  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.
