Divide-and-conquer manipulation planning by lazily searching a weighted two-layer manipulation graph

When people fail to move his or her arms from one configuration to another, they attempt to break the task into smaller tasks and finish them separately. This kind of solution is usually named “divide and conquer”. In this paper, we propose an implementation of “divide and conquer” where the robot attempts to divide one difficult manipulation task into smaller but easier problems according to the results of lazy planning. It leverages the planning of different levels to build a weighted two-layer manipulation graph, and divides and conquer the original task by lazily searching the weighted two-layer manipulation graph. In the lowest level, the planning is motion planning. In the middle level, the planning is grasp planning and placement planning. In the highest level, the planning is manipulation planning. Our implementation uses the grasps and placements computed in the middle level to construct a weighted two-layer manipulation graph for the highest level. It finds a manipulation path through the weighted two-layer manipulation graph in the highest level using lazy searching, and uses motion planning in the lowest level to find the motions that connect the vertices of the weighted two-layer manipulation path. Simulation is developed to demonstrate the the performance of our implementation. The manipulation task in the simulation is divided and separately conquered by leveraging the planning at different levels.