Functional significance of stiffness in adaptation of multijoint arm movements to stable and unstable dynamics.

This study compared the mechanisms of adaptation to stable and unstable dynamics from the perspective of changes in joint mechanics. Subjects were instructed to make point to point movements in force fields generated by a robotic manipulandum which interacted with the arm in either a stable or an unstable manner. After subjects adjusted to the initial disturbing effects of the force fields they were able to produce normal straight movements to the target. In the case of the stable interaction, subjects modified the joint torques in order to appropriately compensate for the force field. No change in joint torque or endpoint force was required or observed in the case of the unstable interaction. After adaptation, the endpoint stiffness of the arm was measured by applying displacements to the hand in eight different directions midway through the movements. This was compared to the stiffness measured similarly during movements in a null force field. After adaptation, the endpoint stiffness under both the stable and unstable dynamics was modified relative to the null field. Adaptation to unstable dynamics was achieved by selective modification of endpoint stiffness in the direction of the instability. To investigate whether the change in endpoint stiffness could be accounted for by change in joint torque or endpoint force, we estimated the change in stiffness on each trial based on the change in joint torque relative to the null field. For stable dynamics the change in endpoint stiffness was accurately predicted. However, for unstable dynamics the change in endpoint stiffness could not be reproduced. In fact, the predicted endpoint stiffness was similar to that in the null force field. Thus, the change in endpoint stiffness seen after adaptation to stable dynamics was directly related to changes in net joint torque necessary to compensate for the dynamics in contrast to adaptation to unstable dynamics, where a selective change in endpoint stiffness occurred without any modification of net joint torque.

Different mechanisms involved in adaptation to stable and unstable dynamics.

Recently, we demonstrated that humans can learn to make accurate movements in an unstable environment by controlling magnitude, shape, and orientation of the endpoint impedance. Although previous studies of human motor learning suggest that the brain acquires an inverse dynamics model of the novel environment, it is not known whether this control mechanism is operative in unstable environments. We compared learning of multijoint arm movements in a "velocity-dependent force field" (VF), which interacted with the arm in a stable manner, and learning in a "divergent force field" (DF), where the interaction was unstable. The characteristics of error evolution were markedly different in the 2 fields. The direction of trajectory error in the DF alternated to the left and right during the early stage of learning; that is, signed error was inconsistent from movement to movement and could not have guided learning of an inverse dynamics model. This contrasted sharply with trajectory error in the VF, which was initially biased and decayed in a manner that was consistent with rapid feedback error learning. EMG recorded before and after learning in the DF and VF are also consistent with different learning and control mechanisms for adapting to stable and unstable dynamics, that is, inverse dynamics model formation and impedance control. We also investigated adaptation to a rotated DF to examine the interplay between inverse dynamics model formation and impedance control. Our results suggest that an inverse dynamics model can function in parallel with an impedance controller to compensate for consistent perturbing force in unstable environments.

Adaptation to stable and unstable dynamics achieved by combined impedance control and inverse dynamics model.

This study compared adaptation in novel force fields where trajectories were initially either stable or unstable to elucidate the processes of learning novel skills and adapting to new environments. Subjects learned to move in a null force field (NF), which was unexpectedly changed either to a velocity-dependent force field (VF), which resulted in perturbed but stable hand trajectories, or a position-dependent divergent force field (DF), which resulted in unstable trajectories. With practice, subjects learned to compensate for the perturbations produced by both force fields. Adaptation was characterized by an initial increase in the activation of all muscles followed by a gradual reduction. The time course of the increase in activation was correlated with a reduction in hand-path error for the DF but not for the VF. Adaptation to the VF could have been achieved solely by formation of an inverse dynamics model and adaptation to the DF solely by impedance control. However, indices of learning, such as hand-path error, joint torque, and electromyographic activation and deactivation suggest that the CNS combined these processes during adaptation to both force fields. Our results suggest that during the early phase of learning there is an increase in endpoint stiffness that serves to reduce hand-path error and provides additional stability, regardless of whether the dynamics are stable or unstable. We suggest that the motor control system utilizes an inverse dynamics model to learn the mean dynamics and an impedance controller to assist in the formation of the inverse dynamics model and to generate needed stability.

Generalization in Adaptation to Stable and Unstable Dynamics

Humans skillfully manipulate objects and tools despite the inherent instability. In order to succeed at these tasks, the sensorimotor control system must build an internal representation of both the force and mechanical impedance. As it is not practical to either learn or store motor commands for every possible future action, the sensorimotor control system generalizes a control strategy for a range of movements based on learning performed over a set of movements. Here, we introduce a computational model for this learning and generalization, which specifies how to learn feedforward muscle activity in a function of the state space. Specifically, by incorporating co-activation as a function of error into the feedback command, we are able to derive an algorithm from a gradient descent minimization of motion error and effort, subject to maintaining a stability margin. This algorithm can be used to learn to coordinate any of a variety of motor primitives such as force fields, muscle synergies, physical models or artificial neural networks. This model for human learning and generalization is able to adapt to both stable and unstable dynamics, and provides a controller for generating efficient adaptive motor behavior in robots. Simulation results exhibit predictions consistent with all experiments on learning of novel dynamics requiring adaptation of force and impedance, and enable us to re-examine some of the previous interpretations of experiments on generalization. © 2012 Kadiallah et al.

Learning the dynamics of the external world: Brain inspired learning for robotic applications

Humans have exceptional abilities to learn new skills, manipulate tools and objects, and interact with our environment. In order to be successful at these tasks, our brain has become exceptionally well adapted to learning to deal not only with the complex dynamics of our own limbs but also with novel dynamics in the external world. While learning of these dynamics includes learning the complex time-varying forces at the end of limbs through the updating of internal models, it must also include learning the appropriate mechanical impedance in order to stabilize both the limb and any objects contacted in the environment. This article reviews the field of human learning by examining recent experimental evidence about adaptation to novel unstable dynamics and explores how this knowledge about the brain and neuro-muscular system can expand the learning capabilities of robotics and prosthetics. © 2006.

How are internal models of unstable tasks formed?

The results of recent studies suggest that humans can form internal models that they use in a feedforward manner to compensate for both stable and unstable dynamics. To examine how internal models are formed, we performed adaptation experiments in novel dynamics, and measured the endpoint force, trajectory and EMG during learning. Analysis of reflex feedback and change of feedforward commands between consecutive trials suggested a unified model of motor learning, which can coherently unify the learning processes observed in stable and unstable dynamics and reproduce available data on motor learning. To our knowledge, this algorithm, based on the concurrent minimization of (reflex) feedback and muscle activation, is also the first nonlinear adaptive controller able to stabilize unstable dynamics.

Impedance control balances stability with metabolically costly muscle activation.

Humans are able to stabilize their movements in environments with unstable dynamics by selectively modifying arm impedance independently of force and torque. We further investigated adaptation to unstable dynamics to determine whether the CNS maintains a constant overall level of stability as the instability of the environmental dynamics is varied. Subjects performed reaching movements in unstable force fields of varying strength, generated by a robotic manipulator. Although the force fields disrupted the initial movements, subjects were able to adapt to the novel dynamics and learned to produce straight trajectories. After adaptation, the endpoint stiffness of the arm was measured at the midpoint of the movement. The stiffness had been selectively modified in the direction of the instability. The stiffness in the stable direction was relatively unchanged from that measured during movements in a null force field prior to exposure to the unstable force field. This impedance modification was achieved without changes in force and torque. The overall stiffness of the arm and environment in the direction of instability was adapted to the force field strength such that it remained equivalent to that of the null force field. This suggests that the CNS attempts both to maintain a minimum level of stability and minimize energy expenditure.

Impedance control is tuned to multiple directions of movement

Humans are able to learn tool-handling tasks, such as carving, demonstrating their competency to make and vary the direction of movements in unstable environments. It has been shown that when a single reaching movement is repeated in unstable dynamics, the central nervous system (CNS) learns an impedance internal model to compensate for the environment instability. However, there is still no explanation for how humans can learn to move in various directions in such environments. In this study, we investigated whether and how humans compensate for instability while learning two different reaching movements simultaneously. Results show that when performing movements in two different directions, separated by a 35° angle, the CNS was able to compensate for the unstable dynamics. After adaptation, the force was found to be similar to the free movement condition, but stiffness increased in the direction of instability, specifically for each direction of movement. Our findings suggest that the CNS either learned an internal model generalizing over different movements, or alternatively that it was able to switch between specific models acquired simultaneously. © 2008 IEEE.

Central representation of dynamics when manipulating handheld objects.

To explore the neural mechanisms related to representation of the manipulation dynamics of objects, we performed whole-brain fMRI while subjects balanced an object in stable and highly unstable states and while they balanced a rigid object and a flexible object in the same unstable state, in all cases without vision. In this way, we varied the extent to which an internal model of the manipulation dynamics was required in the moment-to-moment control of the object's orientation. We hypothesized that activity in primary motor cortex would reflect the amount of muscle activation under each condition. In contrast, we hypothesized that cerebellar activity would be more strongly related to the stability and complexity of the manipulation dynamics because the cerebellum has been implicated in internal model-based control. As hypothesized, the dynamics-related activation of the cerebellum was quite different from that of the primary motor cortex. Changes in cerebellar activity were much greater than would have been predicted from differences in muscle activation when the stability and complexity of the manipulation dynamics were contrasted. On the other hand, the activity of the primary motor cortex more closely resembled the mean motor output necessary to execute the task. We also discovered a small region near the anterior edge of the ipsilateral (right) inferior parietal lobule where activity was modulated with the complexity of the manipulation dynamics. We suggest that this is related to imagining the location and motion of an object with complex manipulation dynamics.

Flexible representations of dynamics are used in object manipulation.

To manipulate an object skillfully, the brain must learn its dynamics, specifying the mapping between applied force and motion. A fundamental issue in sensorimotor control is whether such dynamics are represented in an extrinsic frame of reference tied to the object or an intrinsic frame of reference linked to the arm. Although previous studies have suggested that objects are represented in arm-centered coordinates [1-6], all of these studies have used objects with unusual and complex dynamics. Thus, it is not known how objects with natural dynamics are represented. Here we show that objects with simple (or familiar) dynamics and those with complex (or unfamiliar) dynamics are represented in object- and arm-centered coordinates, respectively. We also show that objects with simple dynamics are represented with an intermediate coordinate frame when vision of the object is removed. These results indicate that object dynamics can be flexibly represented in different coordinate frames by the brain. We suggest that with experience, the representation of the dynamics of a manipulated object may shift from a coordinate frame tied to the arm toward one that is linked to the object. The additional complexity required to represent dynamics in object-centered coordinates would be economical for familiar objects because such a representation allows object use regardless of the orientation of the object in hand.