Constraint propagation on interval bounds for dealing with geometric backtracking

The combination of task and motion planning presents us with a new problem that we call geometric backtracking. This problem arises from the fact that a single symbolic state or action may be geometrically instantiated in infinitely many ways. When a symbolic action cannot be geometrically validated, we may need to backtrack in the space of geometric configurations, which greatly increases the complexity of the whole planning process. In this paper, we address this problem using intervals to represent geometric configurations, and constraint propagation techniques to shrink these intervals according to the geometric constraints of the problem. After propagation, either (i) the intervals are shrunk, thus reducing the search space in which geometric backtracking may occur, or (ii) the constraints are inconsistent, indicating the non-feasibility of the sequence of actions without further effort. We illustrate our approach on scenarios in which a two-arm robot manipulates a set of objects, and report experiments that show how the search space is reduced.