  Nonlinear optimal control problems for trajectory planning with obstacle
avoidance present several challenges. While general-purpose optimizers and
dynamic programming methods struggle when adopted separately, their combination
enabled by a penalty approach is capable of handling highly nonlinear systems
while overcoming the curse of dimensionality. Nevertheless, using dynamic
programming with a fixed state space discretization limits the set of reachable
solutions, hindering convergence or requiring enormous memory resources for
uniformly spaced grids. In this work we solve this issue by incorporating an
adaptive refinement of the state space grid, splitting cells where needed to
better capture the problem structure while requiring less discretization points
overall. Numerical results on a space manipulator demonstrate the improved
robustness and efficiency of the combined method with respect to the single
components.
