Collision-free path planning in cluttered, real-world environments relies on a representation of the collision-free space, and existing representations broadly fall into two categories. Explicit representations, such as unions of convex sets, can be plugged into optimization-based planners as hard collision-free constraints, but their parameters scale poorly with configuration-space dimension. Implicit representations, by contrast, are flexible and scale well to complex geometries, yet typically lack such guarantees. We bridge this gap with ILD (Invertible Latent Decomposition), a framework that jointly learns an invertible mapping and a union of explicit convex polytopes in the resulting latent space. Planning is carried out over these latent convex sets, and the invertible mapping decodes the resulting paths back to the original configuration space while preserving feasibility with respect to the refined explicit safe regions. We further propose Visibility-Guided Sampling (VGS) to keep the convex sets connected for path planning. Across 2D navigation, 6-DoF, and 14-DoF manipulation environments, ILD achieves broader coverage, better inter-set connectivity, and higher path-planning success rates than prior baselines, with zero observed false positives after test-time refinement. On a 14-DoF bimanual manipulator, we further demonstrate real-time collision-free planning, with test-time refinement adapting to scene-geometry changes during real-world deployment on a single 6-DoF arm.

翻译：在杂乱的真实环境中进行无碰撞路径规划依赖于对无碰撞空间的表示，现有表示方法大致分为两类。显式表示（如凸集并集）可作为硬性无碰撞约束嵌入基于优化的规划器中，但其参数规模随配置空间维度增长而扩展性较差。相比之下，隐式表示灵活且能良好适应复杂几何形状，但通常缺乏此类保证。我们通过ILD（可逆潜在分解）框架弥合这一差距，该框架联合学习可逆映射与结果潜在空间中的显式凸多面体并集。规划在潜在凸集内执行，可逆映射将路径解码回原始配置空间，同时保持相对于精细化显式安全区域的可行性。我们进一步提出可见性引导采样（VGS）以保持凸集连通性，便于路径规划。在二维导航、六自由度及十四自由度操作环境中，ILD相比先前基线方法实现了更广的覆盖范围、更强的集间连通性以及更高的路径规划成功率，且测试时精细化后未观察到假阳性。在十四自由度双臂操作器上，我们进一步展示了实时无碰撞规划能力，通过测试时精细化适应真实部署中单六自由度臂的场景几何变化。