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Planning multi-contact motions in a receding horizon fashion requires a valuefunction to guide the planning with respect to the future, e.g., buildingmomentum to traverse large obstacles. Traditionally, the value function isapproximated by computing trajectories in a prediction horizon (never executed)that foresees the future beyond the execution horizon. However, given thenon-convex dynamics of multi-contact motions, this approach is computationallyexpensive. To enable online Receding Horizon Planning (RHP) of multi-contactmotions, we find efficient approximations of the value function. Specifically,we propose a trajectory-based and a learning-based approach. In the former,namely RHP with Multiple Levels of Model Fidelity, we approximate the valuefunction by computing the prediction horizon with a convex relaxed model. Inthe latter, namely Locally-Guided RHP, we learn an oracle to predict localobjectives for locomotion tasks, and we use these local objectives to constructlocal value functions for guiding a short-horizon RHP. We evaluate bothapproaches in simulation by planning centroidal trajectories of a humanoidrobot walking on moderate slopes, and on large slopes where the robot cannotmaintain static balance. Our results show that locally-guided RHP achieves thebest computation efficiency (95\%-98.6\% cycles converge online). Thiscomputation advantage enables us to demonstrate online receding horizonplanning of our real-world humanoid robot Talos walking in dynamic environmentsthat change on-the-fly.

Online Multi-Contact Receding Horizon Planning via Value Function Approximation