Amir Karniel

Does the motor control system use multiple models and context switching to cope with a variable environment

Studies of arm movements have shown that subjects learn to compensate predictable mechanical perturbations by developing a representation of the relation between the state of motion of the arm and the perturbing forces. Here, we tested the hypothesis that subjects construct internal representations of two different force fields and switch between them when presented with an alternating sequence of these fields. Our results do not support this hypothesis. Subjects performed reaching movements in four sessions over 4 days. On the 1st day the robotic manipulandum perturbed the movement by perpendicular force that alternated its direction after each movement. Subjects were unable to construct the two underlying models and switch between them. On the 2nd day only one field was applied and well learned. On the 3rd day only the other field was applied and well learned. Then the experiment of the 1st day was repeated on the 4th day. Even after this extensive training subjects showed no signs of improved performance with alternating fields. This result combined with previous studies suggests that the central nervous system has a strong tendency to employ a single internal model when dealing with a sequence of perturbations.

A model for learning human reaching-movements

Abstract. Reaching movement is a fast movement towards a given target. The main characteristics of such a movement are straight path and a bell-shaped speed profile. In this work a mathematical model for the control of the human arm during ballistic reaching movements is presented. The model of the arm contains a 2 degrees of freedom planar manipulator, and a Hill-type, non-linear mechanical model of six muscles. The arm model is taken from the literature with minor changes. The nervous system is modeled as an adjustable pattern generator that creates the control signals to the muscles. The control signals in this model are rectangular pulses activated at various amplitudes and timings, that are determined according to the given target. These amplitudes and timings are the parameters that should be related to each target and initial conditions in the workspace. The model of the nervous system consists of an artificial neural net that maps any given target to the parameter space of the pattern generator. In order to train this net, the nervous system model includes a sensitivity model that transforms the error from the arm end-point coordinates to the parameter coordinates. The error is assessed only at the termination of the movement from knowledge of the results. The role of the non-linearity in the muscle model and the performance of the learning scheme are analysed, illustrated in simulations and discussed. The results of the present study demonstrate the central nervous system’s (CNS) ability to generate typical reaching movements with a simple feedforward controller that controls only the timing and amplitude of rectangular excitation pulses to the muscles and adjusts these parameters based on knowledge of the results. In this scheme, which is based on the adjustment of only a few parameters instead of the whole trajectory, the dimension of the control problem is reduced significantly. It is shown that the non-linear properties of the muscles are essential to achieve this simple control. This conclusion agrees with the general concept that motor control is the result of an interaction between the nervous system and the musculoskeletal dynamics.

Minimum acceleration criterion with constraints implies bang-bang control as an underlying principle for optimal trajectories of arm reaching movements

Rapid arm-reaching movements serve as an excellent test bed for any theory about trajectory formation. How are these movements planned? A minimum acceleration criterion has been examined in the past, and the solution obtained, based on the Euler-Poisson equation, failed to predict that the hand would begin and end the movement at rest (i.e., with zero acceleration). Therefore, this criterion was rejected in favor of the minimum jerk, which was proved to be successful in describing many features of human movements. This letter follows an alternative approach and solves the minimum acceleration problem with constraints using Pontryagins minimum principle. We use the minimum principle to obtain minimum acceleration trajectories and use the jerk as a control signal. In order to find a solution that does not include nonphysiological impulse functions, constraints on the maximum and minimum jerk values are assumed. The analytical solution provides a three-phase piecewise constant jerk signal (bang-bang control) where the magnitude of the jerk and the two switching times depend on the magnitude of the maximum and minimum available jerk values. This result fits the observed trajectories of reaching movements and takes into account both the extrinsic coordinates and the muscle limitations in a single framework. The minimum acceleration with constraints principle is discussed as a unifying approach for many observations about the neural control of movements.

Perception of Delayed Stiffness

Advanced technology has recently provided truly immersive virtual environments with teleoperated robotic devices. In order to control movements from a distance, the human sensorimotor system has to overcome the e fects of delay. Currently, little is known about the mechanisms that underlie haptic estimation in delayed environments. The aim of this research is to explore the e fect of a delay on perception of surfaces sti fness. A forced choice paradigm was used in which subjects were asked to identify the sti fer of two virtual spring-like surfaces based on manipulation without visual feedback. Virtual surfaces were obtained by generating an elastic force proportional to the penetration of the handle of a manipulandum inside a virtual boundary. The elastic force was either an instantaneous function of the displacement, delayed at 30 or 60 milliseconds after the displacement or led the displacement (by means of Kalman predictor) by 50 milliseconds. It was assumed that, to estimate sti fness, the brain relates the experienced interaction forces with the amount of penetration. The results of the experiment indicate a systematic dependence of the estimated sti fness upon the delay between position and force. When the force lagged the penetration, surfaces were perceived as sti fer. Conversely, when the force led the penetration, surfaces were perceived as softer. The perceptual findings were compared with different regression models. This allowed some candidate models to be discarded. To further refine the analysis, a second experiment was carried out in which the delay was introduced only during part of the hand/surface interaction, either while the hand was moving into the spring-like surface or when it was moving out of it. Findings are consistent with sti fness estimates based on dividing the maximum force by the perceived amount of penetration. Findings are not consistent with an estimate of compliance based on the maximum position or local sti fness on the way out nor with linear estimates of sti fness based on the entire force/motion history.

Automated measurement of proprioception following stroke

Background. Proprioception provides feedback which is essential for adequate motor control. Despite having detrimental functional implications, the assessment of proprioception deficits in current clinical practice is mostly qualitative and inadequate for diagnosis and longitudinal monitoring of subtle impairments and their effect on motor function. Purpose. To evaluate a novel quantitative approach to the assessment of proprioception deficits in stroke patients. Method. We designed and implemented an automated protocol where a magnetic motion tracking system and a sensor attached to each of the patients hands, enables registration of trajectories in 3D coordinates. In this protocol the patients affected and healthy hands are placed respectively below and above a square board. With vision blocked, the subjects affected hand is passively moved to one of four locations, and then the patient is instructed to actively position the healthy hand directly above his/her perceived location of the affected hand. The positional difference between the two hands is automatically recorded by the system. This procedure is repeated several times and the magnitude and direction of errors are used to quantify the proprioception deficit. The data for this pilot study was collected in a sample of 22 stroke patients and an age-matched group of neurologically intact subjects. Results. Stroke patients had significantly higher mean distance error compared with the control group (average values of 7.9 and 5.3 cm, respectively), and showed higher instability (variance) in repeated performance (average values of the standard deviation of errors 3.4 and 1.8 cm, respectively). Significant correlation was found between the mean distance error and the results of semi-quantitative clinical tests of proprioception. Conclusion. The system provides a reliable quantitative measure of upper limb proprioception, offering considerable advantage over the traditional means applied in the clinic.

A Regression and Boundary-Crossing-Based Model for the Perception of Delayed Stiffness

The stiffness of the environment with which we come in contact is the local derivative of a force field. The boundary of an elastic field is a singular region where local stiffness is ill-defined. We found that subjects interacting with delayed force fields tend to underestimate stiffness if they do not move across the boundary. In contrast, they tend to overestimate stiffness when they move across the elastic field boundary. We propose a unifying computational model of stiffness perception based on an active process that combines the concurrent operations of a force and of a position-control system.

Human motor control: learning to control a time-varying, nonlinear, many-to-one system

Human motor control has always presented a great challenge to both scientists and engineers. It has presented most of the problems they have found difficult to handle and manipulate, which is a consequence of it being a distributed, nonlinear, time-varying system with multiple degrees of freedom that include redundancy on many levels. In recent years, the fast development of computers and the emergence of the new scientific field of neural computation have enabled consideration of complex, adaptive, parallel architectures in the modeling of human motor-control performance. In this paper, some of the models that have been used in the study of motor control are reviewed, and some open questions are formalized and discussed. The main topics are adaptive and artificial neural-network control, parameter estimation, nonlinear properties of the muscles, and parallelism and redundancy.

New perspectives on the dialogue between brains and machines

Brain-machine interfaces (BMIs) are mostly investigated as a means to provide paralyzed people with new communication channels with the external world. However, the communication between brain and artificial devices also offers a unique opportunity to study the dynamical properties of neural systems. This review focuses on bidirectional interfaces, which operate in two ways by translating neural signals into input commands for the device and the output of the device into neural stimuli. We discuss how bidirectional BMIs help investigating neural information processing and how neural dynamics may participate in the control of external devices. In this respect, a bidirectional BMI can be regarded as a fancy combination of neural recording and stimulation apparatus, connected via an artificial body. The artificial body can be designed in virtually infinite ways in order to observe different aspects of neural dynamics and to approximate desired control policies.

Dynamical dimension of a hybrid neurorobotic system

The goal of this work is to understand how neural tissue can be programed to execute predetermined functions. We developed a research tool that includes the brainstem of a lamprey and a two-wheeled robot interconnected in a closed loop. We report here the development of a framework for studying the dynamics of the neural tissue based on the interaction of this tissue with the robot.

OPEN QUESTIONS IN COMPUTATIONAL MOTOR CONTROL

Computational motor control covers all applications of quantitative tools for the study of the biological movement control system. This paper provides a review of this field in the form of a list of open questions. After an introduction in which we define computational motor control, we describe: a Turing-like test for motor intelligence; internal models, inverse model, forward model, feedback error learning and distal teacher; time representation, and adaptation to delay; intermittence control strategies; equilibrium hypotheses and threshold control; the spatiotemporal hierarchy of wide sense adaptation, i.e., feedback, learning, adaptation, and evolution; optimization based models for trajectory formation and optimal feedback control; motor memory, the past and the future; and conclude with the virtue of redundancy. Each section in this paper starts with a review of the relevant literature and a few more specific studies addressing the open question, and ends with speculations about the possible answer and its implications to motor neuroscience. This review is aimed at concisely covering the topic from the authors perspective with emphasis on learning mechanisms and the various structures and limitations of internal models.