  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
