-perturbation CM(AP) position. These results provide quantitative support for the argument that the CM position is a planned variable of the postural system and that its control is achieved through selective, motor equivalent changes in the joint configuration in response to support surface perturbations. The results suggest that the nervous system accomplishes postural control by a control strategy that considers all DOFs. This strategy presumably resists combinations of DOFs that affect the stability of important task-relevant variables (CM(AP) position) while, to a large extent, freeing from control combinations of those DOFs that have no effect on the task-relevant variables (Schöner in Ecol Psychol 8:291-314, 1995).

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.

This paper analyzed the locomotion of a snake robot in narrow spaces such as a pipe or channel. We developed a unique experimental snake robot with one revolute and one linear joint on each module, with the ability to perform planar motion. The designed locomotion pattern was simulated in MATLAB R2015b and subsequently verified by the experimental snake robot. The locomotion of the developed snake robot was also experimentally analyzed on dry and viscous surfaces. The paper further describes the investigation of locomotion stability by three symmetrical curves used to anchor static modules between the walls of the pipe. The stability was experimentally analyzed by digital image correlation using a Q-450 Dantec Dynamics high-speed correlation system. The paper presents some input symmetrical elements of locomotion and describes their influence on the results of locomotion. The results of simulations and experiments show possibilities of snake robot locomotion in a pipe.

In many situations, the human movement system has more degrees of freedom than needed to achieve a given movement task. Martin et al. (Neural Comput 21(5):1371–1414, 2009 ) accounted for signatures of such redundancy like self-motion and motor equivalence in a process model in which a neural oscillator generated timed end-effector virtual trajectories that a neural dynamics transformed into joint virtual trajectories while decoupling task-relevant and task-irrelevant combinations of joint angles. Neural control of muscle activation and the biomechanical dynamics of the arm were taken into account. The model did not address the main signature of redundancy, however, the UCM structure of variance: Many experimental studies have shown that across repetitions, variance of joint configuration trajectories is structured. Combinations of joint angles that affect task variables (lying in the uncontrolled manifold, UCM) are much more variable than combinations of joint angles that do not. This finding has been robust across movement systems, age, and tasks and is often preserved in clinical populations as well. Here, we provide an account for the UCM structure of variance by adding four types of noise sources to the model of Martin et al. (Neural Comput 21(5):1371–1414, 2009 ). Comparing the model to human pointing movements and systematically examining the role of each noise source and mechanism, we identify three causes of the UCM effect, all of which, we argue, contribute: (1) the decoupling of motor commands across the task-relevant and task-irrelevant subspaces together with “neural” noise at the level of these motor commands; (2) “muscle noise” combined with imperfect control of the limb; (3) back-coupling of sensed joint configurations into the motor commands which then yield to the sensed joint configuration within the UCM.