We discuss assembly stability as a constraint for assembly sequence planning. An assembly sequence plan is a high-level plan for constructing a mechanical product from its component parts. The analysis of (sub)assembly stability avoids mating parts which tend to disassemble under the influence of gravity. Furthermore, the number of reorientations which gives a good idea on the value of an assembly sequence depends on the stability of the parts to be assembled. We present algorithms to calculate the set of potentially stable orientations of an (sub)assembly considering static friction under uniform gravity. This set is used for the evaluation of assembly sequences and the minimization of the number of reorientations during plan execution. Therefore, a new evaluation function based on the set of potentially stable assembly orientations is proposed and integrated into the assembly cost evaluation of a high level assembly planning system.

Regrasping must be performed whenever a robot's grasp of an object is not compatible with the pick-and-place operation the robot must perform. This paper presents a new approach to the problem of regrasping for a robot arm equipped with a parallel-jaw end-effector. The method employs an evaluated breadth-first search in the space of compatible regrasp operations taking into account several criteria rating about the grasp and placement quality. We pay particular attention to online computational efficiency. The presented system is the first planning system performing as much of offline computation as possible for solving the regrasp problem efficiently online.

We discuss the stability of assemblies consisting of arbitrary configurations of rigid bodies considering Coulomb friction under uniform gravity. We give a method to calculate the set of all stable orientations of an assembly considering the frictional properties. The presented algorithm is a new method for automatically determining all stable orientations of assemblies considering friction. The potential stability criterion describes a necessary but not a sufficient condition for the stability of assemblies. To compute the potential stability of an assembly we consider the forces which arise at contact points of objects touching each other. Constraints which must be satisfied for a set of valid contact forces are expressed by linear inequalities; we use linear programming to determine such valid contact forces. Beside this we describe a method based on the concepts of the enumeration of vertices of polyhedra to compute the set of stable orientations considering Coulomb friction even in the case of degeneracy in the linear program, Furthermore, we discuss the space and time complexity of the underlying algorithm.