一种求解轨迹优化问题的改进多分辨率技术

针对轨迹优化多分辨率技术可能发生细化遗漏或者细化失败的缺陷，设计了一种改进多分辨率技术。该方法通过在每次网格细化迭代过程中增加两层高分辨率节点并且引入节点检测算法，确保在轨迹的非光滑区域能够高效、持续地细化网格。针对原始多分辨率技术的初始网格的节点数目存在二进限制的弊端，定义了一种新的广义二分网格，使得多分辨率技术的初始网格节点数目可以为任意奇数。采用多个轨迹优化算例验证了本文方法的有效性并且与其它方法进行了对比。此外，仿真结果还表明，网格充分细化对目标函数影响不大，但是能够更加准确地满足路径约束和终端状态约束。

Improved Multiresolution Technique for Solving Trajectory Optimization

 An improved multiresolution-based approach is proposed to refine the mesh points in all the nonsmooth regions along the trajectory and avoid the omissions or failures of the mesh refinement that have been encountered for the existing multiresolution techniques. The method is designed by adding the mesh points from two higher resolution levels in each refinement iteration and introducing a mesh point checking algorithm. A generalized dyadic mesh is proposed so that the modified multiresolution technique can start with any uniform initial mesh with an odd number of the mesh points, thus overcoming the dyadic restrictions of the original multiresolution techniques. The effectiveness of the method is demonstrated on several examples and its performance is compared against other mesh refinement methods. In addition, the numerical results show that a fully refined mesh has little impact on the objective but it ensures that the path or terminal constraints are more accurately satisfied.