University of Isfahan Computational Intelligence in Electrical Engineering 2821-0689 17 1 2026 05 22 Fast Trajectory Replanning of Racing UAVs in Restricted Space via Sepa-rating Hyperplanes and Disturbance Effects Estimation Fast Trajectory Replanning of Racing UAVs in Restricted Space via Sepa-rating Hyperplanes and Disturbance Effects Estimation 19 44 30466 10.22108/isee.2026.146562.1763 FA Nour َAbbas PhD Candidate, Mechanical Engineering Department, Faculty of Engineering, University of Isfahan, Isfahan, Iran Hossein Karimpour Assistant Professor, Mechanical Engineering Department, Faculty of Engineering, University of Isfahan, Isfahan, Iran Journal Article 2025 09 06 Maintaining safe and reliable trajectories for multiple Unmanned Aerial Vehicles (UAVs) in environments with obsta-cles and external disturbances, such as wind, remains a significant challenge. This paper presents a novel trajectory replanning approach for a group of UAVs in the presence of wind disturbances. The proposed method is based on re-flecting the impact of any uncertainty caused by disturbances as an uncertainty in the dynamic response of the quad-rotor, through the application of the forward reachable sets (FRSs) theory on the motion equations. This results in a location ellipsoid error for each quadrotor. Combining this error ellipsoid with the quadrotor's physical dimensions via a Minkowski sum yields an expanded safety ellipsoid. To avoid inter-UAV collisions, a separating hyperplane is con-structed between pairs of safety ellipsoids at each replanning instant. Furthermore, the adaptation of the trajectory to instantaneous conditions is made possible through the application of a virtual force field at each point on the trajecto-ry. This force field accounts for both the intensity of wind disturbance and the proximity of the trajectory to surround-ing obstacles and other quadrotors (delimited by hyperplanes), allowing the trajectory to be reconfigured while preserv-ing some key optimal characteristics<strong>. </strong>Simulation results obtained in Matlab demonstrate the effectiveness of the proposed trajectory replanning framework and provide a comparative evaluation of its reduced computational cost. Maintaining safe and reliable trajectories for multiple Unmanned Aerial Vehicles (UAVs) in environments with obsta-cles and external disturbances, such as wind, remains a significant challenge. This paper presents a novel trajectory replanning approach for a group of UAVs in the presence of wind disturbances. The proposed method is based on re-flecting the impact of any uncertainty caused by disturbances as an uncertainty in the dynamic response of the quad-rotor, through the application of the forward reachable sets (FRSs) theory on the motion equations. This results in a location ellipsoid error for each quadrotor. Combining this error ellipsoid with the quadrotor's physical dimensions via a Minkowski sum yields an expanded safety ellipsoid. To avoid inter-UAV collisions, a separating hyperplane is con-structed between pairs of safety ellipsoids at each replanning instant. Furthermore, the adaptation of the trajectory to instantaneous conditions is made possible through the application of a virtual force field at each point on the trajecto-ry. This force field accounts for both the intensity of wind disturbance and the proximity of the trajectory to surround-ing obstacles and other quadrotors (delimited by hyperplanes), allowing the trajectory to be reconfigured while preserv-ing some key optimal characteristics<strong>. </strong>Simulation results obtained in Matlab demonstrate the effectiveness of the proposed trajectory replanning framework and provide a comparative evaluation of its reduced computational cost. https://isee.ui.ac.ir/article_30466_3467b879369b6345670417dd1bd508a6.pdf