In task and motion planning (TAMP), the ambiguity and underdetermination of abstract descriptions used by task planning methods make it difficult to characterize physical constraints needed to successfully execute a task. The usual approach is to overlook such constraints at task planning level and to implement expensive sub-symbolic geometric reasoning techniques that perform multiple calls on unfeasible actions, plan corrections, and re-planning until a feasible solution is found. We propose an alternative TAMP approach that unifies task and motion planning into a single heuristic search. Our approach is based on an object-centric abstraction of motion constraints that permits leveraging the computational efficiency of off-the-shelf AI heuristic search to yield physically feasible plans. These plans can be directly transformed into object and motion parameters for task execution without the need of intensive sub-symbolic geometric reasoning.