Modeling and Control of Legged Locomotion via Switching Max-Plus Systems

We present a class of gait generation and control algorithms based on the Switching Max-Plus modeling framework that allow for the synchronization of multiple legs of walking robots. Transitions between stance and swing phases of each leg are modeled as discrete events in a system described by max-plus-linear state equations. Different gaits can be systematically generated and interleaved during motion by switching between different system matrices. We show that such gait switching can be done in an optimal way, minimizing the tip leg velocity variation for all legs simultaneously touching the ground.