  In order for a bimanual robot to manipulate an object that is held by both
hands, it must construct motion plans such that the transformation between its
end effectors remains fixed. This amounts to complicated nonlinear equality
constraints in the configuration space, which are difficult for trajectory
optimizers. In addition, the set of feasible configurations becomes a measure
zero set, which presents a challenge to sampling-based motion planners. We
leverage an analytic solution to the inverse kinematics problem to parametrize
the configuration space, resulting in a lower-dimensional representation where
the set of valid configurations has positive measure. We describe how to use
this parametrization with existing motion planning algorithms, including
sampling-based approaches, trajectory optimizers, and techniques that plan
through convex inner-approximations of collision-free space.
