DBaS-Log-MPPI: Efficient and Safe Trajectory Optimization via Barrier States

TL;DR

The paper tackles safe, real-time trajectory optimization for nonlinear robots in cluttered environments by addressing the safety-exploration trade-off of MPPI. It introduces DBaS-Log-MPPI, which embeds Discrete Barrier States into the dynamics, adds barrier-state costs to the running objective, and employs a normal–log-normal mixture for adaptive trajectory sampling to maintain safety while improving exploration near obstacles. The method is validated through three simulations and a real-world indoor test with a 2D quadrotor and a ground vehicle, showing higher success rates, lower tracking errors, and more conservative speeds compared to Vanilla MPPI and Log-MPPI. These results demonstrate enhanced safety, feasibility, and real-time performance for autonomous navigation in cluttered environments, with potential applicability to more complex 3D platforms and multi-agent scenarios.

Abstract

Optimizing trajectory costs for nonlinear control systems remains a significant challenge. Model Predictive Control (MPC), particularly sampling-based approaches such as the Model Predictive Path Integral (MPPI) method, has recently demonstrated considerable success by leveraging parallel computing to efficiently evaluate numerous trajectories. However, MPPI often struggles to balance safe navigation in constrained environments with effective exploration in open spaces, leading to infeasibility in cluttered conditions. To address these limitations, we propose DBaS-Log-MPPI, a novel algorithm that integrates Discrete Barrier States (DBaS) to ensure safety while enabling adaptive exploration with enhanced feasibility. Our method is efficiently validated through three simulation missions and one real-world experiment, involving a 2D quadrotor and a ground vehicle navigating through cluttered obstacles. We demonstrate that our algorithm surpasses both Vanilla MPPI and Log-MPPI, achieving higher success rates, lower tracking errors, and a conservative average speed.

Figures (5)

• Figure 1: Demonstration of trajectory sampling: ours (left) vs. vanilla MPPI (right).
• Figure 2: Proposed DBaS-Log-MPPI control scheme.
• Figure 3: 2D quadrotor simulation results. Black and red circles denote the obstacles and destinations, respectively. The grey, purple and red curves depict the sampled trajectories, near-optimal trajectories and executed trajectories.
• Figure 4: Ground vehicle simulation result. Black circles denote the obstacles. The grey, purple, red and black doted curves depict the sampled trajectories, near-optimal trajectories, executed trajectory and reference trajectory, respectively.
• Figure 5: Real-world experiment details and trial comparisons for DBaS-Log-MPPI (green), Vanilla-MPPI (yellow), and Log-MPPI (blue).