PAD-TRO: Projection-Augmented Diffusion for Direct Trajectory Optimization

2025-10-05

AI Summary

Diffusion models struggle to generate dynamically feasible trajectories that satisfy nonlinear dynamical equality constraints—i.e., exact adherence to system dynamics—during trajectory optimization. Method: This paper proposes a model-driven diffusion approach that directly generates state sequences and integrates a gradient-free dynamical projection mechanism into the reverse diffusion process, enabling end-to-end generation of dynamically feasible trajectories. The method unifies single-step denoising with forward dynamical propagation, and enforces strict compliance with system dynamics via projection-augmented denoising. Contribution/Results: Evaluated on a quadrotor waypoint navigation task in dense obstacle environments, the method achieves zero dynamic feasibility error and improves solution success rate by approximately 4× over the current state-of-the-art. It effectively mitigates suboptimality arising in single-shot frameworks where state constraints cannot be explicitly enforced, thereby significantly enhancing trajectory quality and reliability.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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 feasi- bility, 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.

Problem

• Addresses nonlinear equality constraints in diffusion-based trajectory optimization
• Enhances dynamic feasibility through gradient-free projection mechanism
• Improves success rates in quadrotor navigation with obstacle avoidance

Innovation

• Direct trajectory optimization via model-based diffusion
• Gradient-free projection in reverse diffusion process
• Generates state sequences ensuring dynamic feasibility