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.
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