Task and Motion Planning (TAMP)
A task planner happily plans "pick up the cup, put it in the box" without noticing that a bottle stands right where the gripper has to go. Task and motion planning interleaves the two levels: every symbolic step is checked with real geometry, and when a check fails, the reason is turned back into a fact the task planner can work around.
Two levels, checked against each other
The task planner proposes a symbolic plan. A motion planner then checks each step: is there a collision-free grasp, a reachable placement, a path between them? If a step fails, the failure becomes a new fact, such as blocked(cup, bottle), and the task planner plans again with it:
Real systems, such as PDDLStream, interleave the two searches more tightly, sampling grasps and placements as they go.
What to notice
With the bottle in the way, the first plan fails its grasp check. The planner learns the cup is blocked and adds two steps: move the bottle aside, then pick the cup. If the box is too full, placing fails too, and the plan grows a step to make room first. Each extra step comes from geometry, not from the task description, which only said "cup in box".