Generalizations of the capture point to nonlinear center of mass paths and uneven terrain

The classical Capture Point (CP) technique allows biped robots to take protective footsteps in case of a push or other disturbance, but only applies to flat terrain and a horizontally-moving Center of Mass (CoM). This paper generalizes the Capture Point technique to arbitrary terrains and CoM paths. Removing the CoM path constraint leads to an infinite number of Capture Points, each corresponding to a different path. A numerical algorithm is presented that, given an uneven terrain, enumerates Capture Points and their respective CoM trajectories. It is suitable for real-time usage as it produces all capture points in less than a millisecond on a standard PC. Proof-of-concept results are also demonstrated on a humanoid robot in a dynamic simulator.