Orienting polyhedral parts by pushing

A common task in automated manufacturing processes is to orient parts prior to assembly. We consider sensorless orientation of an asymmetric polyhedral part by a sequence of push actions, and show that is it possible to move any such part from an unknown initial orientation into a known final orientation if these actions are performed by a jaw consisting of two orthogonal planes. We also show how to compute an orienting sequence of push actions.We propose a three-dimensional generalization of conveyor belts with fences consisting of a sequence of tilted plates with curved tips; each of the plates contains a sequence of fences. We show that it is possible to compute a set-up of plates and fences for any given asymmetric polyhedral part such that the part gets oriented on its descent along plates and fences

Models and motion planning

AbstractWe study the complexity of the motion planning problem for a bounded-reach robot in the situation where the n obstacles in its workspace satisfy two of the realistic models proposed in the literature, namely unclutteredness and small simple-cover complexity. We show that the maximum complexity of the free space of a robot with f degrees of freedom in the plane is Θ(nf/2+n) for uncluttered environments as well as environments with small simple-cover complexity. The maximum complexity of the free space of a robot moving in a three-dimensional uncluttered environment is Θ(n2f/3+n). All these bounds fit nicely between the Θ(n) bound for the maximum free-space complexity for low-density environments and the Θ(nf) bound for unrestricted environments. Surprisingly—because contrary to the situation in the plane—the maximum free-space complexity is Θ(nf) for a three-dimensional environment with small simple-cover complexity