Task Planning for Multiple Item Insertion using ADMM

Mixed-integer nonlinear programmings (MINLPs) are powerful formulation tools for task planning. However, it suffers from long solving time especially for large scale problems. In this work, we first formulate the task planning problem for item stowing into a mixed-integer nonlinear programming problem, then solve it using Alternative Direction Method of Multipliers (ADMM). ADMM separates the complete formulation into a nonlinear programming problem and mixed-integer programming problem, then iterate between them to solve the original problem. We show that our ADMM converges better than non-warm-started nonlinear complementary formulation. Our proposed methods are demonstrated on hardware as a high level planner to insert books into the bookshelf.