Optimal trajectory design is computationally expensive for nonlinear and high-dimensional dynamical systems. The challenge arises from the non-convex nature of the optimization problem with multiple local optima, which usually requires a global search. Traditional numerical solvers struggle to find diverse solutions efficiently without appropriate initial guesses. In this paper, we introduce DiffuSolve, a general diffusion model-based solver for non-convex trajectory optimization. An expressive diffusion model is trained on pre-collected locally optimal solutions and efficiently samples initial guesses, which then warm-starts numerical solvers to fine-tune the feasibility and optimality. We also present DiffuSolve+, a novel constrained diffusion model with an additional loss in training that further reduces the problem constraint violations of diffusion samples. Experimental evaluations on three tasks verify the improved robustness, diversity, and a 2$\times$ to 11$\times$ increase in computational efficiency with our proposed method, which generalizes well to trajectory optimization problems of varying challenges.

翻译：对于非线性和高维动力系统，最优轨迹设计在计算上代价高昂。这一挑战源于优化问题的非凸性及其多重局部最优解，通常需要进行全局搜索。传统数值求解器在缺乏合适初始猜测的情况下，难以高效地找到多样化解。本文提出DiffuSolve，一种基于扩散模型的通用非凸轨迹优化求解器。该方法在预先收集的局部最优解上训练一个表达能力强的扩散模型，以高效采样初始猜测值，进而热启动数值求解器以微调解的可行性与最优性。我们还提出了DiffuSolve+，这是一种新颖的约束扩散模型，通过在训练中添加额外损失函数，进一步降低扩散样本对问题约束的违反程度。在三个任务上的实验评估验证了所提方法在鲁棒性、多样性方面的提升，以及2倍至11倍的计算效率增益，且该方法能很好地泛化至具有不同挑战性的轨迹优化问题。