In this paper, a reaching law-based adaptive fixed-time terminal sliding mode control law, which is used for coupled spacecraft tracking maneuver in the presence of large inertia parametric uncertainties and external disturbances, is proposed. The coupled 6-DOF kinematics and dynamics for spacecraft motion are modeled on Lie group SE(3). The relative configuration is expressed by a local coordinate (exponential coordinate) of SE(3). In order to estimate the inertia parameters and external disturbances, we also propose a novel adaptive update law, which can make the control law be applied without the inertia parameters of the spacecraft a priori. Fixed-time convergence property of the closed-loop feedback system is proved in the framework of Lyapunov. Numerical simulations are performed to demonstrate the performances of the proposed control scheme for coupled spacecraft tracking maneuver.

Kinematics of a free-floating space-robot system is a fundamental and complex subject. Problems at the position level, however, are not considered sufficiently because of the nonholonomic property of the system. Current methods cannot handle these problems simply and efficiently. A novel and systematical modeling approach is provided; forward and inverse kinematics at the position level are deduced based on the product of exponentials (POE) formula and conservation of linear momentum. The whole deduction process is concise and clear. More importantly, inertial tensor parameters are not introduced. Then, three situations with different known variables are mainly studied. Due to the complexity of inverse kinematical equations, a numerical method is proposed based on Newton’s iteration method. Two calculation examples are given, a dual-arm planar model and a single-arm spatial model; both forward and inverse kinematical solutions are given, while inverse kinematical results are compared with simulation results of Adams. The results indicate that the proposed methods are quite accurate and efficient.

This article proposed an extended state observer (ESO)–based output feedback control scheme for rigid spacecraft pose tracking without velocity feedback, which accounts for inertial uncertainties, external disturbances, and control input constraints. In this research, the 6-DOF tracking error dynamics is described by the exponential coordinates on SE(3). A novel continuous finite-time ESO is proposed to estimate the velocity information and the compound disturbance, and the estimations are utilized in the control law design. The ESO ensures a finite-time uniform ultimately bounded stability of the observation states, which is proved utilizing the homogeneity method. A non-singular finite-time terminal sliding mode controller based on super-twisting technology is proposed, which would drive spacecraft tracking the desired states. The other two observer-based controllers are also proposed for comparison. The superiorities of the proposed control scheme are demonstrated by theory analyses and numerical simulations.

This paper aims to solve the control problem of coupled spacecraft tracking maneuver in the case of actuator faults, inertia parametric uncertainties, and external disturbances. Firstly, the spacecraft attitude and position coupling kinematics and dynamics model are established on the Lie group SE(3), and the coupled relative motion tracking error model is derived by exponential coordinates. Then, considering the actuator faults, an adaptive fuzzy scheme is proposed to estimate the lumped disturbances in real time, and a novel modified fixed-time terminal sliding mode fault-tolerant control law is developed to deal with the actuator faults and compensate the lumped disturbances. Next, the Lyapunov method is used to prove the stability and convergence of the system. Finally, the proposed controller can achieve fast and high-precision fault-tolerant control goals, and its effectiveness and feasibility are verified by numerical simulation.

This paper aims to address an integrated relative attitude and position fault-tolerant control strategy between a follower spacecraft and a leader spacecraft for coupled spacecraft tracking maneuver in the case of inertia parametric uncertainties, external disturbances, actuator failures, and saturation. The coupled rotational and translational kinematics and dynamics of the rigid spacecraft are derived on the Lie group SE(3), where the actuator failures and saturation are taken into account. Then, a 6-DOF extended state observer is proposed by using terminal sliding mode technique to estimate the lumped disturbance in finite time. An adaptive generalized super twisting algorithm of fault-tolerant controller is developed to guarantee the finite-time stability based on the estimated lumped disturbance information. The stability of the closed-loop system is proved in spite of the aforementioned disturbances via the Lyapunov analysis. Finally, the numerical simulation illustrates the effectiveness of the proposed control strategy.

Trajectory planning is a prerequisite for the tracking control of a free-floating space robot. There are usually multiple planning objectives, such as the pose of the end-effector and the base attitude. In efforts to achieve these goals, joint variables are often taken as exclusive operable parameters, while the berth position is neglected. This paper provides a novel trajectory planning strategy that considers the berth position by applying screw theory and an optimization method. First, kinematic equations at the position level are established on the basis of the product of exponential formula and the conservation of the linear momentum of the system. Then, generalized Jacobian matrices of the base and end-effector are derived separately. According to the differential relationship, an ordinary differential equation for the base attitude is established, and it is solved by the modified Euler method. With these sufficient and necessary preconditions, a parametric optimization strategy is proposed for two trajectory planning cases: zero attitude disturbance and attitude adjustment of the base. First, the berth position is transformed into the desired position of the end-effector, and its constraints are described. Joint variables are parameterized using a sinusoidal function combined with a five-order polynomial function. Then, objective functions are constructed. Finally, a genetic algorithm with a modified mutation operator is used to solve this optimization problem. The optimal berth position and optimized trajectory are obtained synchronously. The simulation of a planar dual-link space robot demonstrates that the proposed strategy is feasible, concise, and efficient.