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Achievable balancing motions for a humanoid robot

We consider the motion-planning problem for a three-link planar pendulum equipped with two actuators. The goal is to create a synchronized periodic motion of all three degrees of freedom, which represents a human-like behavior. It can be orbitally stabilized with some known technique. The approach is motivated by analysis of recorded motion data of human actors and is based on the idea of imposing a set of virtual holonomic constraints to ensure invariance of linear geometric relations among the three generalized coordinates. The main contribution of the paper is a description of the set of achievable periodic motions in terms of amplitudes and periods.