Maura Casadio

A model of postural control in quiet standing: robust compensation of delay-induced instability using intermittent activation of feedback control.

The main purpose of this study is to compare two different feedback controllers for the stabilization of quiet standing in humans, taking into account that the intrinsic ankle stiffness is insufficient and that there is a large delay inducing instability in the feedback loop: 1) a standard linear, continuous-time PD controller and 2) an intermittent PD controller characterized by a switching function defined in the phase plane, with or without a dead zone around the nominal equilibrium state. The stability analysis of the first controller is carried out by using the standard tools of linear control systems, whereas the analysis of the intermittent controllers is based on the use of Poincaré maps defined in the phase plane. When the PD-control is off, the dynamics of the system is characterized by a saddle-like equilibrium, with a stable and an unstable manifold. The switching function of the intermittent controller is implemented in such a way that PD-control is ‘off’ when the state vector is near the stable manifold of the saddle and is ‘on’ otherwise. A theoretical analysis and a related simulation study show that the intermittent control model is much more robust than the standard model because the size of the region in the parameter space of the feedback control gains (P vs. D) that characterizes stable behavior is much larger in the latter case than in the former one. Moreover, the intermittent controller can use feedback parameters that are much smaller than the standard model. Typical sway patterns generated by the intermittent controller are the result of an alternation between slow motion along the stable manifold of the saddle, when the PD-control is off, and spiral motion away from the upright equilibrium determined by the activation of the PD-control with low feedback gains. Remarkably, overall dynamic stability can be achieved by combining in a smart way two unstable regimes: a saddle and an unstable spiral. The intermittent controller exploits the stabilizing effect of one part of the saddle, letting the system evolve by alone when it slides on or near the stable manifold; when the state vector enters the strongly unstable part of the saddle it switches on a mild feedback which is not supposed to impose a strict stable regime but rather to mitigate the impending fall. The presence of a dead zone in the intermittent controller does not alter the stability properties but improves the similarity with biological sway patterns. The two types of controllers are also compared in the frequency domain by considering the power spectral density (PSD) of the sway sequences generated by the models with additive noise. Different from the standard continuous model, whose PSD function is similar to an over-damped second order system without a resonance, the intermittent control model is capable to exhibit the two power law scaling regimes that are typical of physiological sway movements in humans.

Bounded stability of the quiet standing posture: an intermittent control model.

The paper presents a control model of body sway in quiet standing, which aims at achieving bounded stability by means of an intermittent control mechanism. Control bursts are generated when the current state vector exits an area of uncertainty around the reference point in the phase plane. This area is determined by the limited resolution of proprioceptive signals and the burst generation mechanism is predictive in the sense that it incorporates a rough, but working knowledge (internal model) of the biomechanics of the human inverted pendulum. We show that such a model, in spite of its simplicity and of the fact that it relies on very noisy measurements, is robust and can explain in a detailed way the measured sway patterns.

Self-adaptive robot training of stroke survivors for continuous tracking movements

BackgroundAlthough robot therapy is progressively becoming an accepted method of treatment for stroke survivors, few studies have investigated how to adapt the robot/subject interaction forces in an automatic way. The paper is a feasibility study of a novel self-adaptive robot controller to be applied with continuous tracking movements.MethodsThe haptic robot Braccio di Ferro is used, in relation with a tracking task. The proposed control architecture is based on three main modules: 1) a force field generator that combines a non linear attractive field and a viscous field; 2) a performance evaluation module; 3) an adaptive controller. The first module operates in a continuous time fashion; the other two modules operate in an intermittent way and are triggered at the end of the current block of trials. The controller progressively decreases the gain of the force field, within a session, but operates in a non monotonic way between sessions: it remembers the minimum gain achieved in a session and propagates it to the next one, which starts with a block whose gain is greater than the previous one. The initial assistance gains are chosen according to a minimal assistance strategy. The scheme can also be applied with closed eyes in order to enhance the role of proprioception in learning and control.ResultsThe preliminary results with a small group of patients (10 chronic hemiplegic subjects) show that the scheme is robust and promotes a statistically significant improvement in performance indicators as well as a recalibration of the visual and proprioceptive channels. The results confirm that the minimally assistive, self-adaptive strategy is well tolerated by severely impaired subjects and is beneficial also for less severe patients.ConclusionsThe experiments provide detailed information about the stability and robustness of the adaptive controller of robot assistance that could be quite relevant for the design of future large scale controlled clinical trials. Moreover, the study suggests that including continuous movement in the repertoire of training is acceptable also by rather severely impaired subjects and confirms the stabilizing effect of alternating vision/no vision trials already found in previous studies.

Abnormal sensorimotor control, but intact force field adaptation, in multiple sclerosis subjects with no clinical disability

In MS subjects with no clinical disability, we assessed sensorimotor organization and their ability to adapt to an unfamiliar dynamical environment. Eleven MS subjects performed reaching movements while a robot generated a speed-dependent force field. Control and adaptation performance were compared with that of an equal number of control subjects. During a familiarization phase, when the robot generated no forces, the movements of MS subjects were more curved, displayed greater and more variable directional errors and a longer deceleration phase. During the force field phase, both MS and control subjects gradually learned to predict the robot-generated forces. The rates of adaptation were similar, but MS subjects showed a greater variability in responding to the force field. These results suggest that MS subjects have a preserved capability of learning to predict the effects of the forces, but make greater errors when actually using such predictions to generate movements. Inaccurate motor commands are then compensated later in the movement through an extra amount of sensory-based corrections. This indicates that early in the disease MS subjects have intact adaptive capabilities, but impaired movement execution. Multiple Sclerosis 2008; 14: 330—342. http://msj.sagepub.com

Minimally assistive robot training for proprioception enhancement

In stroke survivors, motor impairment is frequently associated with degraded proprioceptive and/or somatosensory functions. Here we address the question of how to use robots to improve proprioception in these patients. We used an ‘assist-as-needed’ protocol, in which robot assistance was kept to a minimum and was continuously adjusted during exercise. To specifically train proprioceptive functions, we alternated blocks of trials with and without vision. A total of nine chronic stroke survivors participated in the study, which consisted of a total of ten 1-h exercise sessions. We used a linear mixed-effects statistical model to account for the effects of exercise, vision and the degree of assistance on the overall performance, and to capture both the systematic effects and the individual variations. Although there was not always a complete recovery of autonomous movements, all subjects exhibited an increased amount of voluntary control. Moreover, training with closed eyes appeared to be beneficial for patients with abnormal proprioception. Our results indicate that training by alternating vision and no-vision blocks may improve the ability to use proprioception as well as the ability to integrate it with vision. We suggest that the approach may be useful in the more general case of motor skill acquisition, in which enhancing proprioception may improve the ability to physically interact with the external world.

Reorganization of finger coordination patterns during adaptation to rotation and scaling of a newly learned sensorimotor transformation.

We examined how people organize redundant kinematic control variables (finger joint configurations) while learning to make goal-directed movements of a virtual object (a cursor) within a low-dimensional task space (a computer screen). Subjects participated in three experiments performed on separate days. Learning progressed rapidly on day 1, resulting in reduced target capture error and increased cursor trajectory linearity. On days 2 and 3, one group of subjects adapted to a rotation of the nominal map, imposed either stepwise or randomly over trials. Another group experienced a scaling distortion. We report two findings. First, adaptation rates and memory-dependent motor command updating depended on distortion type. Stepwise application and removal of the rotation induced a marked increase in finger motion variability but scaling did not, suggesting that the rotation initiated a more exhaustive search through the space of viable finger motions to resolve the target capture task than did scaling. Indeed, subjects formed new coordination patterns in compensating the rotation but relied on patterns established during baseline practice to compensate the scaling. These findings support the idea that the brain compensates direction and extent errors separately and in computationally distinct ways, but are inconsistent with the idea that once a task is learned, command updating is limited to those degrees of freedom contributing to performance (thereby minimizing energetic or similar costs of control). Second, we report that subjects who learned a scaling while moving to just one target generalized more narrowly across directions than those who learned a rotation. This contrasts with results from whole-arm reaching studies, where a learned scaling generalizes more broadly across direction than rotation. Based on inverse- and forward-dynamics analyses of reaching with the arm, we propose the difference in results derives from extensive exposure in reaching with familiar arm dynamics versus the novelty of the manual task.

Functional reorganization of upper-body movement after spinal cord injury

Survivors of spinal cord injury need to reorganize their residual body movements for interacting with assistive devices and performing activities that used to be easy and natural. To investigate movement reorganization, we asked subjects with high-level spinal cord injury (SCI) and unimpaired subjects to control a cursor on a screen by performing upper-body motions. While this task would be normally accomplished by operating a computer mouse, here shoulder motions were mapped into the cursor position. Both the control and the SCI subjects were rapidly able to reorganize their movements and to successfully control the cursor. The majority of the subjects in both groups were successful in reducing the movements that were not effective at producing cursor motions. This is inconsistent with the hypothesis that the control system is merely concerned with the accurate acquisition of the targets and is unconcerned with motions that are not relevant to this goal. In contrast, our findings suggest that subjects can learn to reorganize coordination so as to increase the correspondence between the subspace of their upper-body motions with the plane in which the controlled cursor moves. This is effectively equivalent to constructing an inverse internal model of the map from body motions to cursor motions, established by the experiment. These results are relevant to the development of interfaces for assistive devices that optimize the use of residual voluntary control and enhance the learning process in disabled users, searching for an easily learnable map between their body motor space and control space of the device.

Eye-hand coordination during dynamic visuomotor rotations.

Background for many technology-driven visuomotor tasks such as tele-surgery, human operators face situations in which the frames of reference for vision and action are misaligned and need to be compensated in order to perform the tasks with the necessary precision. The cognitive mechanisms for the selection of appropriate frames of reference are still not fully understood. This study investigated the effect of changing visual and kinesthetic frames of reference during wrist pointing, simulating activities typical for tele-operations. Methods using a robotic manipulandum, subjects had to perform center-out pointing movements to visual targets presented on a computer screen, by coordinating wrist flexion/extension with abduction/adduction. We compared movements in which the frames of reference were aligned (unperturbed condition) with movements performed under different combinations of visual/kinesthetic dynamic perturbations. The visual frame of reference was centered to the computer screen, while the kinesthetic frame was centered around the wrist joint. Both frames changed their orientation dynamically (angular velocity = 36°/s) with respect to the head-centered frame of reference (the eyes). Perturbations were either unimodal (visual or kinesthetic), or bimodal (visual+kinesthetic). As expected, pointing performance was best in the unperturbed condition. The spatial pointing error dramatically worsened during both unimodal and most bimodal conditions. However, in the bimodal condition, in which both disturbances were in phase, adaptation was very fast and kinematic performance indicators approached the values of the unperturbed condition. Conclusions this result suggests that subjects learned to exploit an “affordance” made available by the invariant phase relation between the visual and kinesthetic frames. It seems that after detecting such invariance, subjects used the kinesthetic input as an informative signal rather than a disturbance, in order to compensate the visual rotation without going through the lengthy process of building an internal adaptation model. Practical implications are discussed as regards the design of advanced, high-performance man-machine interfaces.

A neural mechanism of synergy formation for whole body reaching

The present study proposes a computational model for the formation of whole body reaching synergy, i.e., coordinated movements of lower and upper limbs, characterized by a focal component (the hand must reach a target) and a postural component (the center of mass must remain inside the support base). The model is based on an extension of the equilibrium point hypothesis that has been called Passive Motion Paradigm (PMP), modified in order to achieve terminal attractor features and allow the integration of multiple constraints. The model is a network with terminal attractor dynamics. By simulating it in various conditions it was possible to show that it exhibits many of the spatio-temporal features found in experimental data. In particular, the motion of the center of mass appears to be synchronized with the motion of the hand and with proportional amplitude. Moreover, the joint rotation patterns can be accounted for by a single functional degree of freedom, as shown by principal component analysis. It is also suggested that recent findings in motor imagery support the idea that the PMP network may represent the motor cognitive part of synergy formation, uncontaminated by the effect of execution.

Learning, Retention, and Slacking: A Model of the Dynamics of Recovery in Robot Therapy

Quantitative descriptions of the process of recovery of motor functions in impaired subjects during robot-assisted exercise might help to understand how to use these devices to make recovery faster and more effective. Linear dynamical models have been used to describe the dynamics of sensorimotor adaptation. Here, we extend this formalism to characterize the neuromotor recovery process. We focus on a robot therapy experiment that involved chronic stroke survivors, based on a robot-assisted arm extension task. The results suggest that modeling the recovery process with dynamical models is feasible, and could allow predicting the long-term outcome of a robot-assisted rehabilitation treatment.