Reduction-based control with application to three-dimensional bipedal walking robots

This paper develops the concept of reduction-based control, which is founded on a controlled form of geometric reduction known as functional Routhian reduction. We introduce a geometric property of general serial-chain robots termed recursive cyclicity, leading to our presentation of the subrobot theorem. This shows that reduction-based control can arbitrarily reduce the dimensionality of any serial-chain robot, so that it may be controlled as a simpler "subrobot" while separately controlling the divided coordinates through their conserved momenta. This method is applied to construct stable directional 3-D walking gaits for a 4-d.o.f. hipped bipedal robot. The walker's sagittal-plane subsystem can be decoupled from its yaw and lean modes, and on this planar subsystem we use passivity-based control to construct limit cycles on flat ground. Due to the controlled reduction, the unstable yaw and lean modes are separately controlled to 2-periodic orbits. We numerically verify the existence of stable 2-periodic limit cycles and demonstrate turning capabilities for the controlled biped.