Variable-Impedance Muscle Coordination under Slow-Rate Control Frequencies and Limited Observation Conditions Evaluated through Legged Locomotion

TL;DR

This work investigates how variable-impedance muscle coordination can offload high-frequency control demands in legged locomotion. By implementing a bio-inspired hierarchical controller with a slow-rate high-level network and a low-level muscle-coordination module, and testing under delayed, partial, and substituted observations, the study demonstrates stable locomotion even at 3 Hz control. The results show self-organization around equilibrium-angle trajectories and robustness to observation constraints, supporting the role of morphological computation in simplifying high-level control. These findings offer practical design principles for integrating low-level embodied mechanics with high-level controllers in robotics and inform theories of motor control that emphasize morphology-enabled computation.

Abstract

Human motor control remains agile and robust despite limited sensory information for feedback, a property attributed to the body's ability to perform morphological computation through muscle coordination with variable impedance. However, it remains unclear how such low-level mechanical computation reduces the control requirements of the high-level controller. In this study, we implement a hierarchical controller consisting of a high-level neural network trained by reinforcement learning and a low-level variable-impedance muscle coor dination model with mono- and biarticular muscles in monoped locomotion task. We systematically restrict the high-level controller by varying the control frequency and by introducing biologically inspired observation conditions: delayed, partial, and substituted observation. Under these conditions, we evaluate how the low-level variable-impedance muscle coordination contributes to learning process of high-level neural network. The results show that variable-impedance muscle coordination enables stable locomotion even under slow-rate control frequency and limited observation conditions. These findings demonstrate that the morphological computation of muscle coordination effectively offloads high-frequency feedback of the high-level controller and provide a design principle for the controller in motor control.

Figures (13)

• Figure 1: Proposed bio-inspired hierarchical control architecture. The high-level neural-network controller operates at a slow-rate control frequency with limited observations, while the low-level controller, implemented by variable-impedance muscle coordination, generates torques through mechanical feedback. Morphological computation in the low-level controller simplifies the control requirement of the high-level controller.
• Figure 2: Comparison of controller architectures: (a) Fixed impedance (FI): joint gains are fixed and do not change during learning. (b) Monoarticular variable impedance (MO): each joint stiffness is varied at every time step. (c) Variable impedance muscle coordination (MC): in addition to joint-wise gains, biarticular impedance spanning two joints is varied.
• Figure 3: Monoped locomotion model. The model consists of a torso, thigh, shank, and foot.
• Figure 6: Biped locomotion model. The model consists of a torso, two thighs, and two shanks with no foot.
• Figure 9: Learning curve of monoped locomotion task under nominal observation condition. The slower the control frequency is, the more apparent the advantage of MC and MO becomes.