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A computational model of limb impedance control based on principles of internal model uncertainty.

Mitrovic D, Klanke S, Osu R, Kawato M, Vijayakumar S - PLoS ONE (2010)

Bottom Line: In contrast to previously proposed models, our framework predicts a wide range of impedance control patterns, during stationary and adaptive tasks.This indicates that many well-known impedance control phenomena naturally emerge from the first principles of a stochastic optimization process that minimizes for internal model prediction uncertainties, along with energy and accuracy demands.The insights from this computational model could be used to interpret existing experimental impedance control data from the viewpoint of optimality or could even govern the design of future experiments based on principles of internal model uncertainty.

View Article: PubMed Central - PubMed

Affiliation: IPAB, School of Informatics, University of Edinburgh, Edinburgh, United Kingdom. d.mitrovic@ed.ac.uk

ABSTRACT
Efficient human motor control is characterized by an extensive use of joint impedance modulation, which is achieved by co-contracting antagonistic muscles in a way that is beneficial to the specific task. While there is much experimental evidence available that the nervous system employs such strategies, no generally-valid computational model of impedance control derived from first principles has been proposed so far. Here we develop a new impedance control model for antagonistic limb systems which is based on a minimization of uncertainties in the internal model predictions. In contrast to previously proposed models, our framework predicts a wide range of impedance control patterns, during stationary and adaptive tasks. This indicates that many well-known impedance control phenomena naturally emerge from the first principles of a stochastic optimization process that minimizes for internal model prediction uncertainties, along with energy and accuracy demands. The insights from this computational model could be used to interpret existing experimental impedance control data from the viewpoint of optimality or could even govern the design of future experiments based on principles of internal model uncertainty.

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Comparison of the results from stochastic OFC using standard SDN (a) and extended SDN (b).We performed 50 OFC reaching movements (only 20 trajectories plotted) under both stochastic conditions. The shaded green area indicates the region and amount of co-contraction in the extended SDN solution. The plots in (c) quantify the results (mean +/− standard deviation). Left: average joint angle error (absolute values) at final time T = 500 msec. Middle: Joint angle velocity (absolute values) at time T. Right: integrated muscle commands (of both muscles) over trials. The extended SDN outperforms the reaching performance of the standard SDN case at the expense of higher energy consumption.
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pone-0013601-g003: Comparison of the results from stochastic OFC using standard SDN (a) and extended SDN (b).We performed 50 OFC reaching movements (only 20 trajectories plotted) under both stochastic conditions. The shaded green area indicates the region and amount of co-contraction in the extended SDN solution. The plots in (c) quantify the results (mean +/− standard deviation). Left: average joint angle error (absolute values) at final time T = 500 msec. Middle: Joint angle velocity (absolute values) at time T. Right: integrated muscle commands (of both muscles) over trials. The extended SDN outperforms the reaching performance of the standard SDN case at the expense of higher energy consumption.

Mentions: In order to test this hypothesis, we compared two stochastic OFC-LD solutions using internal dynamics models learned from a plant that either exhibits standard (Fig. 3a) or extended SDN (Fig. 3b). The optimal strategy found in this case is to try to avoid large commands u mostly at the end of the movement, where disturbances can not be corrected anymore. Notably, as is evident from Fig. 3a (right), there is still no co-contraction at all. In the extended noise scenario, a solution is found that minimizes the negative effects of the noise by increasing co-contraction at the end of the motion (see Fig. 3b (right)). The results reveal that the extended SDN performs significantly better than the standard SDN in terms of end point accuracy and end point velocity (Fig. 3c). By minimizing the uncertainty in a scenario with a neurophysiologically realistic model of kinematic variability, impedance control naturally emerges from the optimization, producing the characteristic tri-phasic control signals observed in human reaching [37]. Next we present the model's prediction on a set of well known impedance control phenomena in human arm reaching under stationary dynamics conditions.


A computational model of limb impedance control based on principles of internal model uncertainty.

Mitrovic D, Klanke S, Osu R, Kawato M, Vijayakumar S - PLoS ONE (2010)

Comparison of the results from stochastic OFC using standard SDN (a) and extended SDN (b).We performed 50 OFC reaching movements (only 20 trajectories plotted) under both stochastic conditions. The shaded green area indicates the region and amount of co-contraction in the extended SDN solution. The plots in (c) quantify the results (mean +/− standard deviation). Left: average joint angle error (absolute values) at final time T = 500 msec. Middle: Joint angle velocity (absolute values) at time T. Right: integrated muscle commands (of both muscles) over trials. The extended SDN outperforms the reaching performance of the standard SDN case at the expense of higher energy consumption.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2964289&req=5

pone-0013601-g003: Comparison of the results from stochastic OFC using standard SDN (a) and extended SDN (b).We performed 50 OFC reaching movements (only 20 trajectories plotted) under both stochastic conditions. The shaded green area indicates the region and amount of co-contraction in the extended SDN solution. The plots in (c) quantify the results (mean +/− standard deviation). Left: average joint angle error (absolute values) at final time T = 500 msec. Middle: Joint angle velocity (absolute values) at time T. Right: integrated muscle commands (of both muscles) over trials. The extended SDN outperforms the reaching performance of the standard SDN case at the expense of higher energy consumption.
Mentions: In order to test this hypothesis, we compared two stochastic OFC-LD solutions using internal dynamics models learned from a plant that either exhibits standard (Fig. 3a) or extended SDN (Fig. 3b). The optimal strategy found in this case is to try to avoid large commands u mostly at the end of the movement, where disturbances can not be corrected anymore. Notably, as is evident from Fig. 3a (right), there is still no co-contraction at all. In the extended noise scenario, a solution is found that minimizes the negative effects of the noise by increasing co-contraction at the end of the motion (see Fig. 3b (right)). The results reveal that the extended SDN performs significantly better than the standard SDN in terms of end point accuracy and end point velocity (Fig. 3c). By minimizing the uncertainty in a scenario with a neurophysiologically realistic model of kinematic variability, impedance control naturally emerges from the optimization, producing the characteristic tri-phasic control signals observed in human reaching [37]. Next we present the model's prediction on a set of well known impedance control phenomena in human arm reaching under stationary dynamics conditions.

Bottom Line: In contrast to previously proposed models, our framework predicts a wide range of impedance control patterns, during stationary and adaptive tasks.This indicates that many well-known impedance control phenomena naturally emerge from the first principles of a stochastic optimization process that minimizes for internal model prediction uncertainties, along with energy and accuracy demands.The insights from this computational model could be used to interpret existing experimental impedance control data from the viewpoint of optimality or could even govern the design of future experiments based on principles of internal model uncertainty.

View Article: PubMed Central - PubMed

Affiliation: IPAB, School of Informatics, University of Edinburgh, Edinburgh, United Kingdom. d.mitrovic@ed.ac.uk

ABSTRACT
Efficient human motor control is characterized by an extensive use of joint impedance modulation, which is achieved by co-contracting antagonistic muscles in a way that is beneficial to the specific task. While there is much experimental evidence available that the nervous system employs such strategies, no generally-valid computational model of impedance control derived from first principles has been proposed so far. Here we develop a new impedance control model for antagonistic limb systems which is based on a minimization of uncertainties in the internal model predictions. In contrast to previously proposed models, our framework predicts a wide range of impedance control patterns, during stationary and adaptive tasks. This indicates that many well-known impedance control phenomena naturally emerge from the first principles of a stochastic optimization process that minimizes for internal model prediction uncertainties, along with energy and accuracy demands. The insights from this computational model could be used to interpret existing experimental impedance control data from the viewpoint of optimality or could even govern the design of future experiments based on principles of internal model uncertainty.

Show MeSH