Online Walking Motion Generation with Automatic Footstep Placement

Abstract

The goal of this paper is to demonstrate the capacity of Model Predictive Control to generate stable walking motions without the use of predefined foot steps. Building up on well-known Model Predictive Control schemes for walking motion generation, we show that a minimal modification of these schemes allows designing an online walking motion generator which can track a given reference speed of the robot and decide automatically the foot step placement. Simulation results are proposed on the HRP-2 humanoid robot, showing a significant improvement over previous approaches.

Optimized humanoid walking with soft soles

“…The force distribution constraint between feet in DSP is detailed in AppendixB. For λ = 1 in (4) we obtain a walking pattern close to [7][9], while for λ = 0 we obtain a ZMP trajectory similar to [8]. Intermediate values of λ give compromises between the two extreme behaviors.…”

“…Several works formulate the walking gait as an optimization problem [7][8] [9]. They use an inverted pendulum model with a point mass to study feet convex-hull ZMP and not the whole ZMP trajectory of each foot.…”

“…i coefficients are known from (7). This is the difference between (9) and the system of equations in [10].…”

Vision based persistent localization of a humanoid robot for locomotion tasks

“…Herdt et al (2010) cope with this problem by regulating the velocity of the CoM to a desired mean valueẋ r . Considering the current position of the foot on the ground, x c (k), the positions of the following steps x f (k) are adapted automatically using the selection matrices S c (k + 678 P.A.…”

“…Thus, they are linear with respect to the position of the foot step but nonlinear with respect to its orientation. As a consequence, there is no feasible way to solve QP for reorienting the foot steps (Herdt et al, 2010). Algorithm 1.…”