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.

翻译：近年来，基于扩散的生成模型在图像和自然语言处理领域取得的成功，激发了将其应用于非线性控制系统轨迹优化的研究兴趣。然而，现有方法无法处理直接轨迹优化所必需的非线性等式约束。因此，当前基于扩散的轨迹优化器仅限于射击法，其中非线性动力学通过前向推演来保证。这使其无法享受直接方法的诸多优势，包括灵活的状态约束、降低的数值敏感性以及便捷的初始猜测设定。本文提出了一种支持等式约束的基于扩散的优化方法。这使得我们能够执行直接轨迹优化，通过约束而非推演来保证动态可行性。据我们所知，这是首个支持直接轨迹优化所需通用非线性等式约束的基于扩散的优化算法。