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：零阶优化近期在机器人系统最优轨迹与策略设计领域受到广泛关注。然而，现有方法（如MPPI、CEM、CMA-ES）本质上均属局部优化方法，其核心依赖梯度估计。本文首次将基于共识的优化（CBO）引入机器人领域，该算法在温和假设下可保证收敛至全局最优解。我们通过理论分析与示例阐释揭示了CBO与现有方法的本质差异。为展示CBO在机器人问题中的可扩展性，我们设置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；（3）仅含终端代价的高维问题。结果表明，在上述三种困难场景中，CBO相比现有方法均能实现更低的代价函数值。这为机器人全局轨迹优化研究开辟了新范式。