RISMO: Riemannian Information-Geometric Swarm Motion Orchestration for Heterogeneous UAV–UGV Cooperative Exploration in Unknown Environments

The orchestration of heterogeneous swarm systems, such as Unmanned Aerial Vehicle (UAV) and Unmanned Ground Vehicle (UGV) teams, in unknown, GPS-denied environments requires coordination among active perception, collision avoidance, and topological flexibility. Traditional Artificial Potential Field (APF) methods can suffer from local-minimum deadlocks, while optimization-based Control Barrier Function Quadratic Programs (CBF-QPs) may produce high-frequency control variation in narrow corridors. To address these limitations, this paper proposes the Riemannian Information-geometric Swarm Motion Orchestration (RISMO) framework. RISMO integrates objective-driven navigation, perception-aware motion generation, and obstacle avoidance within a common non-Euclidean metric representation. We construct a Riemannian metric tensor that incorporates the Fisher Information Matrix (FIM) to encourage the UGVs to preserve line-of-sight tracking of the UAVs. To accommodate formation deformation in narrow passages, the swarm topology is modeled as a Semi-Markov Jump System (S-MJS). Under the enforced positive per-agent inter-event bound and the stated Average Dwell Time (ADT) condition, the modeled switching sequence has a bounded transition frequency and cannot exhibit Zeno accumulation. Furthermore, a goal-aligned tangential flux supplies a deterministic local directional bias near saddle-like stagnation. The numerical and ablation results show that this mechanism facilitates escape from the tested non-convex traps. In the planar simulations, RISMO reduces the observed gradient stagnation of APF and the high-frequency control variation of CBF-QP while preserving positive obstacle clearance and cooperative perception.