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

Anjian Li, Zihan Ding, Adji Bousso Dieng, Ryne Beeson

TL;DR

Improved robustness, diversity, and a 2$\times$ to 11$\times$ increase in computational efficiency are verified with the proposed method, which generalizes well to trajectory optimization problems of varying challenges.

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.

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

TL;DR

Improved robustness, diversity, and a 2 to 11 increase in computational efficiency are verified with the proposed method, which generalizes well to trajectory optimization problems of varying challenges.

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 to 11 increase in computational efficiency with our proposed method, which generalizes well to trajectory optimization problems of varying challenges.
Paper Structure (41 sections, 13 equations, 5 figures, 3 tables)

This paper contains 41 sections, 13 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Machine Learning for Optimization.
  4. Diffusion Models.
  5. Diffusion-based Trajectory Generation with Constraints.
  6. Preliminaries
  7. Non-Convex Trajectory Optimization.
  8. Diffusion Probabilistic Model.
  9. Methodology
  10. DiffuSolve Framework
  11. DiffuSolve+ with Constrained Diffusion Model
  12. DiffuSolve+ Training.
  13. Conditional Diffusion Sampling.
  14. Experiment
  15. Task setup
  16. ...and 26 more sections

Figures (5)

  • Figure 1: Three trajectory optimization tasks in our experiments (from left to right): two-car reach-avoid problem; quadrotor navigation problem; cislunar transfer problem. The dimensions of the decision variables are 81, 241, and 64, respectively.
  • Figure 2: The DiffuSolve framework for solving non-convex trajectory optimization problems.
  • Figure 3: In two-car reach-avoid problem: First row: raw samples (no solver); Second row: corresponding solver derived locally optimal and feasible solutions.
  • Figure 4: Diverse trajectory solutions for two-car reach-avoid, quadrotor navigation and cislunar transfer problem with DiffuSolve method, given the same conditional input.
  • Figure 5: The histogram of computational time (including model sampling time and solver time) for different methods to find locally optimal and feasible solutions.