On Time Optimization of Centroidal Momentum Dynamics

TL;DR

This paper introduces two convex relaxation methods for time-optimized centroidal momentum dynamics, enabling real-time, dynamically consistent motion planning for humanoid robots in multi-contact scenarios.

Contribution

It presents novel convex relaxations based on trust regions and soft constraints that allow efficient, real-time timing optimization in centroidal momentum dynamics planning.

Findings

Convex relaxations achieve solutions close to original non-convex problem.

Timing optimization improves motion planning flexibility.

Approach demonstrated in multi-contact humanoid robot scenarios.

Abstract

Recently, the centroidal momentum dynamics has received substantial attention to plan dynamically consistent motions for robots with arms and legs in multi-contact scenarios. However, it is also non convex which renders any optimization approach difficult and timing is usually kept fixed in most trajectory optimization techniques to not introduce additional non convexities to the problem. But this can limit the versatility of the algorithms. In our previous work, we proposed a convex relaxation of the problem that allowed to efficiently compute momentum trajectories and contact forces. However, our approach could not minimize a desired angular momentum objective which seriously limited its applicability. Noticing that the non-convexity introduced by the time variables is of similar nature as the centroidal dynamics one, we propose two convex relaxations to the problem based on trust regions and soft constraints. The resulting approaches can compute time-optimized dynamically consistent trajectories sufficiently fast to make the approach realtime capable. The performance of the algorithm is demonstrated in several multi-contact scenarios for a humanoid robot. In particular, we show that the proposed convex relaxation of the original problem finds solutions that are consistent with the original non-convex problem and illustrate how timing optimization allows to find motion plans that would be difficult to plan with fixed timing.