When to make a step? Tackling the timing problem in multi-contact locomotion by TOPP-MPC

We present a model predictive controller (MPC) for multi-contact locomotion where predictive optimizations are realized by time-optimal path parameterization (TOPP). A key feature of this solution is that, contrary to existing planners where step timings are provided as inputs, here the timing between contact switches is computed as output of a fast nonlinear optimization. This is particularly appealing to multi-contact locomotion, where proper timings depend on terrain topology and suitable heuristics are unknown. We show how to formulate legged locomotion as a TOPP problem and demonstrate the behavior of the resulting TOPP-MPC controller in simulations with a model of the HRP-4 humanoid robot.