Bouncing between model and data: stability, passivity, and optimality in hybrid dynamics

Motor control beyond reach-how humans hit a target with a whip

Humans are strikingly adept at manipulating complex objects, from tying shoelaces to cracking a bullwhip. These motor skills have highly nonlinear interactive dynamics that defy reduction into parts. Yet, despite advances in data recording and processing, experiments in motor neuroscience still prioritize experimental reduction over realistic complexity. This study embraced the fully unconstrained behaviour of hitting a target with a 1.6-m bullwhip, both in rhythmic and discrete fashion. Adopting an object-centered approach to test the hypothesis that skilled movement simplifies the whip dynamics, the whip's evolution was characterized in relation to performance error and hand speed. Despite widely differing individual strategies, both discrete and rhythmic styles featured a cascade-like unfolding of the whip. Whip extension and orientation at peak hand speed predicted performance error, at least in the rhythmic style, suggesting that humans accomplished the task by setting initial conditions. These insights may inform further studies on human and robot control of complex objects.

Learning and transfer of complex motor skills in virtual reality: a perspective review

The development of more effective rehabilitative interventions requires a better understanding of how humans learn and transfer motor skills in real-world contexts. Presently, clinicians design interventions to promote skill learning by relying on evidence from experimental paradigms involving simple tasks, such as reaching for a target. While these tasks facilitate stringent hypothesis testing in laboratory settings, the results may not shed light on performance of more complex real-world skills. In this perspective, we argue that virtual environments (VEs) are flexible, novel platforms to evaluate learning and transfer of complex skills without sacrificing experimental control. Specifically, VEs use models of real-life tasks that afford controlled experimental manipulations to measure and guide behavior with a precision that exceeds the capabilities of physical environments. This paper reviews recent insights from VE paradigms on motor learning into two pressing challenges in rehabilitation research: 1) Which training strategies in VEs promote complex skill learning? and 2) How can transfer of learning from virtual to real environments be enhanced? Defining complex skills by having nested redundancies, we outline findings on the role of movement variability in complex skill acquisition and discuss how VEs can provide novel forms of guidance to enhance learning. We review the evidence for skill transfer from virtual to real environments in typically developing and neurologically-impaired populations with a view to understanding how differences in sensory-motor information may influence learning strategies. We provide actionable suggestions for practicing clinicians and outline broad areas where more research is required. Finally, we conclude that VEs present distinctive experimental platforms to understand complex skill learning that should enable transfer from therapeutic practice to the real world.

The self-organization of ball bouncing

The hybrid rhythmic ball-bouncing task considered in this study requires a participant to hit a ball in a virtual environment by moving a paddle in the real environment. It allows for investigation of the online visual control of action in humans. Changes in gravity acceleration in the virtual environment affect the ball dynamics and modify the ball-paddle system limit cycle. These changes are shown to be accurately reproduced through simulation by a model integrating continuous information-movement couplings between the ball trajectory and the paddle trajectory, giving rise to a resonance-tuning phenomenon. On the contrary, the tested models integrating only intermittent sensorimotor couplings were unable to replicate the observed human behavior. Results suggest that the visual control of action is achieved online, in a prospective way. Human rhythmic motor control would benefit from the timing and phase control emerging from the low-level continuous coupling between the central pattern generator and the visual perception of the ball trajectory. This control strategy, which precludes the need for internal clock and explicit environmental representation, is also able to explain the empirical result that the bounces tend to converge toward a passive stability regime during human ball bouncing.

Stability and predictability in human control of complex objects

Previous research on movement control suggested that humans exploit stability to reduce vulnerability to internal noise and external perturbations. For interactions with complex objects, predictive control based on an internal model of body and environment is needed to preempt perturbations and instabilities due to delays. We hypothesize that stability can serve as means to render the complex dynamics of the body and the task more predictable and thereby simplify control. However, the assessment of stability in complex interactions with nonlinear and underactuated objects is challenging, as for existent stability analyses the system needs to be close to a (known) attractor. After reviewing existing methods for stability analysis of human movement, we argue that contraction theory provides a suitable approach to quantify stability or convergence in complex transient behaviors. To test its usefulness, we examined the task of carrying a cup of coffee, an object with internal degrees of freedom. A simplified model of the task, a cart with a suspended pendulum, was implemented in a virtual environment to study human control strategies. The experimental task was to transport this cart-and-pendulum on a horizontal line from rest to a target position as fast as possible. Each block of trials presented a visible perturbation, which either could be in the direction of motion or opposite to it. To test the hypothesis that humans exploit stability to overcome perturbations, the dynamic model of the free, unforced system was analyzed using contraction theory. A contraction metric was obtained by numerically solving a partial differential equation, and the contraction regions with respect to that metric were computed. Experimental results showed that subjects indeed moved through the contraction regions of the free, unforced system. This strategy attenuated the perturbations, obviated error corrections, and made the dynamics more predictable. The advantages and shortcomings of contraction analysis are discussed in the context of other stability analyses.

Interacting Learning Processes during Skill Acquisition: Learning to control with gradually changing system dynamics

There is increasing evidence that sensorimotor learning under real-life conditions relies on a composition of several learning processes. Nevertheless, most studies examine learning behaviour in relation to one specific learning mechanism. In this study, we examined the interaction between reward-based skill acquisition and motor adaptation to changes of object dynamics. Thirty healthy subjects, split into two groups, acquired the skill of balancing a pole on a cart in virtual reality. In one group, we gradually increased the gravity, making the task easier in the beginning and more difficult towards the end. In the second group, subjects had to acquire the skill on the maximum, most difficult gravity level. We hypothesized that the gradual increase in gravity during skill acquisition supports learning despite the necessary adjustments to changes in cart-pole dynamics. We found that the gradual group benefits from the slow increment, although overall improvement was interrupted by the changes in gravity and resulting system dynamics, which caused short-term degradations in performance and timing of actions. In conclusion, our results deliver evidence for an interaction of reward-based skill acquisition and motor adaptation processes, which indicates the importance of both processes for the development of optimized skill acquisition schedules.

Model of rhythmic ball bouncing using a visually controlled neural oscillator

The present paper investigates the sensory-driven modulations of central pattern generator dynamics that can be expected to reproduce human behavior during rhythmic hybrid tasks. We propose a theoretical model of human sensorimotor behavior able to account for the observed data from the ball-bouncing task. The novel control architecture is composed of a Matsuoka neural oscillator coupled with the environment through visual sensory feedback. The architecture's ability to reproduce human-like performance during the ball-bouncing task in the presence of perturbations is quantified by comparison of simulated and recorded trials. The results suggest that human visual control of the task is achieved online. The adaptive behavior is made possible by a parametric and state control of the limit cycle emerging from the interaction of the rhythmic pattern generator, the musculoskeletal system, and the environment.NEW & NOTEWORTHY The study demonstrates that a behavioral model based on a neural oscillator controlled by visual information is able to accurately reproduce human modulations in a motor action with respect to sensory information during the rhythmic ball-bouncing task. The model attractor dynamics emerging from the interaction between the neuromusculoskeletal system and the environment met task requirements, environmental constraints, and human behavioral choices without relying on movement planning and explicit internal models of the environment.

Implicit guidance to stable performance in a rhythmic perceptual-motor skill

Feedback about error or reward is regarded essential for aiding learners to acquire a perceptual-motor skill. Yet, when a task has redundancy and the mapping between execution and performance outcome is unknown, simple error feedback does not suffice in guiding the learner toward the optimal solutions. The present study developed and tested a new means of implicitly guiding learners to acquire a perceptual-motor skill, rhythmically bouncing a ball on a racket. Due to its rhythmic nature, this task affords dynamically stable solutions that are robust to small errors and noise, a strategy that is independent from actively correcting error. Based on the task model implemented in a virtual environment, a time-shift manipulation was designed to shift the range of ball-racket contacts that achieved dynamically stable solutions. In two experiments, subjects practiced with this manipulation that guided them to impact the ball with more negative racket accelerations, the indicator for the strategy with dynamic stability. Subjects who practiced under normal conditions took longer time to acquire this strategy, although error measures were identical between the control and experimental groups. Unlike in many other haptic guidance or adaptation studies, the experimental groups not only learned, but also maintained the stable solution after the manipulation was removed. These results are a first demonstration that more subtle ways to guide the learner to better performance are needed especially in tasks with redundancy, where error feedback may not be sufficient.

The Effect of Haptic Guidance on Learning a Hybrid Rhythmic-Discrete Motor Task

Bouncing a ball with a racket is a hybrid rhythmic-discrete motor task, combining continuous rhythmic racket movements with discrete impact events. Rhythmicity is exceptionally important in motor learning, because it underlies fundamental movements such as walking. Studies suggested that rhythmic and discrete movements are governed by different control mechanisms at different levels of the Central Nervous System. The aim of this study is to evaluate the effect of fixed/fading haptic guidance on learning to bounce a ball to a desired apex in virtual reality with varying gravity. Changing gravity changes dominance of rhythmic versus discrete control: The higher the value of gravity, the more rhythmic the task; lower values reduce the bouncing frequency and increase dwell times, eventually leading to a repetitive discrete task that requires initiation and termination, resembling target-oriented reaching. Although motor learning in the ball-bouncing task with varying gravity has been studied, the effect of haptic guidance on learning such a hybrid rhythmic-discrete motor task has not been addressed. We performed an experiment with thirty healthy subjects and found that the most effective training condition depended on the degree of rhythmicity: Haptic guidance seems to hamper learning of continuous rhythmic tasks, but it seems to promote learning for repetitive tasks that resemble discrete movements.

Haptic feedback enhances rhythmic motor control by reducing variability, not improving convergence rate

Stability and performance during rhythmic motor behaviors such as locomotion are critical for survival across taxa: falling down would bode well for neither cheetah nor gazelle. Little is known about how haptic feedback, particularly during discrete events such as the heel-strike event during walking, enhances rhythmic behavior. To determine the effect of haptic cues on rhythmic motor performance, we investigated a virtual paddle juggling behavior, analogous to bouncing a table tennis ball on a paddle. Here, we show that a force impulse to the hand at the moment of ball-paddle collision categorically improves performance over visual feedback alone, not by regulating the rate of convergence to steady state (e.g., via higher gain feedback or modifying the steady-state hand motion), but rather by reducing cycle-to-cycle variability. This suggests that the timing and state cues afforded by haptic feedback decrease the nervous system's uncertainty of the state of the ball to enable more accurate control but that the feedback gain itself is unaltered. This decrease in variability leads to a substantial increase in the mean first passage time, a measure of the long-term metastability of a stochastic dynamical system. Rhythmic tasks such as locomotion and juggling involve intermittent contact with the environment (i.e., hybrid transitions), and the timing of such transitions is generally easy to sense via haptic feedback. This timing information may improve metastability, equating to less frequent falls or other failures depending on the task.

Trial-to-trial reoptimization of motor behavior due to changes in task demands is limited

Each task requires a specific motor behavior that is tuned to task demands. For instance, writing requires a lot of accuracy while clapping does not. It is known that the brain adjusts the motor behavior to different task demands as predicted by optimal control theory. In this study, the mechanism of this reoptimization process is investigated by varying the accuracy demands of a reaching task. In this task, the width of the reaching target (0.5 or 8 cm) was varied either on a trial-to-trial basis (random schedule) or in blocks (blocked schedule). On some trials, the hand of the subjects was clamped to a rectilinear trajectory that ended 2 cm on the left or right of the target center. The rejection of this perturbation largely varied with target width in the blocked schedule but not in the random schedule. That is, subjects exhibited different motor behavior in the different schedules despite identical accuracy demands. Therefore, while reoptimization has been considered immediate and automatic, the differences in motor behavior observed across schedules suggest that the reoptimization of the motor behavior is neither happening on a trial-by-trial basis nor obligatory. The absence of trial-to-trial mechanisms, the inability of the brain to adapt to two conflicting task demands and the existence of a switching cost are discussed as possible sources of the non-optimality of motor behavior during the random schedule.