  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.
