  To achieve high-dexterity motion planning on floating-base systems, the base
dynamics induced by arm motions must be treated carefully. In general, it is a
significant challenge to establish a fixed-base frame during tasking due to
forces and torques on the base that arise directly from arm motions (e.g. arm
drag in low Reynolds environments and arm momentum in high Reynolds
environments). While thrusters can in theory be used to regulate the vehicle
pose, it is often insufficient to establish a stable pose for precise tasking,
whether the cause be due to underactuation, modeling inaccuracy, suboptimal
control parameters, or insufficient power. We propose a solution that asks the
thrusters to do less high bandwidth perturbation correction by planning arm
motions that induce zero perturbation on the base. We are able to cast our
motion planner as a nonholonomic rapidly-exploring random tree (RRT) by
representing the floating-base dynamics as pfaffian constraints on joint
velocity. These constraints guide the manipulators to move on zero-perturbation
manifolds (which inhabit a subspace of the tangent space of the internal
configuration space). To invoke this representation (termed a
\textit{perturbation map}) we assume the body velocity (perturbation) of the
base to be a joint-defined linear mapping of joint velocity and describe
situations where this assumption is realistic (including underwater, aerial,
and orbital environments). The core insight of this work is that when
perturbation of the floating-base has affine structure with respect to joint
velocity, it provides the system a class of kinematic reduction that permits
the use of sample-based motion planners (specifically a nonholonomic RRT). We
show that this allows rapid, exploration-geared motion planning for high degree
of freedom systems in obstacle rich environments, even on floating-base systems
with nontrivial dynamics.
