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Nonlinear optimal control problems for trajectory planning with obstacleavoidance present several challenges. While general-purpose optimizers anddynamic programming methods struggle when adopted separately, their combinationenabled by a penalty approach was found capable of handling highly nonlinearsystems while overcoming the curse of dimensionality. Nevertheless, usingdynamic programming with a fixed state space discretization limits the set ofreachable solutions, hindering convergence or requiring enormous memoryresources for uniformly spaced grids. In this work we solve this issue byincorporating an adaptive refinement of the state space grid, splitting cellswhere needed to better capture the problem structure while requiring lessdiscretization points overall. Numerical results on a space manipulatordemonstrate the improved robustness and efficiency of the combined method withrespect to the single components.

Collision Avoidance using Iterative Dynamic and Nonlinear Programming with Adaptive Grid Refinements