Analytical Center of Mass Trajectory Generation for Humanoid Walking and Running with Continuous Gait Transitions

We present an analytical trajectory generation framework for the combined computation of multiple walking and running sequences with continuous gait transitions. This framework builds on the Divergent Component of Motion (DCM)-based walking algorithm and the spline-based trajec-tory generation of the Biologically Inspired Deadbeat (BID) control for running. We describe our approach to generating closed-form center of mass (CoM) trajectories for walking and running by alternately linking the two gaits through continuity constraints. Thereby, we distinguish between vertical and horizontal planning. The vertical trajectory is computed in a forward recursion from the first to the last gait sequence. Due to the coupling of the gait sequences in the horizontal direction, we show the efficient generation of the horizontal CoM trajectory in a single matrix calculation. Subsequently, we unify the control strategies using a DCM tracking controller for the complete trajectory and integrate the proposed framework into an inverse dynamics-based whole-body controller. Finally, the presented approaches are validated in simulations with the humanoid robot Toro.