Optimization-based trajectory generation methods are widely used in whole-body planning for robots. However, existing work either oversimplifies the robot's geometry and environment representation, resulting in a conservative trajectory, or suffers from a huge overhead in maintaining additional information such as the Signed Distance Field (SDF). To bridge the gap, we consider the robot as an implicit function, with its surface boundary represented by the zero-level set of its SDF. Based on this, we further employ another implicit function to lazily compute the signed distance to the swept volume generated by the robot and its trajectory. The computation is efficient by exploiting continuity in space-time, and the implicit function guarantees precise and continuous collision evaluation even for nonconvex robots with complex surfaces. Furthermore, we propose a trajectory optimization pipeline applicable to the implicit SDF. Simulation and real-world experiments validate the high performance of our approach for arbitrarily shaped robot trajectory optimization.

翻译：基于优化的轨迹生成方法在机器人全身规划中被广泛应用。然而，现有方法要么过度简化机器人几何模型与环境表征，导致轨迹保守，要么在维护符号距离函数等附加信息时产生巨大开销。为弥合这一差距，我们将机器人视为隐式函数，其表面边界由其符号距离函数的零水平集表示。在此基础上，我们进一步利用另一个隐式函数，惰性计算机器人及其轨迹生成扫掠体积的符号距离。通过利用时空连续性实现高效计算，该隐式函数可确保对具有复杂表面的非凸机器人进行精确且连续的碰撞评估。此外，我们提出了一种适用于隐式符号距离函数的轨迹优化框架。仿真与实物实验验证了该方法在任意形状机器人轨迹优化中的高性能表现。