Abstract
The muscle synergy hypothesis is an archetype of the notion of Dimensionality Reduction (DR) occurring in the central nervous system due to modular organization. Toward validating this hypothesis, it is important to understand if muscle synergies can reduce the state-space dimensionality while maintaining task control. In this paper we present a scheme for investigating this reduction utilizing the temporal muscle synergy formulation. Our approach is based on the observation that constraining the control input to a weighted combination of temporal muscle synergies also constrains the dynamic behavior of a system in a trajectory-specific manner. We compute this constrained reformulation of system dynamics and then use the method of system balancing for quantifying the DR; we term this approach as Trajectory Specific Dimensionality Analysis (TSDA). We then investigate the consequence of minimization of the dimensionality for a given task. These methods are tested in simulations on a linear (tethered mass) and a non-linear (compliant kinematic chain) system. Dimensionality of various reaching trajectories is compared when using idealized temporal synergies. We show that as a consequence of this Minimum Dimensional Control (MDC) model, smooth straight-line Cartesian trajectories with bell-shaped velocity profiles emerged as the optima for the reaching task. We also investigated the effect on dimensionality due to adding via-points to a trajectory. The results indicate that a trajectory and synergy basis specific DR of behavior results from muscle synergy control. The implications of these results for the synergy hypothesis, optimal motor control, motor development, and robotics are discussed.
Highlights
There is increasingly a consensus that the solution to the Degree of Freedom (DoF) Problem of Bernstein (1967) involves some form of Dimensionality Reduction (DR) resulting from modularization, it is unclear how exactly this occurs
We compute this constrained reformulation of system dynamics and use the method of system balancing for quantifying the DR; we term this approach as Trajectory Specific Dimensionality Analysis (TSDA)
When using the temporal synergy formulation, the behavior dynamics are dependent on the synergy basis and the weight matrix
Summary
There is increasingly a consensus that the solution to the Degree of Freedom (DoF) Problem of Bernstein (1967) involves some form of Dimensionality Reduction (DR) resulting from modularization, it is unclear how exactly this occurs. Investigators have begin to examine the theoretical basis (Berniker et al, 2009; Alessandro et al, 2012) and the feasibility of experimentally extracted synergies for task control (Ting and Macpherson, 2005; Neptune et al, 2009; McKay and Ting, 2012; de Rugy et al, 2013) We propose that this task-space perspective (Alessandro et al, 2013) must be extended to incorporate the ability of a given set of muscle synergies to reduce behavior dimensionality. In the context of this paper, we denote behavior dimensionality as the Frontiers in Computational Neuroscience www.frontiersin.org
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