Switching max-plus models for legged locomotion

Reference:
G.A.D. Lopes, R. Babuska, B. De Schutter, and A.J.J. van den Boom, "Switching max-plus models for legged locomotion," Proceedings of the 2009 IEEE International Conference on Robotics and Biomimetics (ROBIO 2009), Guilin, China, pp. 221-226, Dec. 2009.

Abstract:
We present a new class of gait generation and control algorithms based on the Switching Max-Plus modeling framework that allows for the synchronization of multiple legs of walking robots. Transitions between stance and swing phases of each leg are modeled as discrete events on a system described by max-plus-linear state equations. Different gaits and gait parameters can be interleaved by using different system matrices. Switching in max-plus-linear systems offers a powerful collection of modeling, analysis, and control tools that, in particular, allow for safe transitions between different locomotion gaits that may involve breaking/enforcing synchronization or changing the order of leg lift off events. Experimental validation of the proposed algorithms is presented by the implementation of various horse gaits on a simple quadruped robot.