Trajectory optimization using multiresolution techniques

We present a multi-resolution-based approach for solving trajectory optimization problems. The original optimal control problem is solved using a direct method, thereby being transcribed into a nonlinear programming problem that is solved using standard nonlinear programming codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable nonuniform grid over which the nonlinear programming problem is subsequently solved. This tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance conflicting objectives, such as accuracy of the solution, convergence, and speed of computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples.