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

We present a gait generation framework for multi-legged robots based on max-plus algebra that is endowed with intrinsically safe gait transitions. The time schedule of each foot liftoff and touchdown is modeled by sets of max-plus linear equations. The resulting discrete-event system is translated to continuous time via piecewise constant leg phase velocities; thus, it is compatible with traditional central pattern generator approaches. Different gaits and gait parameters are interleaved by utilizing different max-plus system matrices. We present various gait transition schemes and show that optimal transitions, in the sense of minimizing the stance time variation, allow for constant acceleration and deceleration on legged platforms. The framework presented in this paper relies on a compact representation of the gait space, provides guarantees regarding the transient and steady-state behavior, and results in simple implementations on legged robotic platforms.