Singularity-Robust Full-Pose Workspace Control of Space Manipulators
with Non-Zero Momentum
Abstract
We address the end-effector full-pose tracking control problem in
free-floating space manipulators, experiencing constant non-zero linear
and angular momentum. The aim is to develop an output-tracking
(workspace) control law free of singularities due to parameterizing the
end-effector motion and being robust against singularities of the
input-output decoupling matrix (generalized Jacobian matrix). Space
manipulators are modelled as open-chain multi-body systems with single-
and multidegree-of-freedom joints, whose kinematics and dynamics are
formulated on the Special Euclidean group SE(3). Such systems exhibit
conserved (not necessarily zero) total momentum when operating in the
free-floating regime, which we use to systematically reduce their
dynamical equations by eliminating the base spacecraft’s motion. To
avoid parameterizing the end-effector motion, we consider its full pose
as the system output and develop a novel feedback linearization
technique on the matrix Lie group SE(3) in the reduced phase space of
the space manipulator. We then propose an intrinsic feedforward,
feedback proportional-integral-derivative workspace controller involving
a coordinate-free pose error function on SE(3) and velocity error on its
Lie algebra. Using a Lyapunov candidate, this controller is proven to
stabilize the end-effector pose to a feasible desired trajectory. The
input-output decoupling matrix in the proposed control law can lose rank
at some regions of the configuration space; hence, we implement a
singularity-robust inverse, derived from the damped least squares
method, to avoid impractical joint torques in these regions. The
developed controller is implemented on a 7-degree-of-freedom manipulator
onboard a spacecraft and its efficacy and robustness are demonstrated
trough series of simulations.