针对机动障碍物的非完整机器人对抗鲁棒几何安全证书
Adversarially Robust Geometric Safety Certificates for Nonholonomic Robots Against Maneuvering Obstacles
- Indian Institute of Science（印度科学研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对有界机动障碍物，提出对抗鲁棒几何安全证书，通过闭式收缩安全集几何，将微分博弈简化为能力比较，并实例化为AR-DPCBF，显著减少违规和碰撞。
AI中文摘要：
针对能够在有界能力范围内主动机动的障碍物进行安全导航仍然具有挑战性：鲁棒控制屏障函数方法通常将障碍物行为视为一般扰动，而微分博弈方法在在线导航中计算成本高昂。我们提出了一种对抗鲁棒几何证书，通过证书参数的闭式收缩，直接在安全集几何中考虑允许的障碍物机动的 worst-case 影响。该构造利用了视线（LoS）证书的一个结构性质：机器人和障碍物的行为通过一个共同的状态相关几何增益进入证书。该增益在 worst-case 比较中抵消，将微分博弈简化为障碍物机动能力与机器人纵向和转向权威中较弱者之间的直接比较。在抛物线证书上实例化，该构造产生了对抗鲁棒动态抛物线控制屏障函数（AR-DPCBF），我们为其建立了在有界输入下运动学自行车动力学中，针对所有允许的障碍物机动，收缩安全集的前向不变性的充分条件。当障碍物能力未知时，滑动窗口估计器提供高概率上界，从而以相应的覆盖概率保留保证。我们进一步制定了软性和缓冲变体，以在密集环境中恢复可行性。跨障碍物能力、密度和能力不匹配的仿真显示，屏障违规和碰撞显著减少，并证明屏障导数的逐点鲁棒化不能替代其几何收缩。
英文摘要：
Safe navigation against obstacles that can actively maneuver within bounded capabilities remains challenging: robust control barrier function methods typically treat obstacle actions as generic disturbances, while differential-game approaches are computationally expensive for online navigation. We propose an adversarially robust geometric certificate that accounts for the worst-case effect of admissible obstacle maneuvers directly in the safe-set geometry through a closed-form contraction of the certificate parameters. The construction exploits a structural property of line-of-sight (LoS) certificates: the robot and obstacle actions enter the certificate through a common state-dependent geometric gain. This gain cancels in the worst-case comparison, reducing the differential game to a direct comparison between obstacle maneuvering capability and the weaker of the robot's longitudinal and steering authorities. Instantiated on the parabolic certificate, the construction yields Adversarially Robust Dynamic Parabolic Control Barrier Functions (AR-DPCBF), for which we establish sufficient conditions for forward invariance of the contracted safe set against all admissible obstacle maneuvers under kinematic bicycle dynamics with bounded inputs. When the obstacle capability is unknown, a sliding-window estimator supplies a high-probability upper bound, allowing the guarantee to be retained with the corresponding coverage probability. We further formulate soft and buffered variants to recover feasibility in dense environments. Simulations across obstacle capabilities, densities, and capability mismatch show substantial reductions in barrier violations and collisions and demonstrate that pointwise robustification of the barrier derivative cannot substitute for contraction of its geometry.
