Generating safe motion plans in real-time is necessary for the wide-scale deployment of robots in unstructured and human-centric environments. These motion plans must be safe to ensure humans are not harmed and nearby objects are not damaged. However, they must also be generated in real-time to ensure the robot can quickly adapt to changes in the environment. Many trajectory optimization methods introduce heuristics that trade-off safety and real-time performance, which can lead to potentially unsafe plans. This paper addresses this challenge by proposing Safe Planning for Articulated Robots Using Reachability-based Obstacle Avoidance With Spheres (SPARROWS). SPARROWS is a receding-horizon trajectory planner that utilizes the combination of a novel reachable set representation and an exact signed distance function to generate provably-safe motion plans. At runtime, SPARROWS uses parameterized trajectories to compute reachable sets composed entirely of spheres that overapproximate the swept volume of the robot's motion. SPARROWS then performs trajectory optimization to select a safe trajectory that is guaranteed to be collision-free. We demonstrate that SPARROWS' novel reachable set is significantly less conservative than previous approaches. We also demonstrate that SPARROWS outperforms a variety of state-of-the-art methods in solving challenging motion planning tasks in cluttered environments. Code, data, and video demonstrations can be found at \url{https://roahmlab.github.io/sparrows/}.

翻译：在非结构化及人机共存环境中实现实时安全运动规划，是大规模部署机器人的必要条件。这类规划必须兼顾安全性（避免伤害人类或损坏物体）与实时性（快速适应环境变化）。现有轨迹优化方法常通过引入启发式策略在安全性与实时性之间权衡，可能导致潜在危险规划。本文提出"采用基于球体的可达性避障算法的关节机器人安全规划方法"（SPARROWS），该滚动时域轨迹规划器结合新型可达集表示与精确符号距离函数，可生成可证明安全的运动规划。运行时，SPARROWS利用参数化轨迹构建完全由球体组成的可达集，这些球体能够上近似机器人运动扫掠体积，进而通过轨迹优化选择保证无碰撞的安全轨迹。实验表明：SPARROWS的新型可达集保守性显著低于传统方法，且在复杂环境下的运动规划任务中优于多种最新方法。代码、数据及视频演示可访问\url{https://roahmlab.github.io/sparrows/}获取。