Quadrupedal walking motion and footstep placement through Linear Model Predictive Control

Abstract

The present work addresses the generation of a walking gait with automatic footstep placement for a quadrupedal robot, within a Linear Model Predictive Control framework. Existing work has shown how this is only possible within a non-convex programming framework, finding a solution of which is well-known to be very hard. We propose a way to formulate the joint optimization problem as an approximate QP with linear constraints, whose global optimum can be quickly found with off-the-shelf solvers. More specifically, this is done by introducing auxiliary states and control inputs, each of which is subject to linear constraints that are inspired from the literature on bipedal locomotion. Finally, we validate our method on the CENTAURO robot, a hybrid wheeled-legged quadruped with a humanoid upper-body.