arXiv:2610.09652v1 Announce Type: cross Abstract: Autonomous navigation in dynamic environments requires computing spatiotemporal trajectories that satisfy non-holonomic motion constraints. When the trajectories of the moving obstacles are predictable or known, a promising approach is to rely on the combination of state lattices constructed from precomputed feasible motion primitives and Safe Interval Path Planning -- a search-based algorithm with strong theoretical guarantees. While this approach yields feasible paths, the rich primitive sets needed for smooth navigation induce a large branching factor, which becomes costly when coupled with time-dependent obstacle intervals. To this end, we present MeshSIPP, an efficient planner that removes the computational bottleneck by exploiting the fact that many primitives sweep the same regions and can therefore be validated together. MeshSIPP propagates primitives as spatial bundles, screens them with lightweight bounding-interval checks, and defers the expensive exact departure-time search until a primitive reaches its terminal state. A time-aware pruning rule additionally discards redundant space-time branches early in the search. We prove that the resulting search is complete and optimal. Extensive experiments over more than 6,000 benchmark instances and real-time ROS~2 simulations show that MeshSIPP achieves up to a 3$\times$ speedup over state-of-the-art spatiotemporal planners.