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

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 multijoint systems. Typical control algorithms are model-based and thus fail to adjust to unexpected mechanical environments or make limited use of mechanical resonance properties. Here, we apply numerical optimal control theory to demonstrate that close-to-optimal energy-efficient movements can be induced from a one-dimensional (1-D) submanifold in jumping systems that show nonlinear hybrid dynamics. Linear weights transform sensory information into this 1-D controller space and reverse transform 1-D motor signals back into the multidimensional 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.