Simulating closed- and open-loop voluntary movement: a nonlinear control-systems approach

Contributions of open-loop and closed-loop control in a continuous tracking task differ depending on attentional demands during practice

Improving tracking performance requires numerous adjustments in the motor system, including peripheral muscle functions and central motor commands. These commands can rely on sensory feedback processing during tracking, i.e., closed-loop control. In the case of repeated tracking sequences, these commands can rely on an inner representation of the target trajectory to optimize pre-planning, i.e., open-loop control. Implicit learning in a continuous tracking task with repeated sequences proves the availability of an inner target representation, which emerges by learning task regularities, even without explicit knowledge. We hypothesize that the actual use of open-loop or closed-loop control is influenced by the demand for attention. Specifically, we suggest that closed-loop control and its development during practice need attentional resources, whereas open-loop control can work and evolve in a more automatic way without attentional demands. To test this, we investigated motor-control strategies when extensively practicing a continuous compensatory force-tracking task using isometric leg muscle activation, either as a single-motor task or as a motor-cognitive dual task. After training, we found evidence for predominantly closed-loop control in the single-task training group and for open-loop control in the dual-task training group. In particular, we ascertained dual-task motor costs and a weakly developed implicit knowledge of task regularities in the single-task training group. In contrast, in the dual-task training group dual-task motor costs disappeared, while implicit learning was clearly observed. We conclude that motor-cognitive dual-task training may boost implicit motor learning, without necessarily impeding concurrent improvement in the cognitive task. Data repository: reserved doi: https://doi.org/10.5281/zenodo.6759377.

DESIGN OF A THRESHOLD FES CONTROL SYSTEM FOR ARM MOVEMENT

The existing functional electrical stimulation (FES) techniques often required to solve the complex "inverse dynamic problem" to calculate the muscle torques for moving along a desired trajectory. According to the threshold control theory of voluntary motor control, a bio-mimetic threshold control strategy for the FES controller is designed and tested in the human arm movement. The arm is modeled as three segments connected by two hinges joints. The movement is driven by seven muscles and limited in the horizontal plane. All muscles are described by a modified Hill-type muscle model. Simulation results suggest that the threshold FES control system can realize point to point movement and can approximately follow the desired traces in presence of feedback delays up to 20 ms. The movement can also maintain stability under external perturbation or external load. The control system can be employed in clinical application because of the following advantages: (1) The control strategy includes some mature control techniques which had been realized in hardware. (2) Only sophisticated sensors of goniometer and the surface electrodes are needed to provide feedbacks and muscle stimulation. (3) The performance of the control system will not be critically influenced by the slight change of musculo-tendon parameters and feedback delays, and even the parameters of controller are fixed.

Assessing manual pursuit tracking in Parkinson's disease via linear dynamical systems

Quantitative assessment of motor performance is important for diseases of motor control, such as Parkinson's disease (PD). Manual tracking tasks are well suited for motor assessment, as they can be performed concomitantly with brain mapping techniques. Here we propose utilizing second-order linear dynamical systems to assess manual pursuit tracking performance. With the desired trajectory as the input, and the subject's actual motor response as the output, a linear model characterized by natural frequency and damping ratio is identified for each subject. We applied this method to 10 PD subjects (on and off L: -dopa medication) and 10 normal subjects performing a multi-frequency sinusoidal tracking task. Model parameters were more sensitive than overall tracking errors in determining significant differences between groups. The effect of L: -dopa medication was to reduce the damping ratio and make the range in natural frequency across individuals approach that of normal subjects. We interpret the changes in damping ratio and natural frequency as possibly related to suppression of compensatory cerebellar activity and/or improvement of motor program selection, and the changes in natural frequency as an implicit strategy to maintain settling time in the face of reduce damping ratio. Our results suggest that simple linear dynamical system models can be a powerful method to assess tracking performance in Parkinson's disease because of the additional insight they can provide into neurological processes.

The BUMP model of response planning: intermittent predictive control accounts for 10 Hz physiological tremor

Physiological tremor during movement is characterized by ∼10 Hz oscillation observed both in the electromyogram activity and in the velocity profile. We propose that this particular rhythm occurs as the direct consequence of a movement response planning system that acts as an intermittent predictive controller operating at discrete intervals of ∼100 ms. The BUMP model of response planning describes such a system. It forms the kernel of Adaptive Model Theory which defines, in computational terms, a basic unit of motor production or BUMP. Each BUMP consists of three processes: (1) analyzing sensory information, (2) planning a desired optimal response, and (3) execution of that response. These processes operate in parallel across successive sequential BUMPs. The response planning process requires a discrete-time interval in which to generate a minimum acceleration trajectory to connect the actual response with the predicted future state of the target and compensate for executional error. We have shown previously that a response planning time of 100 ms accounts for the intermittency observed experimentally in visual tracking studies and for the psychological refractory period observed in double stimulation reaction time studies. We have also shown that simulations of aimed movement, using this same planning interval, reproduce experimentally observed speed-accuracy tradeoffs and movement velocity profiles. Here we show, by means of a simulation study of constant velocity tracking movements, that employing a 100 ms planning interval closely reproduces the measurement discontinuities and power spectra of electromyograms, joint-angles, and angular velocities of physiological tremor reported experimentally. We conclude that intermittent predictive control through sequential operation of BUMPs is a fundamental mechanism of 10 Hz physiological tremor in movement.

Modeling biological motor control for human locomotion with functional electrical stimulation

This paper develops a novel control system for functional electrical stimulation (FES) locomotion, which aims to generate normal locomotion for paraplegics via FES. It explores the possibility of applying ideas from biology to engineering. The neural control mechanism of the biological motor system, the central pattern generator, has been adopted in the control system design. Some artificial control techniques such as neural network control, fuzzy logic, control and impedance control are incorporated to refine the control performance. Several types of sensory feedback are integrated to endow this control system with an adaptive ability. A musculoskeletal model with 7 segments and 18 muscles is constructed for the simulation study. Satisfactory simulation results are achieved under this FES control system, which indicates a promising technique for the potential application of FES locomotion in future.

An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control

Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.

A new view on visuomotor channels: The case of the disappearing dynamics

A considerable body of kinematic data supports the proposal that independent visuomotor channels are involved in the control of the transport and grip components of reach and grasp. These channels are seen as having separate perceptual inputs, outputs and internal processing and are thought by some to correspond to independent neuroanatomical pathways. The idea that different groups of muscles and biomechanical structures can be controlled independently is attractive, but this kinematically-inspired hypothesis fails to take into account the complexity of the dynamic relationships and their interactions within the neuromusculoskeletal system. Inertial, viscous, centrifugal, coriolis, gravitational and reflex cross couplings exist between efferent drives to muscles and resulting body movements. Rotation at even a single joint generates a complex set of dynamic reaction forces and requires coordinated activation of many muscles throughout the body to maintain posture and balance. In this theoretical paper we present a new view of independent visuomotor channels in the form of an adaptive neural controller that can compensate for the above interactions and decouple the relationships between efferent drives to muscles and resulting body movements. At the same time, the neural controller renders all the dynamics (linear and nonlinear), other than time delays, of the neuromusculoskeletal system, unobservable in the visuomotor relationships. Using the geometry of nonlinear dynamical systems we show that, providing certain constraints on the structure of time delays within the system are satisfied, there exists a neural controller that can render all the dynamics of the neuromusculoskeletal system (except for time delays) unobservable in the responses. The controller simultaneously decouples all the interactive dynamics so that each of the m independent inputs controls one and only one degree of freedom of the response. This means that each degree of freedom in a multi-joint response can be controlled by an independent component of the visual input, a behaviour that has long been observed in visual tracking experiments. The controller effectively establishes m independent visuomotor channels. However, rather than reflecting separate neuroanatomical pathways, the independent channels result from a neural controller with convergent and divergent connections to compensate for the interactive nonlinear dynamics within the neuromusculoskeletal system. This new view of visuomotor channels has implications for neural control processes involved in the acquisition and adaptability of skilled perceptual-motor behaviour in general, as well as for the design of robotic controllers.