Energy-Time-based Docking-Return Path Planning for Cooperative UAV–UGV Systems in GPS-Denied Environments

Unmanned Aerial Vehicles (UAVs) and Unmanned Ground Vehicles (UGVs) offer complementary capabilities for long-duration autonomous missions, where UAV recovery by a ground platform can significantly reduce aerial energy consumption. In practical GPS-denied environments, however, such docking-return operations are limited by three coupled difficulties: establishing an initial relative configuration without external localization infrastructure, selecting an energy-efficient docking point under heterogeneous vehicle constraints, and maintaining feasibility when unknown obstacles are encountered. This paper proposes a relative-initialization and online-replanning framework for cooperative UAV–UGV docking-return. A lightweight front-end initialization module is first developed using a minimal three-node UWB configuration, onboard IMU/odometry increments, and a short excitation trajectory to recover a consistent UAV–UGV-base relative geometry. The initialized configuration is then used in an energy-time docking-point planner that incorporates UAV flight energy, UGV Dubins-type kinematic constraints, asynchronous arrival coordination, Field-Of-View (FOV) feasibility, and obstacle avoidance. The proposed method is positioned as a task-level docking-point planning and replanning framework, rather than a complete low-level docking controller or a full localization system. The relative-initialization module is evaluated in simulation, while the docking-point planning and online replanning layers are validated through Monte Carlo simulations, Gazebo tests, and real-world experiments with controlled initial relative configurations. These results demonstrate the effectiveness of the proposed task-level planner in improving energy-time performance, reducing UAV waiting, and maintaining feasible docking-return execution under the considered cluttered GPS-denied settings.