Legged Elastic Multibody Systems: Adjusting Limit Cycles to Close-To-Optimal Energy Efficiency

Abstract

Compliant elements in robotic systems can strongly increase the energy efficiency of highly dynamic periodic motions with large energy consumption such as jumping. Their control is a challenging task for multi-joint systems. It is typically solved either by model-based approaches that hardly adjust to varying mechanical conditions or by algorithms that make strongly limited use of mechanical resonance conditions. Here, we apply numerical optimal control theory to demonstrate that close-to-optimal energy-efficient movements can be induced from a one-dimensional sub-manifold in jumping systems that show nonlinear hybrid dynamics. Linear weights transform sensory information into this one-dimensional controller space and reverse transform one-dimensional motor signals back into the multi-dimensional joint space. In Monte-Carlo-based simulations and experiments, we show that an algorithm that we derived previously can extract these weights online from sensory information about joint positions of a moving system. The algorithm is computationally cheap, modular, and adjusts to varying mechanical conditions. Our results demonstrate that it reduces the problem of energy-efficient control of multiple compliant joints that move with high synchronicity to a low-dimensional task.