Robotics and neuroscience: a rhythmic interaction

A survey on CPG-inspired control models and system implementation

This paper surveys the developments of the last 20 years in the field of central pattern generator (CPG) inspired locomotion control, with particular emphasis on the fast emerging robotics-related applications. Functioning as a biological neural network, CPGs can be considered as a group of coupled neurons that generate rhythmic signals without sensory feedback; however, sensory feedback is needed to shape the CPG signals. The basic idea in engineering endeavors is to replicate this intrinsic, computationally efficient, distributed control mechanism for multiple articulated joints, or multi-DOF control cases. In terms of various abstraction levels, existing CPG control models and their extensions are reviewed with a focus on the relative advantages and disadvantages of the models, including ease of design and implementation. The main issues arising from design, optimization, and implementation of the CPG-based control as well as possible alternatives are further discussed, with an attempt to shed more light on locomotion control-oriented theories and applications. The design challenges and trends associated with the further advancement of this area are also summarized.

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

Rhythmically bouncing a ball with a racket is a seemingly simple task, but it poses all the challenges critical for coordinative behavior: perceiving the ball's trajectory to adapt position and velocity of the racket for the next ball contact. To gain insight into the underlying control strategies, the authors conducted a series of studies that tested models with experimental data, with an emphasis on deriving model-based hypotheses and trying to falsify them. Starting with a simple dynamical model of the racket and ball interactions, stability analyses showed that open-loop dynamics affords dynamical stability, such that small perturbations do not require corrections. To obtain this passive stability, the ball has to be impacted with negative acceleration--a strategy that subjects adopted in a variety of conditions at steady state. However, experimental tests that applied perturbations revealed that after perturbations, subjects applied active perceptually guided corrections to reestablish steady state faster than by relying on the passive model's relaxation alone. Hence, the authors derived a model with active control based on optimality principles that considered each impact as a separate reaching-like movement. This model captured some additional features of the racket trajectory but failed to predict more fine-grained aspects of performance. The authors proceed to present a new model that accounts not only for fine-grained behavior but also reconciles passive and active control approaches with new predictions that will be put to test in the next set of experiments.

Optimal control of a hybrid rhythmic-discrete task: the bouncing ball revisited

Rhythmically bouncing a ball with a racket is a hybrid task that combines continuous rhythmic actuation of the racket with the control of discrete impact events between racket and ball. This study presents experimental data and a two-layered modeling framework that explicitly addresses the hybrid nature of control: a first discrete layer calculates the state to reach at impact and the second continuous layer smoothly drives the racket to this desired state, based on optimality principles. The testbed for this hybrid model is task performance at a range of increasingly slower tempos. When slowing the rhythm of the bouncing actions, the continuous cycles become separated into a sequence of discrete movements interspersed by dwell times and directed to achieve the desired impact. Analyses of human performance show increasing variability of performance measures with slower tempi, associated with a change in racket trajectories from approximately sinusoidal to less symmetrical velocity profiles. Matching results of model simulations give support to a hybrid control model based on optimality, and therefore suggest that optimality principles are applicable to the sensorimotor control of complex movements such as ball bouncing.

Open-loop, closed-loop and compensatory control: performance improvement under pressure in a rhythmic task

According to explicit monitoring theories, the phenomenon of choking under pressure is due to actors focusing their attention on the execution of the skill. This step-by-step perceptually guided control may then interfere with automatic execution. In order to examine the changes in control at the sensorimotor level, we examined the rhythmic task of ball bouncing which affords detailed quantification of indicators of control based on previous research. The hypothesis was that under psychological pressure perceptually guided control should lead to decreased performance due to over-emphasis on closed-loop control and decreased compensatory control. In two experiments of different difficulty psychological stress was induced via setting up a fake competition. Results showed that, contrary to the hypothesis, performance accuracy and consistency improved together with an increase in compensatory control. Indicators for open- and closed-loop processes did not change. Only under more challenging conditions in Experiment 2, enhanced performance under pressure was accompanied by more active, closed-loop and less passive control. The results are discussed in light of task demands and the continuous rhythmic nature of the task: in more challenging tasks, control appears to be more prone to disturbance due to psychological stress. The different control demands in continuous rhythmic tasks may be less prone to interference due to psychological stress than in discrete tasks.

A computational model for rhythmic and discrete movements in uni- and bimanual coordination

Current research on discrete and rhythmic movements differs in both experimental procedures and theory, despite the ubiquitous overlap between discrete and rhythmic components in everyday behaviors. Models of rhythmic movements usually use oscillatory systems mimicking central pattern generators (CPGs). In contrast, models of discrete movements often employ optimization principles, thereby reflecting the higher-level cortical resources involved in the generation of such movements. This letter proposes a unified model for the generation of both rhythmic and discrete movements. We show that a physiologically motivated model of a CPG can not only generate simple rhythmic movements with only a small set of parameters, but can also produce discrete movements if the CPG is fed with an exponentially decaying phasic input. We further show that a particular coupling between two of these units can reproduce main findings on in-phase and antiphase stability. Finally, we propose an integrated model of combined rhythmic and discrete movements for the two hands. These movement classes are sequentially addressed in this letter with increasing model complexity. The model variations are discussed in relation to the degree of recruitment of the higher-level cortical resources, necessary for such movements.

Completely inelastic ball

This Rapid Communication presents an analytical study of the bouncing of a completely inelastic ball on a vertically vibrated plate. The interplay of saddle-node and period-doubling bifurcations leads to an intricate structure of the bifurcation diagram with uncommon properties, such as an infinity of bifurcation cascades in a finite range of the control parameter Gamma. A pseudochaotic behavior, consisting in arbitrarily long and complex periodic sequences, is observed through this generic system.

Forward models of inertial loads in weightlessness

In this experiment, we investigated whether the CNS uses internal forward models of inertial loads to maintain the stability of a precision grip when manipulating objects in the absence of gravity. The micro-gravity condition causes profound changes in the profile of tangential constraints at the finger-object interface. In order to assess the ability to predict the micro-gravity-specific variation of inertial loads, we analyzed the grip force adjustments that occurred when naive subjects held an object in a precision grip and performed point-to-point movements under the weightless condition induced by parabolic flight. Such movements typically presented static and dynamic phases, which permitted distinction between a static component of the grip force (measured before the movement) and a dynamic component of the grip force (measured during the movement). The static component tended to gradually decrease across the parabolas, whereas the dynamic component was rapidly modulated with the micro-gravity-specific inertial loads. In addition, the amplitude of the modulation significantly correlated with the amplitude of the tangential constraints for the dynamic component. These results strongly support the hypothesis that the internal representation of arm and object dynamics adapts to new gravitational contexts. In addition, the difference in time scales of adaptation of static and dynamic components suggests that they can be processed independently. The prediction of self-induced variation of inertial loads permits fine modulation of grip force, which ensures a stable grip during manipulation of an object in a new environment.

Control of bimanual rhythmic movements: trading efficiency for robustness depending on the context

This paper investigates how the efficiency and robustness of a skilled rhythmic task compete against each other in the control of a bimanual movement. Human subjects juggled a puck in 2D through impacts with two metallic arms, requiring rhythmic bimanual actuation. The arms kinematics were only constrained by the position, velocity and time of impacts while the rest of the trajectory did not influence the movement of the puck. In order to expose the task robustness, we manipulated the task context in two distinct manners: the task tempo was assigned at four different values (hence manipulating the time available to plan and execute each impact movement individually); and vision was withdrawn during half of the trials (hence reducing the sensory inflows). We show that when the tempo was fast, the actuation was rhythmic (no pause in the trajectory) while at slow tempo, the actuation was discrete (with pause intervals between individual movements). Moreover, the withdrawal of visual information encouraged the rhythmic behavior at the four tested tempi. The discrete versus rhythmic behavior give different answers to the efficiency/robustness trade-off: discrete movements result in energy efficient movements, while rhythmic movements impact the puck with negative acceleration, a property preserving robustness. Moreover, we report that in all conditions the impact velocity of the arms was negatively correlated with the energy of the puck. This correlation tended to stabilize the task and was influenced by vision, revealing again different control strategies. In conclusion, this task involves different modes of control that balance efficiency and robustness, depending on the context.