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 modeled as open-chain multi-body systems with single- and multi-degree-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 through a series of simulations.