Terrain-Coupled Hierarchical Optimization for Multi-Robot Deployment with a Global Reachability-Cost Atlas

Autonomous multi-robot deployment (MRD) aims to determine feasible and task-effective deployment poses for robots to accomplish cooperative missions. When applied to unstructured outdoor environments, MRD must contend with irregular terrain geometry, uneven contact surfaces, and terrain-dependent traversability, challenging purely geometric MRD methods. This work proposes a hierarchical MRD framework that unifies terrain-coupled feasibility modeling and execution-aware optimization into a coherent deployment process. An upper-stage nonlinear programming, constrained by a signed-distance field derived from a multi-layer terrain assessment map (MTAM), enforces strict geometric deployment feasibility and yields high-quality candidate fleet configurations. A lower-stage multi-objective evolutionary optimizer then refines fleet poses using a global reachability-cost atlas (GRCA) that precomputes reachability and minimal traversal cost of each robot to every map cell, enabling constant-time candidate evaluation. Terrain coupling is achieved by embedding terrain-risk layers of the MTAM into the optimization objectives, guiding pose refinement toward stable and traversable regions. Extensive simulations and field trials on vibroseis fleet demonstrate system-level integration within a seismic source excitation pipeline, achieving task-level geometric accuracy, stable terrain contact at deployment poses, and real-time onboard optimization with an average latency below 10 s.