For robots to successfully execute tasks assigned to them, they must be capable of planning the right sequence of actions. These actions must be both optimal with respect to a specified objective and satisfy whatever constraints exist in their world. We propose an approach for robot task planning that is capable of planning the optimal sequence of grounded actions to accomplish a task given a specific objective function while satisfying all specified numerical constraints. Our approach accomplishes this by encoding the entire task planning problem as a single mixed integer convex program, which it then solves using an off-the-shelf Mixed Integer Programming solver. We evaluate our approach on several mobile manipulation tasks in both simulation and on a physical humanoid robot. Our approach is able to consistently produce optimal plans while accounting for all specified numerical constraints in the mobile manipulation tasks. Open-source implementations of the components of our approach as well as videos of robots executing planned grounded actions in both simulation and the physical world can be found at this url: https://adubredu.github.io/gtpmip

翻译：机器人要成功执行指派给他们的任务, 就必须能够规划正确的行动序列。 这些行动必须既符合特定目标, 也符合他们世界中存在的任何制约。 我们提出一个机器人任务规划方法, 能够规划有根据行动的最佳序列, 完成给定任务的特定目标功能, 同时满足所有指定的数字限制。 我们的方法是通过将整个任务规划问题编码成一个单一的混合整数 convex 程序来完成这个任务规划问题, 然后用一个现成的混合整数编程程序解答它。 我们评估了模拟和体形机器人中若干移动操作任务的方法。 我们的方法能够在计算移动操作任务中所有特定数字限制的同时, 一致地制定最佳计划。 我们的方法以及机器人在模拟和物理世界中执行有计划的有计划的行动的视频可以在这个 url 上找到 : https://adubredu.github.io/gtpmipip