Rapid Convex Optimization of Centroidal Dynamics using Block Coordinate Descent

TL;DR

This paper introduces a fast, convex optimization method using block coordinate descent for centroidal dynamics in robots, enabling efficient and physically feasible multi-contact motion planning.

Contribution

It exploits the structure of centroidal dynamics to decompose a non-convex problem into convex subproblems, improving speed and practicality over existing methods.

Findings

Achieves over four times faster computation than previous methods.

Produces trajectories with comparable or better cost quality.

Successfully tracks generated motions on a quadruped robot in simulation.

Abstract

In this paper we explore the use of block coordinate descent (BCD) to optimize the centroidal momentum dynamics for dynamically consistent multi-contact behaviors. The centroidal dynamics have recently received a large amount of attention in order to create physically realizable motions for robots with hands and feet while being computationally more tractable than full rigid body dynamics models. Our contribution lies in exploiting the structure of the dynamics in order to simplify the original non-convex problem into two convex subproblems. We iterate between these two subproblems for a set number of iterations or until a consensus is reached. We explore the properties of the proposed optimization method for the centroidal dynamics and verify in simulation that motions generated by our approach can be tracked by the quadruped Solo12. In addition, we compare our method to a recently proposed convexification using a sequence of convex relaxations as well as a more standard interior point method used in the off- the-shelf solver IPOPT to show that our approach finds similar, if not better, trajectories (in terms of cost), and is more than four times faster than both approaches. Finally, compared to previous approaches, we note its practicality due to the convex nature of each subproblem which allows our method to be used with any off-the-shelf quadratic programming solver.