Robust Control of Free-Flying Space Manipulator for Capturing Uncontrolled Thumbling Objects
Authors:   Politecnico di Milano, Milan, Italy, Massari Mauro , Invernizzi Davide , Lovera Marco , Ghignoni Pietro , Ticozzi Lorenzo 
Published: January 2024

The potential of In-Orbit Servicing (IOS) to extend the operational life of satellites and the need to implement Active Debris Removal (ADR) to effectively tackle the space debris problem are well known among the space community. Research on technical solutions to enable this class of missions is thriving, also pushed by the development of new control systems. Several solutions have been proposed over the years to safely capture orbital objects, the majority of which rely on robotic systems. A promising solution is the employment of an autonomous spacecraft (chaser) equipped with a highly dexterous robotic arm able to perform the berthing with a resident space object. In this respect, the design of an effective, reliable, and robust Guidance Navigation and Control (GNC) system, for which several architectures and hardware configurations are possible, plays a key role to ensure a safe mission execution. The proposed solution aims at the implementation of a combined control strategy wherein the spacecraft base and the robotic arm are controlled together. As shown by recent works, a combined architecture has several advantages over decoupled control strategies, from fuel efficiency improvement to performance improvement. Robust control methods are adopted to design control laws for the uncertain, nonlinear dynamics of the chaser and of the complete chaser-target stack after capture.
Space robots are characterized by a high level of complexity due to the kinematic and dynamic coupling between its elements. The motion of a single body (be it the base or one of the links) is transmitted downstream (in the direction of the end-effector) according to the properties of the kinematic chain, while it dynamically affects the system also in the upstream direction (towards the satellite-base). From a practical standpoint this means that, unlike ground-fixed robots, the motion of the manipulator causes a motion of the base. Keeping these aspects in mind, the dynamic model of a space robot is mostly built upon the traditional theory of rigid multibody system. In this work a recursive method has been applied to the system of interconnected rigid bodies which, unlike the direct equivalent, models the interconnections in terms of forces and kinematic constraints acting at a single-body level. This results in a large set of equations which can be solved by exploiting recurrence relations descending from the tree-like structure of the system. The proposed recursive method leverages a floating-base version of both the Newton-Euler algorithm (RNEA) and the composite rigid-body algorithm (CRBA); in particular, spatial vector algebra has been used to increase compactness and efficiency of the algorithms. Following this approach, a rigid multi-body model of the system has been developed including the chaser platform and a 7 degrees-of-freedom redundant manipulator mounted on the spacecraft base.
As for control design, the chosen architecture is based on a combined approach wherein base and manipulator states are controlled together, following ideas recently proposed in the literature. The specific approach developed in this work consists in using nonlinear control laws, based on extensions of the well–known computed torque controller to space robot, together with a systematic tuning procedure based on the H-Infinity framework. Indeed, while computed torque controllers deliver good tracking performance in a large domain of operating conditions, they suffer from modelling uncertainty (they are based feedback linearization) and no rule is given to tune the gains of the feedback component of the control law, which is typically based on a (nonlinear) Proportional Derivative (PD) law. Hence, trial and error procedures are often employed in practice to select the gains and achieve acceptable performance. Such an approach is made more challenging by the large number of states of space robots. Therefore, the following systematic tuning approach has been considered: first, both the plant and the control law are linearized about a nominal operating point and a linear uncertain description of the closed–loop system is derived; then, the gains of the control law are tuned by leveraging the structured H∞ framework. In this manner, the control law handles by design the rigid body nonlinearities while performance requirements can be imposed in the neighborhood of the desired configurations when tuning the gains. The proposed synthesis approach allows accounting for dynamics effects at synthesis time, such as sloshing, actuator dynamics, flexibility, orbital dynamics, which are neglected when deriving the nonlinear control law. The proposed robust control is designed in joint space and thus requires computing a reference trajectory in joint space. However, the capture of uncontrolled thumbling objects poses requirements to the trajectory generation in task space. A trajectory generation for the end effector in task space is proposed together with an inverse kinematic approach which exploits the manipulator redundancy to locally optimize the manipulability index. In addition, a feedback term is added in the inverse kinematic algorithm to make up for possible location and attitude errors, according to the Closed-Loop Inverse Kinematics (CLIK) algorithm. As the target is in an uncontrolled thumbling state, the reference trajectory generation is generated propagating forward in time the target motion, but continuously updating the propagation with information on the current state of the target coming from the Navigation System.
After the controller synthesis, a robustness analysis with respect to rigid-body uncertainties (mass, moments of inertia (MoI), products of inertia (PoI) and center of mass (CoM) position) and sloshing is performed, while the performances of the proposed controller are evaluated on a representative scenario for the capturing of an uncontrolled thumbling object using a full nonlinear model of the dynamics.