Pietro Morasso

Human hand impedance characteristics during maintained posture

The present paper examines human hand impedance characteristics, including inertia and viscosity as well as stiffness, in multi-joint arm movements. While a subject maintains a given hand location, small external disturbances are applied to his hand by a manipulandum. The corresponding force-displacement vectors are measured and sampled over time in order to estimate the hand impedance by means of a second-order linear model. The experimental results in different subjects and hand locations are summarized as follows: (1) the estimated inertia matrices of the human hand well agrees with computed values using a twojoint arm model, (2) spatial variations of the stiffness ellipses are consistent with the experimental results of Mussa-Ivaldi et al. (1985), (3) hand stiffness and viscosity increase with the grip force of the subject, and (4) viscosity and stiffness ellipses tend to have similar orientation. The accuracy of the impedance estimation method is validated with a mechanical spring-mass system with known parameters.

Trajectory formation and handwriting: A computational model

This paper proposes a computational model for different aspects of trajectory formation, from point-to-point movements to handwriting. The proposed model is based on a mechanism of composition of basic curve elements (strokes) which separates the spatial and the temporal aspects of trajectory formation. At the same time, the model suggests a method for storing and describing arm movements, as a list of stroke descriptors. Experimental trajectories were digitized and analyzed with regard to several types of movements: i) point-to-point trajectories, ii) closed trajectories, iii) trajectories with inflection points, iv) spiral-like trajectories, v) handwritten trajectories. Velocity and curvature profiles were computed for the trajectories and the model was fitted to the data. The implications of the model and its “credibility” in the general context of motor control are discussed.

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.

Three dimensional arm trajectories

Planar arm trajectories are characterized by a segmentation of the hand velocity profile and by a coupling between shape and speed. The question addressed in this paper is whether such coupling, observed in two dimensions, still holds in three dimensions. This matter was investigated experimentally by recording three dimensional “aimless” movements of the arm, particularly three dimensional scribbles, and the answer suggested by the experimental data is that only the “bending” of the trajectory is coupled with speed, whereas the “twisting” is independent of speed. The same behaviour was also found to characterize a computational model of trajectory formation which is based on the spatial composition of chains of planar strokes, overlapped in time.

Self-organizing body schema for motor planning

Abstract This article presents a distributed computational architecture for the motor planning functions of the posterior parietal cortex, which is organized as a computational map and combines a paradigm of self-organization (for building robust and coherent maps of the different motor spaces) with an attractor dynamics (for run-time integration of task constraints). The model, named SO-BoS (self-organizing body-schema), is illustrated with simple simulation results.

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.

Bio-mimetic trajectory generation of robots via artificial potential field with time base generator

This paper proposes a new trajectory generation method that allows full control of transient behavior, namely, time-to-target and velocity profile, based on the artificial potential field approach for a real-time robot motion planning problem. Little attention, in fact, has been paid to the temporal aspects of this class of path planning methods. The ability to control the motion time to the target as well as the velocity profile of the generated trajectories, however, is of great interest in real-life applications. In the paper, we argue that such transient behavior should be taken into account within the framework of the artificial potential field approach.