发表机构
University of New Mexico（新墨西哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Exact-Safe MPPI方法，利用精确最小值和CBF二次规划处理非光滑多障碍约束，保证安全集前向不变性，并验证其在狭窄通道导航中的有效性。
AI 中文摘要
模型预测路径积分（MPPI）控制通过采样和评估轨迹来规划动作，但标准MPPI不保证安全性。将控制障碍函数（CBF）滤波器纳入每次滚动中，使规划器能够考虑安全修正。然而，通过软最小值近似组合多个CBF可能会排除满足原始安全约束的状态，从而限制规划器可用的轨迹。本文提出精确安全MPPI（Exact-Safe MPPI），该方法使用多个障碍函数的精确最小值，并在规划和执行控制过程中应用基于CBF的二次规划。为处理多个障碍达到最小值处的不可微性，滤波器同时对所有δ-活跃障碍强制执行CBF条件，这些障碍的值位于最小值的规定容差δ>0范围内。在适当的可行性和正则性假设下，我们建立了认证安全集的前向不变性，而不会出现软最小值平滑引入的收缩。我们还刻画了状态相关的近似间隙，并解释了多个值处于或接近最小值的障碍如何增加这种收缩。此外，我们表明增加MPPI样本数量无法恢复被软最小值滤波器排除的轨迹。我们在需要穿过两个障碍物之间狭窄间隙的导航任务中展示了所提方法的有效性。视频演示可在该https URL获取。
英文摘要
Model predictive path integral (MPPI) control plans actions by sampling and evaluating trajectories, but standard MPPI does not guarantee safety. Incorporating control barrier function (CBF) filters into each rollout allows the planner to account for safety corrections. However, combining multiple CBFs through a soft-minimum approximation can exclude states that satisfy the original safety constraints, restricting the trajectories available to the planner. This paper proposes Exact-Safe MPPI, which uses the exact minimum of multiple barrier functions and applies a CBF-based quadratic program during both planning and control execution. To handle nondifferentiability where multiple barriers attain the minimum, the filter simultaneously enforces the CBF conditions for all $δ$-active barriers, whose values lie within a prescribed tolerance $δ>0$ of the minimum. Under suitable feasibility and regularity assumptions, we establish forward invariance of the certified safe set without the shrinkage introduced by soft-minimum smoothing. We also characterize the state-dependent approximation gap and explain how multiple barriers with values at or near the minimum increase this shrinkage. Furthermore, we show that increasing the number of MPPI samples cannot recover trajectories excluded by the soft-minimum filter. We demonstrate the effectiveness of the proposed approach in a navigation task requiring passage through a narrow gap between two obstacles. Video demonstrations are available at https://github.com/lc-lab25/Exact-Safe-MPPI .
Comments8 pages, 5 figures, 1 table. Submitted to the 2027 American Control Conference (ACC)
