This study addresses the problem of detumbling a non-cooperative space target, such as a malfunctioning satellite, using a space robot for the purpose of performing on-orbit servicing. The space robot is denoted as the servicer and consists of a satellite base equipped with a robotic manipulator. The formulation of a detumbling control strategy must respect limits on the grasping force and torque at the servicer’s end-effector without knowledge of the target’s inertial parameters (mass, inertia tensor, location of center of mass). In the literature, prior studies have formulated detumbling strategies under the assumption of accurate knowledge of the target’s inertial parameters. However, obtaining accurate estimates of the target’s inertial parameters is difficult, and parameter uncertainty may lead to instability and violation of the end-effector force/torque limits. This study will address the problem of detumbling a noncooperative target with unknown but bounded inertial parameters subjected to force/torque limits at the servicer’s end-effector.
In this study, two detumbling control strategies are presented. The first detumbling strategy is presented under the assumption that force/torque measurements at the end-effector are available. Detumbling of the target is achieved by applying a reference force/torque to the target that is designed to bring the target’s tumbling motion to rest subjected to force/torque limits. To ensure stable detumbling of the target, a robust compensator is designed based on bounds of the target’s unknown inertial parameters. Furthermore, once the detumbling process starts, in order to reduce the robust control gains, bounds on the target’s unknown inertial parameters are estimated in real-time. The resultant detumbling controller enables the servicer to detumble the target while complying with the target’s unknown residual tumbling motion.
The second detumbling control strategy is developed without the need of end-effector’s force/torque measurements and takes into account magnitude constraints on servicer’s control inputs in the detumbling controller’s design. Detumbling is achieved by tracking a desired detumbling trajectory that is delineated subjected to end-effector force/torque limits and requires bounds on the target’s inertial parameters. The hyperbolic tangent function is utilized to model the magnitude constraints on the servicer’s control inputs, resulting in a system that is non-affine in its control inputs. As a result, an augmented model of the servicer is presented to allow the formulation of the detumbling controller. Using bounds on the target’s inertial parameters, robust adaptive control approach is utilized to design the detumbling controller with the backstepping technique in order to track the desired detumbling trajectory and to reject the gained target’s momentum.
Numerical simulation studies were conducted for both detumbling control strategies utilizing a servicer equipped with a 7-degree-of-freedom (DOF) manipulator. The results demonstrate that both control strategies are capable of detumbling a non-cooperative target with unknown inertial parameters subjected to force/torque limits. Experiments conducted with a 3-DOF manipulator demonstrate that the design procedure utilized to delineate the desired detumbling trajectory in the second detumbling strategy respects force/torque limits at the end effector. The study is concluded with a discussion comparing the two proposed detumbling strategies by highlighting their advantages and disadvantages.
Adaptive pose and inertial parameters estimation of free-floating tumbling space objects using dual vector quaternions