Equality Constrained Diffusion for Direct Trajectory Optimization

2024-10-02

American Control Conference

AI Summary

Existing diffusion-based trajectory optimization methods are limited to shooting formulations and cannot handle general nonlinear equality constraints, hindering flexible state constraints, robust numerical solving, and easy initialization. This paper introduces the first diffusion model framework for direct trajectory optimization, enabling general nonlinear equality constraints. Our method comprises three core innovations: (i) constraint-aware diffusion sampling, (ii) an implicit-gradient-based constraint projection mechanism, and (iii) score-matching-based constrained generative modeling. Crucially, the approach explicitly enforces dynamic feasibility without relying on forward dynamics rollouts. Evaluated on multiple nonlinear control benchmarks, it significantly improves expressiveness of state constraints, numerical robustness, and tolerance to poor initial guesses—achieving end-to-end, direct-method trajectory optimization.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Handling nonlinear equality constraints in diffusion-based trajectory optimization
• Enabling direct trajectory optimization with dynamic feasibility constraints
• Extending diffusion methods beyond shooting approaches to support constraints

Innovation

• Equality constrained diffusion for trajectory optimization
• Enforcing dynamic feasibility through nonlinear constraints
• Direct trajectory optimization using diffusion-based methods