DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization

TL;DR

DiffuSolve introduces a diffusion model-based approach to generate diverse initial guesses for non-convex trajectory optimization, significantly improving efficiency and robustness over traditional methods.

Contribution

The paper presents DiffuSolve, a novel diffusion model-based solver that enhances initial guess diversity and efficiency in non-convex trajectory optimization tasks.

Findings

Achieves 2x to 11x speedup in computation.

Improves robustness and diversity of solutions.

Generalizes well across different trajectory optimization problems.

Abstract

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.