Variable time GS-MPSP collaborative trajectory planning algorithm

Aiming at the problem of collaborative trajectory planning in midcourse, a collaborative trajectory planning algorithm based on generalized quasi-spectral model predictive static planning guidance under variable time is proposed. Firstly, the algorithm employs the Legendre pseudospectral method to solve the weight matrix. Secondly, under the continuous integral form, it establishes a comprehensive performance function with the explicit expression by considering both process constraints and variable terminal time, which reduces the number of discrete points, improves the computational efficiency and maintains the solution accuracy of the classical model predictive static planning method. Finally, the distributed collaborative trajectory planning strategy is applied to the variable time multi-vehicle collaborative trajectory planning. Simulations show that the proposed method demonstrates high computational efficiency, and high accuracy by comparing with common methods and strategies in existing literature to solve the collaborative planning problem under multiple constraints.