Homotopy-Aware Parallel Trajectory Planning for AMRs in Topologically Complex Environments

Global trajectory optimization for autonomous mobile robots (AMRs) in topologically complex environments is prone to getting trapped in local minima due to its sensitivity to topological structures. To overcome this challenge, we propose an integrated homotopy-aware parallel trajectory planning framework that combines skeleton topology graph (STG)-based homotopy exploration, topology-specific smooth obstacle constraints, and parallel optimization control problem (OCP) solving to alleviate local traps caused by single-topology initialization. By constructing STG, the proposed framework extracts diverse homotopy topologies and decomposes the original problem into parallelizable subproblems within distinct topological spaces. For each topological class, we formulate smooth local obstacle-avoidance constraints to suppress the impact of redundant topologies and accelerate convergence. Comparative validation demonstrates the feasibility and superiority of the proposed framework.