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.

翻译：零阶优化方法近来在机器人系统最优轨迹与策略设计方面受到广泛关注。然而，现有大多数方法（如MPPI、CEM和CMA-ES）本质上是局部性的，因为它们依赖于梯度估计。本文首次将基于共识的优化（CBO）引入机器人学领域，该方法在温和假设下可保证收敛至全局最优解。我们提供了理论分析与示例，以阐明CBO与现有方法之间的本质差异。为验证CBO在机器人问题中的可扩展性，我们研究了三个具有挑战性的轨迹优化场景：（1）简单系统的长时域问题，（2）高度欠驱动系统的动态平衡问题，以及（3）仅含终端成本的高维问题。实验结果表明，在所有三种挑战性设定下，CBO相较于现有方法均能获得更低的成本。这为研究机器人学中的全局轨迹优化开辟了新的框架。