We consider the problem of planning collision-free trajectories on distance fields. Our key observation is that querying a distance field at one configuration reveals a region of safe space whose radius is given by the distance value, obviating the need for additional collision checking within the safe region. We refer to such regions as safe bubbles, and show that safe bubbles can be obtained from any Lipschitz-continuous safety constraint. Inspired by sampling-based planning algorithms, we present three algorithms for constructing a safe bubble cover of free space, named bubble roadmap (BRM), rapidly exploring bubble graph (RBG), and expansive bubble graph (EBG). The bubble sampling algorithms are combined with a hierarchical planning method that first computes a discrete path of bubbles, followed by a continuous path within the bubbles computed via convex optimization. Experimental results show that the bubble-based methods yield up to 5- 10 times cost reduction relative to conventional baselines while simultaneously reducing computational efforts by orders of magnitude.

翻译：本文研究在距离场上规划无碰撞轨迹的问题。我们的核心发现是：在单一构型下查询距离场可揭示一个安全空间区域，其半径由距离值确定，从而无需在该安全区域内进行额外的碰撞检测。我们将此类区域称为安全气泡，并证明安全气泡可从任何Lipschitz连续的安全约束中获取。受基于采样的规划算法启发，我们提出了三种构建自由空间安全气泡覆盖的算法：气泡路线图（BRM）、快速探索气泡图（RBG）和扩展气泡图（EBG）。气泡采样算法与分层规划方法相结合：首先生成气泡离散路径，随后通过凸优化在气泡内计算连续路径。实验结果表明，与传统基线方法相比，基于气泡的方法可将规划成本降低5-10倍，同时计算量减少数个数量级。