Humanoid motion generation and swept volumes: theoretical bounds for safe steps

In the context of humanoid robot footstep planning based on a continuous action set, we conduct an analysis of the sensitivity of a walking pattern generator. Given a variation of an input vector, we calculate a bound on the variation of the volume swept by the robot lower body during the corresponding actions (steps). Since the input vector depends on real parameters, there is an infinite number of possible steps, but the calculated bound permits a sound and safe use of only a finite number of swept volumes to account for all the possible motions. After numerical evaluations, we discuss potential applications.