Energy-Aware Predefined-Time Formation Reconfiguration of Heterogeneous UAV Swarms via Gramian-Based Assignment and Safe Terminal Recovery

Vu Quang Luong¹*, Trinh Thi Minh², Hoang Van Ngoi¹, Nguyen Duy Tien¹

Abstract

Predefined-time formation reconfiguration of unmanned aerial vehicle (UAV) swarms requires simultaneous satisfaction of a mission deadline, heterogeneous energy reserves, collision-separation constraints, actuator limits, and external disturbances. This study develops an energy-constrained predefined-time reconfiguration framework in which a single finite-horizon controllability Gramian is used consistently for both discrete slot assignment and continuous terminal recovery. The assignment stage minimizes a state-of-charge- and mass-weighted maneuver index while screening individual energy budgets and nominal pairwise separation. The online stage combines a receding minimum-energy terminal correction, effective-disturbance observation, and a high-order control-barrier-function safety projection. Under compound uncertainty, the method achieves a 0.00529 m formation-reference RMSE, a 0.00176 m deadline error, a 1.997 m minimum separation, and zero acceleration saturation. Relative to direct predefined-time mapping, reference maneuver effort decreases by 75.9%, tracking RMSE by 90.3%, and model-based incremental propulsion energy by 15.8%. Thirty paired common-seed trials retain 100% deadline success and consistent improvement over the strongest baseline. The results demonstrate that coupling deadline selection, energy-aware assignment, and receding terminal control through the same finite-horizon energy metric provides a compact and analytically interpretable solution for deadline-critical UAV-swarm reconfiguration.

Keywords:

Control barrier function; energy-aware assignment; formation reconfiguration; minimum-energy control; predefined-time control; unmanned aerial vehicle swarm