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

We propose enforcing constraints on Model-Based Diffusion by introducing emerging barrier functions inspired by interior point methods. We demonstrate that the standard Model-Based Diffusion algorithm can lead to catastrophic performance degradation in highly constrained environments, 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 expensive projection operations such as projections. We analyze the sampling liveliness of samples at 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.