Guaranteed Global Optimal Path Planning Through Convex Segmentation and Homotopy Guidance

Trajectory planning and optimization in three dimensional space remains fundamental challenges in high dimensional motion planning. This paper presents ConvexSegTopoChainOpt (Csto), a trajectory optimization framework that integrates convex decomposition and topological guidance. The proposed method partitions obstacle space into a sequence of connected, collision-free convex polyhedral via geometric decomposition. Homotopy vectors are introduced to enforce topological consistency, ensuring that the trajectory traverses a continuous chain of convex regions. A global convex optimization problem is formulated using an auxiliary variable relaxation strategy, enabling efficient computation of the optimal trajectory. Csto has been implemented and validated on the Kinova Jaco2 robotic platform, demonstrating its effectiveness in physically realistic experimental settings.