Analyses of experimental data acquired from humans and other vertebrates have suggested that motor commands may emerge from the combination of a limited set of modules. While many studies have focused on physiological aspects of this modularity, in this paper we propose an investigation of its theoretical foundations. We consider the problem of controlling a planar kinematic chain, and we restrict the admissible actuations to linear combinations of a small set of torque profiles (i.e., motor synergies). This scheme is equivalent to the time-varying synergy model, and it is formalized by means of the dynamic response decomposition (DRD). DRD is a general method to generate open-loop controllers for a dynamical system to solve desired tasks, and it can also be used to synthesize effective motor synergies. We show that a control architecture based on synergies can greatly reduce the dimensionality of the control problem, while keeping a good performance level. Our results suggest that in order to realize an effective and low-dimensional controller, synergies should embed features of both the desired tasks and the system dynamics. These characteristics can be achieved by defining synergies as solutions to a representative set of task instances. The required number of synergies increases with the complexity of the desired tasks. However, a possible strategy to keep the number of synergies low is to construct solutions to complex tasks by concatenating synergy-based actuations associated to simple point-to-point movements, with a limited loss of performance. Ultimately, this work supports the feasibility of controlling a non-linear dynamical systems by linear combinations of basic actuations, and illustrates the fundamental relationship between synergies, desired tasks and system dynamics.
A computational analysis of motor synergies by dynamic response decomposition
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