Efficient Target Singulation with Multi-fingered Gripper using Propositional Logic

When multiple tablewares are closely packed on a table, rearranging obstacles to make space is necessary to grasp the target, often called target singulation. Due to the nature of handling fragile tablewares (i.e. plates, bowls), we make a few assumptions for the target singulation problem. First, tableware is grasped with a multi-fingered gripper; second, rearrangement is based on prehensile motions like pick-and-place. Under these assumptions, we aim to generate a relocation plan that guarantees global optimality. Furthermore, if any relocation plan cannot singulate the target, we aim to determine it quickly. Therefore, we propose a search method that utilizes the relationship between the object and its nearby obstacles expressed in propositional logic. We define the problem as determining logical entailment (i.e., whether the target can be singulated) and expand the search tree from the target while generating an optimal relocation plan. We demonstrate the performance of our algorithm by increasing the number of objects and validate the plan in a simulation environment.