模型不确定性下运动预测的快速方向条件可达性

中文摘要 AI 辅助

为了避免碰撞，机器人必须反复预测附近智能体可能移动的位置，通常使用其动力学的非完美模型。可达集提供了这样的预测，但当系统矩阵本身不确定时，计算可达集可能变得计算昂贵且保守，不适合频繁重新规划。此外，规划者通常只需要知道智能体在某个特定方向上（例如朝向机器人）能移动多远，而不是完整的可达集。我们提出了一种针对状态矩阵和输入矩阵不确定的线性系统的方向条件可达性方法。给定查询方向 $d$，该方法选择一个可接受的模型 $(A^\star,B^\star)$，其可达集沿 $d$ 方向延伸的距离几乎与整个不确定模型族的可达集一样远，然后仅使用标准可达性求解器计算该模型的可达集。在一个不确定的线性化自行车模型上，完整的“选择-计算”流程比在 CORA 工具箱中计算完整不确定族的可达集快约三倍，同时在报告的方向上，其沿 $d$ 的延伸范围在完整族的 5% 以内。我们还在一个闭环多车辆仿真中使用了该方法，在该仿真中，机器人在每个重新规划步骤中查询每个附近车辆朝向它移动的距离，并重新规划以避免这些集合。

英文摘要

To avoid collisions, a robot must repeatedly predict where nearby agents may move, usually with an imperfect model of their dynamics. Reachable sets provide such predictions, but computing them when the system matrices themselves are uncertain can become computationally expensive and conservative for frequent replanning. Moreover, a planner often needs to know only how far an agent can move in one particular direction, for example toward the robot, rather than the complete reachable set. We propose a direction-conditioned reachability method for linear systems with uncertain state and input matrices. Given a query direction $d$, the method selects one admissible model $(A^\star,B^\star)$ whose reachable set extends nearly as far along $d$ as the reachable set of the entire uncertain model family, and then computes the reachable set of only this model with a standard reachability solver. On an uncertain linearized bicycle model, the complete selection-and-computation pipeline is about three times faster than computing the reachable set of the full uncertain family in the CORA toolbox, while its extent along $d$ is within $5\%$ of the full family's in the reported directions. We also use the method in a closed-loop multi-vehicle simulation in which the robot queries, at each replanning step, how far each nearby vehicle can move toward it, and replans to avoid the resulting sets.

发表机构

• University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）

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