基于二代小波的轨迹优化节点自适应加密

Node adaptive refinement for trajectory optimization based on second-generation wavelets

针对采用直接法求解轨迹优化问题中精度和效率之间的矛盾,提出了基于二代小波轨迹优化节点自适应加密.采用RK(Runge-Kutta)离散方法将原轨迹优化问题转化为非线性规划问题,并采用成熟的非线性规划算法求解.对控制或状态函数进行小波变换得到小波系数,基于小波系数和二分节点的对应关系,根据小波系数的幅值确定下一个迭代步所使用的节点并进行序列优化.算例结果表明:通过设置合适的小波系数阀值,采用较少的时间离散节点即可使优化结果达到预定的精度.与高斯伪谱法软件相比,节点个数大约减少10%,最优指标的精度大约提高1个数量级.

A mesh adaptive refinement method for solving trajectory optimization problem by using direct method based on second-generation wavelets was proposed to deal with the conflict between accuracy and efficiency.The original trajectory optimization problem was transformed into a nonlinear programming problem that was solved by standard nonlinear programming codes.Then the wavelet transformation of control or state function was performed,and the wavelet coefficients were obtained.A new node could be determined based on the magnitude of coefficients and the relationship between wavelet coefficients and dyadic nodes.The results demonstrate that the proposed method can balance accuracy of the solution and speed of computations by setting appropriate threshold of wavelet coefficients.Compared with the Gauss pseudospectral method software package,the number of nodes are reduced by 10% approximately,and the optimality accuracy is increased by an order of magnitude by using the method.