首次实现带非线性等式约束的扩散优化，支持直接轨迹规划。
Equality Constrained Diffusion for Direct Trajectory Optimization
- 用等式约束替代前向滚动，实现直接轨迹优化
- 首次支持通用非线性等式约束的扩散优化算法
- 适合需精确动力学约束的复杂系统控制任务
基于扩散模型在图像和自然语言处理中的成功，扩散模型在非线性控制系统轨迹优化中的应用受到关注。然而，现有方法无法处理直接轨迹优化所需的非线性等式约束，因此当前扩散优化器仅限于射击法（shooting methods），通过前向滚动强制动力学约束。这使得直接方法的优势——如灵活的状态约束、降低数值敏感性、易于指定初始猜测——无法实现。本文提出一种带有等式约束的扩散优化方法，使直接轨迹优化成为可能，通过约束而非滚动来保证动力学可行性。据我们所知，这是首个支持直接轨迹优化所需一般非线性等式约束的扩散优化算法。
原文摘要 · Abstract (English)
The recent success of diffusion-based generative models in image and natural language processing has ignited interest in diffusion-based trajectory optimization for nonlinear control systems. Existing methods cannot, however, handle the nonlinear equality constraints necessary for direct trajectory optimization. As a result, diffusion-based trajectory optimizers are currently limited to shooting methods, where the nonlinear dynamics are enforced by forward rollouts. This precludes many of the benefits enjoyed by direct methods, including flexible state constraints, reduced numerical sensitivity, and easy initial guess specification. In this paper, we present a method for diffusion-based optimization with equality constraints. This allows us to perform direct trajectory optimization, enforcing dynamic feasibility with constraints rather than rollouts. To the best of our knowledge, this is the first diffusion-based optimization algorithm that supports the general nonlinear equality constraints required for direct trajectory optimization.
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