PAD-TRO: Projection-Augmented Diffusion for Direct Trajectory Optimization
Jushan Chen, Santiago Paternain
TL;DR
The paper tackles nonlinear equality constraints in diffusion-based trajectory optimization by directly sampling state trajectories and enforcing dynamic feasibility with a gradient-free projection integrated into the reverse diffusion process. It introduces Projection-Augmented Diffusion for Direct Trajectory Optimization (PAD-TRO), combining a bi-level noise schedule across diffusion and trajectory horizons with a gradient-free projection that enforces dynamic feasibility ($p_d$) and obstacle constraints ($p_g$) while balancing trajectory optimality via a Boltzmann-type objective ($p_J(X) \\propto e^{-J/\\lambda}$). The approach yields exact convergence to the goal with zero dynamic feasibility error and substantially higher success rates (≈4x) than a recent diffusion-based baseline in a quadrotor-in-clutter scenario. This work advances robust, constraint-satisfying diffusion-based planning, with potential impact on real-time navigation for high-dimensional robotic systems.
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.