Decidability in Robot Manipulation Planning
This work addresses the fundamental decidability issue in robot manipulation planning, which is crucial for robotics researchers and engineers, though it is incremental as it builds on existing theoretical frameworks.
The paper tackled the problem of planning collision-free motion for multiple objects using a robot with limited simultaneous manipulation capacity, proving that this simplified manipulation planning problem is decidable. The result extends to a broader class of systems with stratified configuration spaces, such as legged locomotion and bi-manual manipulation, without imposing dynamics restrictions.
Consider the problem of planning collision-free motion of $n$ objects in the plane movable through contact with a robot that can autonomously translate in the plane and that can move a maximum of $m \leq n$ objects simultaneously. This represents the abstract formulation of a manipulation planning problem that is proven to be decidable in this paper. The tools used for proving decidability of this simplified manipulation planning problem are, in fact, general enough to handle the decidability problem for the wider class of systems characterized by a stratified configuration space. These include, for example, problems of legged and multi-contact locomotion, bi-manual manipulation. In addition, the described approach does not restrict the dynamics of the manipulation system to be considered.