Scalable kinodynamic trajectory planning for RLVs in high-density debris environments via Spatiotemporal Voxel Indexing

With the deployment of mega-constellations and the proliferation of space debris, reusable launch vehicles (RLVs) face severe collision threats during exo-atmospheric orbital transfer operations. Traditional trajectory planning algorithms struggle to balance computational efficiency and kinodynamic feasibility when navigating through these highly cluttered and hyperdynamic Low Earth Orbit (LEO) environments. Rather than relying on computationally exhaustive pairwise checks, this paper proposes a highly scalable spatiotemporal indexing and planning architecture. First, to break the computational bottleneck in large-scale debris fields, a Spatiotemporal Voxel Indexing (SVI) mechanism is established. By integrating a voxel-based hashing scheme for broad-phase culling with precise geometric checks for narrow-phase verification, this approach reduces the average collision detection complexity from linear to near-constant time, enabling the highly efficient processing of massive debris populations. Second, a Reference-Guided Kinodynamic RRT (Ref-KRRT) framework is integrated to ensure rapid convergence under strict orbital mechanics. By utilizing a reference trajectory tube to bias sampling, alongside Continuous Collision Detection (CCD) to reduce high-speed tunneling risks, the framework generates physically executable and safety-constrained trajectories with respect to the predicted debris motion and prescribed safety margin.