An Improved GS-MPSP Algorithm for Time-Cooperative Trajectory Optimization of Multiple CDUAVs

To address the difficulty of simultaneously satisfying terminal state constraints and time cooperation in cooperative missions of multiple cross-domain unmanned aerial vehicles, a cooperative trajectory optimization method based on improved generalized quasi-spectral model predictive static programming (GS-MPSP) is proposed. First, to overcome the local control information coupling and the insufficient accuracy of terminal constraint satisfaction that arise when the conventional (original) GS-MPSP updates the control variables in the spectral coefficient space, the spectral coefficient update scheme is abandoned and the control variables are optimized directly in the Legendre–Gauss–Lobatto (LGL) node space. The node control variables are mapped onto a fine grid by the Legendre orthogonal projection method for trajectory integration so that the control adjustment at each node can respond independently to the terminal constraint requirements. Second, an aerodynamic-drag energy term is introduced into the performance index, and penalty terms for the dynamic pressure, heat flux, and overload constraints are constructed, thereby achieving trajectory design that accounts for both energy optimization and path constraint satisfaction. Furthermore, the improved GS-MPSP algorithm is nested with a time consensus protocol to construct two multi-vehicle cooperation architectures, namely distributed and decentralized ones. Simulation results show that, compared with the conventional (original) GS-MPSP, the proposed method reduces the terminal position error by 83.8% (distributed) and 87.6% (decentralized) on average; that is, the accuracy is improved by a factor of 6.2 and 8.1 (up to 11.1), the time-consensus error is reduced by approximately 20%, and the total energy loss of the three vehicles is reduced by 3.5–4.2%; compared with the Gauss pseudospectral method (GPM), the terminal position error is reduced by 94.5–94.7% and the computation time is shortened by about two orders of magnitude; compared with the trajectory shaping guidance law (TSGL) method, the terminal position error is lower by about five orders of magnitude and the energy loss is lower by 24.9–27.5%. In 300 Monte Carlo simulations, the cooperative mission completion rates are 94.33% and 96.67%, the time-consensus convergence rates are 100% and 97.56%, and all process constraints are satisfied throughout. The proposed method can provide an effective solution for multi-vehicle cooperative trajectory planning in complex autonomous flight missions.