  Planning motions for two robot arms to move an object collaboratively is a
difficult problem, mainly because of the closed-chain constraint, which arises
whenever two robot hands simultaneously grasp a single rigid object. In this
paper, we propose a manipulation planning algorithm to bring an object from an
initial stable placement (position and orientation of the object on the support
surface) towards a goal stable placement. The key specificity of our algorithm
is that it is certified-complete: for a given object and a given environment,
we provide a certificate that the algorithm will find a solution to any
bimanual manipulation query in that environment whenever one exists. Moreover,
the certificate is constructive: at run-time, it can be used to quickly find a
solution to a given query. The algorithm is tested in software and hardware on
a number of large pieces of furniture.
