Motion adaptation with motor invariant theory

Bipedal walking is not fully understood. Motion generated from methods employed in robotics literature is stiff and is not nearly as energy efficient as what we observe in nature. In this paper, we propose validity conditions for motion adaptation from biological principles in terms of the topology of the dynamic system. This allows us to provide a closed-form solution to the problem of motion adaptation to environmental perturbations. We define both global and local controllers that improve structural and state stability, respectively. Global control is achieved by coupling the dynamic system with a neural oscillator, which preserves the periodic structure of the motion primitive and ensures stability by entrainment. A group action derived from Lie group symmetry is introduced as a local control that transforms the underlying state space while preserving certain motor invariants. We verify our method by evaluating the stability and energy consumption of a synthetic passive dynamic walker and compare this with motion data of a real walker. We also demonstrate that our method can be applied to a variety of systems.