Safe Model Predictive Diffusion with Shielding

TL;DR

Safe MPD introduces a training-free diffusion planner with an integrated safety shield to guarantee kinodynamic feasibility and safety during trajectory optimization. The method combines Model Predictive Diffusion for feasible sampling with Shielded Rollout to enforce safety via backup policies, yielding substantial gains in sample efficiency and safety guarantees. Empirical results on non-convex tractor-trailer parking tasks show near-perfect success rates, zero safety violations, and sub-second planning times, even without task-specific hyperparameter tuning. The approach scales to complex dynamics and integrates smoothly with existing planning stacks, enabling real-time, safe robotic motion in challenging environments.

Abstract

Generating safe, kinodynamically feasible, and optimal trajectories for complex robotic systems is a central challenge in robotics. This paper presents Safe Model Predictive Diffusion (Safe MPD), a training-free diffusion planner that unifies a model-based diffusion framework with a safety shield to generate trajectories that are both kinodynamically feasible and safe by construction. By enforcing feasibility and safety on all samples during the denoising process, our method avoids the common pitfalls of post-processing corrections, such as computational intractability and loss of feasibility. We validate our approach on challenging non-convex planning problems, including kinematic and acceleration-controlled tractor-trailer systems. The results show that it substantially outperforms existing safety strategies in success rate and safety, while achieving sub-second computation times.

Figures (3)

• Figure 1: Overview of the Safe Model Predictive Diffusion (Safe MPD$^{\text{\tiny{*}}}$) algorithm. (a) The forward process gradually adds noise to an optimal trajectory. (b) Reverse (denoising) process with shielded rollout: from the current noisy estimate $Y^{(i)}$, $K$ perturbed candidates are drawn; some are initially unsafe (e.g., collisions or jackknifing for the tractor-trailer). Shielded rollout transforms each candidate into a kinodynamically feasible and safe trajectory, after which weighted averaging and score ascent update $Y^{(i-1)}$.
• Figure 2: Illustration of an acceleration-controlled tractor-trailer system.
• Figure 3: Visualization of the diffusion process and final trajectory execution. (a) Snapshots of the diffusion trajectory for a kinematic tractor-trailer at different denoising steps, showing the refinement from a random, high-cost path (e.g., $i=100$) to an optimized solution at the final step ($i=0$). (b) Final trajectory with the tractor–trailer footprint rendered along the path; despite tight clearances, neither hitch-angle nor collision constraints are violated.

Theorems & Definitions (9)

• Remark 1
• Remark 2
• Definition 1: Controlled-Invariant Set
• Definition 2: Invariance Policy
• Definition 3: Recovery Policy
• Definition 4: Valid
• Remark 3
• Theorem 1: Shielded-Rollout$^{\text{\tiny{*}}}$
• proof