EB-MBD: Emerging-Barrier Model-Based Diffusion for Safe Trajectory Optimization in Highly Constrained Environments

TL;DR

This work addresses the degradation of Model-Based Diffusion (MBD) when solving constrained trajectory optimization by integrating an interior-point–inspired, time-varying barrier into the diffusion target distribution. The Emerging Barrier Model-Based Diffusion (EB-MBD) augments $p(x) \propto \exp(-J(x)/\lambda)$ with a barrier term $b(x,s) = -\mu_s \log(g(x) + c_s)$ so that feasible samples are progressively encouraged as the diffusion proceeds, reducing the incidence of dead samples without costly projections. The authors analyze sampling liveliness and barrier schedules, and demonstrate that EB-MBD outperforms MBD and projection-based methods in 2D obstacle avoidance and a 3D UVMS scenario, delivering lower costs and faster runtimes. The approach enables safer, more reliable diffusion-based trajectory optimization in highly constrained environments, with practical benefits for real-time robotic planning. The work also discusses scheduling trade-offs and limitations, pointing to adaptive barrier strategies as future work to further enhance robustness.

Abstract

We propose enforcing constraints on Model-Based Diffusion by introducing emerging barrier functions inspired by interior point methods. We show that constraints on Model-Based Diffusion can lead to catastrophic performance degradation, even on simple 2D systems due to sample inefficiency in the Monte Carlo approximation of the score function. We introduce Emerging-Barrier Model-Based Diffusion (EB-MBD) which uses progressively introduced barrier constraints to avoid these problems, significantly improving solution quality, without the need for computationally expensive operations such as projections. We analyze the sampling liveliness of samples each iteration to inform barrier parameter scheduling choice. We demonstrate results for 2D collision avoidance and a 3D underwater manipulator system and show that our method achieves lower cost solutions than Model-Based Diffusion, and requires orders of magnitude less computation time than projection based methods.

Figures (7)

• Figure 1: Our proposed method improves the performance of Model Based Diffusion by augmenting the underlying target distribution over the reverse process with a log barrier cost
• Figure 2: Increasing obstacle size in a 2D obstacle avoidance problem leads to catastrophic degradation in performance for MBD as the sampling efficiency of the score estimate suffers
• Figure 3: Evolution of relaxed constraint $g(x) + c_s$, the time-varying cost function and the associated normalized density, for the constraint $|x| \leq 1$
• Figure 4: Left: Planned trajectories are noisy for MBD due to inefficient sampling. Right: EB-MBD successfully generates trajectories from diverse high quality modes, all of which reach the vicinity of the target
• Figure 5: Percentage of samples that violate constraints over diffusion time over various $\kappa$ values. $\kappa$ being too high leads to 100% constraint violations and infeasible outputs

Theorems & Definitions (5)

• Lemma 1
• Corollary 1
• Theorem 1
• proof
• proof