Kriegman Research Group

• Computing stable poses of piecewise smooth parts
• Computing capture regions of piecewise smooth parts
• Reorienting parts using a pivotting gripper

When a three dimensional object is known to be lying on a planar surface, its pose is restricted from six to three degrees of freedom. Computer vision algorithms can exploit the few stable poses of modelled objects to simplify scene interpretation and more accurately determine object location. This paper presents necessary and sufficient conditions for the pose of a piecewise smooth curved three dimensional object to be stable. For objects whose surfaces are represented by implicit algebraic equations, these conditions can be expressed as systems of polynomial equations that are readily solved by homotopy continuation. Examples from the implemented algorithm are presented.

Capture Regions

When a three dimensional object is placed in contact with a supporting plane, gravitational forces move it to one of a finite set of stable poses. For each stable pose, there is a region in the part's configuration space called a capture region; for any initial configuration within the region, the object is guaranteed to converge to that pose. The problem of computing maximal capture regions from an object model is analyzed assuming only that the dynamics are dissipative; the precise equations governing the system are unnecessary. An algorithm, based on Morse theory, is first developed for objects with smooth convex hulls. The formulation is then extended to objects with piecewise smooth hulls using a catalogue of critical points derived from stratified Morse theory. Algorithms have been fully implemented for objects with smooth and polyhedral convex hulls. As examples from the implementation demonstrate, calculating these regions from a geometric model is computationally practical.

Reorienting Parts using a Pivotting Gripper

To rapidly feed industrial parts on an assembly line, Carlisle et. al. proposed a flexible part feeding system that drops parts on a flat conveyor belt, determines position and orientation of each part with a vision system, and then moves them into a desired orientation. A robot arm with 4 degrees of freedom (DoF) is capable of moving parts through 6 DoF when equipped with a passive pivoting axis between the parallel jaws of its gripper. The idea is to grasp a part with 2 hard finger contacts such that it pivots, under gravity, into a desired orientation when lifted and replaced on the table. We refer to these actions as pivot grasps.

This paper considers the planning problem. Given a polyhedral part shape, coefficient of friction and a pair of stable configurations as input, find pairs of grasp points that will cause the part to pivot from one stable configuration to the other. For some transitions, pivot grasps may not exist. For a part with n faces and m stable configurations, we give an O(m^2 nlog n) algorithm to generate the m by m matrix of pivot grasps. When the part is star shaped, this reduces to O(m^2 n). We also study a generalization that considers ``capture regions'' around stable configurations. Both algorithms are complete in that they are guaranteed to find pivot grasps when they exist.