| Abstract | In this paper we present a novel geometric approach
to motion planning for constrained robot systems.
This problem is notoriously hard, as classical sampling-based
methods do not easily apply when motion is constrained in
a zero-measure submanifold of the configuration space. Based
on results on the functional controllability theory of dynamical
systems, we obtain a description of the complementary spaces
where rigid body motions can occur, and where interaction
forces can be generated, respectively. Once this geometric setting
is established, the motion planning problem can be greatly
simplified. Indeed, we can relax the geometric constraint, i.e.,
replace the lower–dimensional constraint manifold with a fulldimensional
boundary layer. This in turn allows us to plan
motion using state-of-the-art methods, such as RRT*, on points
within the boundary layer, which can be efficiently sampled. On
the other hand, the same geometric approach enables the design
of a completely decoupled control scheme for interaction forces,
so that they can be regulated to zero (or any other desired
value) without interacting with the motion plan execution.
A distinguishing feature of our method is that it does not
use projection of sampled points on the constraint manifold,
thus largely saving in computational time, and guaranteeing
accurate execution of the motion plan. An explanatory example
is presented, along with an experimental implementation of the
method on a bimanual manipulation workstation.
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