Recently, diffusion models have gained popularity and attention in trajectory optimization due to their capability of modeling multi-modal probability distributions. However, addressing nonlinear equality constraints, i.e, dynamic feasibility, remains a great challenge in diffusion-based trajectory optimization. Recent diffusion-based trajectory optimization frameworks rely on a single-shooting style approach where the denoised control sequence is applied to forward propagate the dynamical system, which cannot explicitly enforce constraints on the states and frequently leads to sub-optimal solutions. In this work, we propose a novel direct trajectory optimization approach via model-based diffusion, which directly generates a sequence of states. To ensure dynamic feasibility, we propose a gradient-free projection mechanism that is incorporated into the reverse diffusion process. Our results show that, compared to a recent state-of-the-art baseline, our approach leads to zero dynamic feasibility error and approximately 4x higher success rate in a quadrotor waypoint navigation scenario involving dense static obstacles.

翻译：近年来，扩散模型因其能够建模多模态概率分布而在轨迹优化领域受到广泛关注。然而，处理非线性等式约束（即动态可行性）仍然是基于扩散的轨迹优化中的一个巨大挑战。现有的基于扩散的轨迹优化框架通常依赖于单次射击式方法，其中去噪后的控制序列被用于前向传播动力学系统，这种方法无法显式地对状态施加约束，并经常导致次优解。在本工作中，我们提出了一种新颖的基于模型的扩散直接轨迹优化方法，该方法直接生成状态序列。为确保动态可行性，我们提出了一种无梯度投影机制，并将其整合到反向扩散过程中。我们的结果表明，与近期的一种先进基线方法相比，在涉及密集静态障碍物的四旋翼飞行器航点导航场景中，我们的方法实现了零动态可行性误差，并将成功率提高了约四倍。