Fast MILP-based Task and Motion Planning for Pick-and-Place with Hard/Soft Constraints of Collision-Free Route

We present new models of optimization-based task and motion planning (TAMP) for robotic pick-and-place (P&P), which plan action sequences and motion trajectory with low computational costs. We improved an existing state-of-the-art TAMP model integrated with the collision avoidance, which is formulated as a mixed-integer linear programing (MILP) problem. To enable the MILP solver to search for solutions efficiently, we introduced two approaches leveraging features of collision avoidance in robotic P&P. The first approach reduces number of binary variables, which is related to the collision avoidance of delivery objects, by reformulating them as continuous variables with additional hard constraints. These hard constraints maintain consistency by conditionally propagating binary values, which is related to the carry action state and collision avoidance of robots, to the reformulated continuous variables. The second approach is more aware of the branch-and-bound method, which is the fundamental algorithm of modern MILP solvers. This approach guides the MILP solver to find integer solutions with shallower branching by adding a soft constraint, which softly restricts a robot's routes around delivery objects. We demonstrate the effectiveness of the proposed models with a modern MILP solver.