Cooperation-Error-Tolerant Pythagorean Hodograph Trajectory Generation for Multi-UAV Systems via Unit Dual Quaternions

Cooperative trajectory generation for multi-UAV systems in cluttered environments requires simultaneously satisfying geometric smoothness, formation consistency, and motion constraints. However, existing Pythagorean Hodograph (PH) trajectory generation methods are primarily designed for single-vehicle systems and do not explicitly account for cooperative tracking errors in multi-UAV maneuvering. To address this issue, this paper proposes a Cooperation-Error-Tolerant Pythagorean Hodograph (CETPH) trajectory generation framework based on unit dual quaternions, which provide a unified singularity-free representation of rigid-body motions on SE(3). A cooperation-error-tolerant deformation mechanism is developed by embedding graph-coupled formation errors into the PH trajectory generator, enabling adaptive trajectory modification while preserving the PH structure. Furthermore, an input-to-state stability analysis is established to characterize the influence of trajectory deformation on cooperative tracking dynamics, yielding an explicit small-gain condition that guarantees uniformly ultimately bounded cooperative tracking errors and asymptotic convergence when disturbances vanish. The proposed framework is validated through simulations and controller hardware-in-the-loop experiments using a real ArduPilot flight controller and a high-fidelity PyBullet simulator. Experimental results demonstrate improved formation consistency, smoother cooperative maneuvers, and stronger robustness compared with representative trajectory generation methods.