Coupled Control Systems: Periodic Orbit Generation With Application to Quadrupedal Locomotion

A robotic system can be viewed as a collection of lower-dimensional systems that are coupled via reaction forces (Lagrange multipliers) enforcing holonomic constraints. Inspired by this viewpoint, letter presents novel formulation for nonlinear control subject to coupling constraints virtual “coupling” inputs abstractly play the role Lagrange multipliers. The main contribution is process - mirroring solving multipliers in wherein we isolate subsystems free provably encode full-order dynamics from which it was derived. This dimension reduction leveraged optimization problem isolated subsystem yields periodic orbits system. We consider application these ideas systems, decomposed into subsystems. Specifically, view quadruped consisting two bipedal robots, applying framework developed allows gaits (periodic orbits) generated individual biped yielding gait quadrupedal dynamics. demonstrated on robot through simulation and walking experiments rough terrains.