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.

翻译：混合整数非线性规划（MINLPs）是任务规划的重要建模工具，但该方法存在求解时间较长的问题，尤其在大规模场景中。本研究首先将物品入库任务规划问题建模为混合整数非线性规划问题，随后采用交替方向乘子法（ADMM）进行求解。ADMM将完整问题解耦为非线性规划子问题和混合整数规划子问题，通过交替迭代求解原始问题。实验证明，本方法相较于无热启动的非线性互补规划方法具有更优的收敛性能。所提方法已在真实硬件平台上作为高层规划器完成书籍入库任务验证。