Safe formation scaling and motion planning for heterogeneous UAV–UGV teams in cluttered environments

Heterogeneous UAV-UGV formations offer significant potential for autonomous missions; however, achieving stable three-dimensional (3-D) formation control with collision-free navigation in dense obstacle environments remains challenging due to heterogeneous dynamics, unknown external disturbances, and strict real-time computational constraints. This paper proposes a distributed rigid graph-based adaptive safe artificial potential field (RG-ASAPF) framework that tightly integrates formation control and motion planning for heterogeneous multi-UAV-UGV systems. The proposed framework addresses three key challenges: (i) maintaining continuous formation integrity during obstacle avoidance, thereby avoiding the conventional disassembly-recovery process; (ii) enabling vertical coordination between UAV and UGV layers with prescribed inter-layer spacing; and (iii) supporting dynamic formation reconfiguration through time-varying scaling to safely navigate narrow passages. A backstepping-based adaptive formation controller is developed using rigid graph theory to enforce distance consensus under Euler-Lagrange dynamics, explicitly accounting for underactuated UAVs and nonholonomic UGVs. An adaptive safe artificial potential field with Widrow-Hoff-based online repulsion tuning generates smooth, collision-free trajectories while respecting formation footprint constraints. Rigorous Lyapunov analysis establishes exponential convergence of formation errors and global uniform ultimate boundedness (GUUB) of tracking errors in the presence of bounded disturbances. Furthermore, a safety-certified fallback mechanism with corridor-aware rerouting enhances robustness when clearance constraints are violated. Extensive simulations involving sparse and dense obstacle environments, formation scaling maneuvers, dynamic obstacles, and formation maneuvers featuring more agents demonstrate that the proposed framework outperforms model predictive control, particle swarm optimization, and conventional artificial potential field methods in terms of computational efficiency, trajectory smoothness, formation stability, and energy consumption. These results highlight the effectiveness of the proposed approach for heterogeneous multi-domain robotic applications such as disaster response, surveillance, and cooperative logistics.