Application of "generalized attractive region" in orienting 3D polyhedral part

In our previous work (Qiao, 2000), the concept of "generalized attractive region" in strategy investigation has been proposed. With this simple concept, a logical way to form strategies to achieve high precision tasks with minimum sensory feedback was achieved. The concept has been successfully applied to 3D high precision sensor-less robotic assembly, 2D sensor-less robotic orientation system and 2D sensor-less posing system with a four-pin gripper. The work was reported by "Advanced Manufacturing Technology Alert" (1999). In this paper, the conditions of the environment in robotic system, which can form attractive regions, are systematically analyzed in theory. Through analysis and simulation results: 1) it shows that there are always some strategic attractive regions which exist in the allowable region of the 3D polyhedral part with a flat environment; 2) therefore the pushing or grasping plan can be given directly; 3) also the vertex which touches the fence or the gripper in given orientation is given directly; and 3) it has been proven that on each rotational vector direction (which lies on any direction on XOY plane) and with the same contact vertex, the distance between the center of the part and the fence is a sinusoid function of the rotation amplitude. Furthermore, the amplitude and the initial angle of the sinusoid function is also investigated.