  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.
