  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.
