In the field of trajectory generation for objects, ensuring continuous collision-free motion remains a huge challenge, especially for non-convex geometries and complex environments. Previous methods either oversimplify object shapes, which results in a sacrifice of feasible space or rely on discrete sampling, which suffers from the "tunnel effect". To address these limitations, we propose a novel hierarchical trajectory generation pipeline, which utilizes the Swept Volume Signed Distance Field (SVSDF) to guide trajectory optimization for Continuous Collision Avoidance (CCA). Our interdisciplinary approach, blending techniques from graphics and robotics, exhibits outstanding effectiveness in solving this problem. We formulate the computation of the SVSDF as a Generalized Semi-Infinite Programming model, and we solve for the numerical solutions at query points implicitly, thereby eliminating the need for explicit reconstruction of the surface. Our algorithm has been validated in a variety of complex scenarios and applies to robots of various dynamics, including both rigid and deformable shapes. It demonstrates exceptional universality and superior CCA performance compared to typical algorithms. The code will be released at https://github.com/ZJU-FAST-Lab/Implicit-SVSDF-Planner for the benefit of the community.

翻译：在物体轨迹生成领域，确保连续无碰撞运动仍是一项巨大挑战，尤其对于非凸几何体和复杂环境而言。先前的方法要么过度简化物体形状导致可行空间损失，要么依赖离散采样而遭受"隧道效应"困扰。为解决这些局限，我们提出了一种新颖的分层轨迹生成流水线，利用扫掠体符号距离场（SVSDF）引导连续碰撞避免（CCA）的轨迹优化。这种融合图形学与机器人学的跨学科方法在解决该问题时展现出卓越的有效性。我们将SVSDF的计算建模为广义半无限规划模型，并通过隐式方式求解查询点处的数值解，从而无需显式重建表面。该算法已在多种复杂场景中得到验证，适用于刚性与可变形形状等不同动力学特性的机器人。相比典型算法，它展现出卓越的通用性和更优的CCA性能。代码将在https://github.com/ZJU-FAST-Lab/Implicit-SVSDF-Planner 开源，以惠及学界。