Constraint-Aware Diffusion Models for Trajectory Optimization
Anjian Li, Zihan Ding, Adji Bousso Dieng, Ryne Beeson
TL;DR
This work addresses constraint violations in diffusion‑based trajectory optimization by introducing a constraint‑aware diffusion model with a hybrid loss that directly penalizes constraint violations. The method augments the DDPM framework with a one‑step reverse sampling and a violation term $V(x;y)$, normalized by the groundtruth violation $\mu_{vio\_GT}$, to steer learned samples toward feasibility while preserving the underlying data distribution $p(x^*|y)$. Grounded in an NLP formulation $J(x;y)$ with constraints $g_i(x;y)\le 0$ and $h_j(x;y)=0$, the approach is trained on locally optimal feasible solutions $x^*$ obtained via SNOPT and evaluated on tabletop manipulation and two‑car reach‑avoid tasks, showing reduced constraint violations and samples close to local optima. The results suggest practical gains in sample quality for warm‑starting numerical trajectory optimizers, with the primary limitation being training time due to constraint evaluation, motivating future efficiency improvements and data augmentation strategies.
Abstract
The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint violations such as unmet goals or collisions. This paper presents a novel constraint-aware diffusion model for trajectory optimization. We introduce a novel hybrid loss function for training that minimizes the constraint violation of diffusion samples compared to the groundtruth while recovering the original data distribution. Our model is demonstrated on tabletop manipulation and two-car reach-avoid problems, outperforming traditional diffusion models in minimizing constraint violations while generating samples close to locally optimal solutions.