Combining Task and Motion Planning is Not Always a Good Idea

Combining task and motion planning requires to interleave causal and geometric reasoning, in order to guarantee the plan to be executable in the real world. The resulting search space, which is the cross product of the symbolic search space and the geometric search space, is huge. Systematically calling a geometric reasoner while evaluating symbolic actions is costly. On the other hand, geometric reasoning can prune out large parts of this search space if geometrically infeasible actions are detected early. Hence, we hypothesized the existence of a search depth level, until which geometric reasoning can be interleaved with symbolic reasoning with tractable combinatorial explosion, while keeping the benefits of this pruning. In this paper, we propose a simple model that proves the existence of such search depth level, and validate it empirically through experiments in simulation.