Optimization-Based Duality Analysis of Velocity and Force in Redundantly Actuated Systems with Application to Gait-Inspired Motion

This study addresses the analysis of velocity–force duality in redundantly actuated systems under actuation constraints. While velocity and force capabilities have typically been evaluated separately, their coupled relationship has not been systematically investigated. To this end, an optimization-based framework is developed to characterize achievable velocity and force along specified directions by incorporating system kinematics and actuator limits. A distributed actuation mechanism is considered as a representative system to demonstrate the proposed formulation. The resulting feasible velocity and force boundaries are interpreted as directional performance limits and are used to examine their intrinsic trade-off. The analysis reveals that velocity and force exhibit complementary characteristics depending on the actuation configuration, providing a basis for performance-oriented selection under task requirements. The proposed framework is further applied to a gait-inspired motion generation problem, where force-oriented characteristics are assigned to the stance phase and velocity-oriented characteristics to the swing phase. The generated motion reflects phase-dependent features consistent with human gait. These results demonstrate that the proposed framework provides a systematic approach for analyzing and utilizing velocity–force duality in redundantly actuated systems.