A rapid trajectory optimization method based on parallel computing

The direct collocation method transforms a trajectory optimization problem into a nonlinear programming (NLP) problem by discretizing both control and state variables. During the NLP solution process, repeated calculations of the first and second derivatives of the NLP and the values of the dynamic system at each discrete point are required, leading to great computational complexities. Therefore, this paper proposes the following method: First, the hyper-dual number method is introduced to accurately identify the sparsity of the second-derivative matrix of the NLP and to determine the locations of the non-zero elements. Then, a multi-core parallel approach is used to rapidly compute the non-zero elements of the first and second derivatives of the NLP as well as the values of the dynamic system at each discrete point. Finally, OpenMP is employed for programming calculation in the C++ environment to further enhance computational efficiency from the perspective of programming language. Simulation results demonstrate that the proposed method effectively improves the efficiency of trajectory optimization and its computational efficiency without compromising accuracy.