Trajectory Optimization for Wheeled-Legged Quadrupedal Robots Using Linearized ZMP Constraints

We present a trajectory optimizer for quadrupedal robots with actuated wheels. By solving for angular, vertical, and planar components of the base and feet trajectories in a cascaded fashion and by introducing a novel linear formulation of the zero-moment point balance criterion, we rely on quadratic programming only, thereby eliminating the need for nonlinear optimization routines. Yet, even for gaits containing full flight phases, we are able to generate trajectories for executing complex motions that involve simultaneous driving, walking, and turning. We verified our approach in simulations of the quadrupedal robot ANYmal equipped with wheels, where we are able to run the proposed trajectory optimizer at 50 Hz. To the best of our knowledge, this is the first time that such dynamic motions are demonstrated for wheeled-legged quadrupedal robots using an online motion planner.