Consensus-based optimization (CBO): Towards Global Optimality in Robotics

TL;DR

This paper introduces consensus-based optimization (CBO) for robotics, providing a globally convergent zero-order method that outperforms existing local optimization techniques in complex trajectory planning scenarios.

Contribution

The paper presents CBO as a novel global optimization approach for robotics, with theoretical guarantees and demonstrated scalability on challenging problems.

Findings

CBO achieves lower costs than existing methods in various trajectory optimization tasks.

CBO guarantees convergence to a global optimum under mild assumptions.

Demonstrated scalability on high-dimensional and underactuated systems.

Abstract

Zero-order optimization has recently received significant attention for designing optimal trajectories and policies for robotic systems. However, most existing methods (e.g., MPPI, CEM, and CMA-ES) are local in nature, as they rely on gradient estimation. In this paper, we introduce consensus-based optimization (CBO) to robotics, which is guaranteed to converge to a global optimum under mild assumptions. We provide theoretical analysis and illustrative examples that give intuition into the fundamental differences between CBO and existing methods. To demonstrate the scalability of CBO for robotics problems, we consider three challenging trajectory optimization scenarios: (1) a long-horizon problem for a simple system, (2) a dynamic balance problem for a highly underactuated system, and (3) a high-dimensional problem with only a terminal cost. Our results show that CBO is able to achieve lower costs with respect to existing methods on all three challenging settings. This opens a new framework to study global trajectory optimization in robotics.