Prescribed performance tracking control of a free-flying flexible-joint space robot with disturbances under input saturation

Abstract

Aiming at the trajectory tracking of a free-flying flexible-joint space robot (FFSR) with unknown time-varying disturbances and input saturation, we develop a robust control law with prescribed performance constraints via backstepping technique. A disturbance observer is employed to estimate the unknown time-varying disturbances and two auxiliary systems are introduced to handle input saturation. Moreover, we use the dynamic surface control (DSC) technique to deal with the complexity explosion caused by multiple derivatives of the virtual control signals. The performance function and transformation function are utilized to improve the tracking performance. It is proved that the designed control law can maintain the tracking error of the FFSR within a predefined region, while guaranteeing the uniform ultimate boundedness of all signals in the FFSR closed-loop control system. Finally, simulations are carried out to demonstrate the effectiveness of the developed prescribed performance tracking control.

Introduction

With the commercialization of space technology, more and more satellite will be manufactured and launched for civil use. A large number of on-orbit servicing missions such as refueling, repairing, upgrading, and recycling could also be followed for more profit. Space robot consisted of multi-manipulator and a base spacecraft with flexible appendages are considered as one of the most promising approaches for these space operations and has attracted extensive attention in recent years [1], [2], [3], [4].

Different from ground-fixed manipulators, the precise and fast motion control of space robots need to take the coupling effect between the base spacecraft and the manipulators into consideration [5]. Especially if the mass of the manipulators is close to the base spacecraft [6]. Attitude maneuver of the base spacecraft is much more likely to excite vibration of the manipulators. On the contrary, the motion of the manipulators may also cause spacecraft attitude vibration and consequently affect the accuracy and stability of the end-effector position [7]. To tackle the coupling effect and achieve a good control performance, various advanced control strategies have been proposed. Yu [8] established the dynamic model of a free-floating space robot with one flexible link and two flexible joints and then developed a robust control law based on singular perturbation theory for it. Cheng and Chen [9] studied the coordinated control problem of a free-floating dual-arm space robot with closed chain and proposed a robust controller based on extended state observer. Zhang et al. [10] adopted a neural network to approximate the unknown uncertainty in a free-floating space robot and presented an adaptive controller to improve control precision of the system. Compared with free-floating space robots, due to the controllability of the base spacecraft, the free-flying space robots (FSRs) can reduce the coupling effect between the flexible appendages such as solar panels and the base spacecraft [11]. Moosavian et al. [12] introduced a multiple impedance control algorithm for FSRs. Wang and Xie [13] investigated the cases when the manipulator of a FSR picks up different tools of unknown lengths and verified the feasibility of the proposed adaptive Jacobian controller. Zhu et al. [14] designed an adaptive sliding mode disturbance observer to compensate for system uncertainty and a composite controller with prescribed performances for FSRs. In [11], [15], Yu and Chen discussed the modeling and control for FSRs with flexible joints and flexible links respectively. The joint elasticity of a flexible joint is mainly caused by the harmonic gear. It has a small size and a large reduction ratio, which is particularly suitable as a transmission device for space manipulators. But it also makes the control of the manipulators more challenging.

Note that most of the above works are concerned only with steady performance, seldom of them take the transient performance into account such as regulation time and overshoot. While in practical missions, due to the constraints of workspace and work-time, a space robot may be requested to follow the desired trajectory within specified time and not allowed a large overshoot [16], [17]. Therefore, it is necessary to study the tracking control of a space robot with prescribed transient performance. Moreover, all aforementioned control designs for free-floating space robots or FSRs have not considered input saturation. It is well known that if the influence of input saturation is ignored, the control system may become unstable. Because the maximum force or torque produced by the actuator limits the commanded control inputs of designed controller. It can become even worse in control systems with prescribed performance because input saturation may cause the tracking error to exceed the predefined boundary, resulting in the collapse of the control system [18], [19]. Input saturation as a kind of nonlinearity exists widely in real systems. A lot of research work has been done over the past few years [20], [21], [22], [23]. Du et al. [24] designed a robust nonlinear control law for the dynamic positioning of ships, and the problem of input saturation is solved by an auxiliary system. Ling et al. [25] developed an adaptive fuzzy dynamic surface control strategy for the single-link flexible-joint robot and employed a smooth function to approximate the saturated input. Richards and Turner [26] adopted the anti-windup compensator which combined both dynamic and static components to cope with the input saturation for quadcopters. Although the above researches have successfully reduced the influence of saturation nonlinearity on the control systems and achieved good results, how to tackle the constraints of actuators while guaranteeing the steady and transient performance for a FFSR is still worth further studying.

The system of the FFSR is a multi-input-multi-output (MIMO), strongly coupled and nonlinear system. For the sake of controlling such a system, the backstepping technique is adopted. As it is well known, the backstepping technique has been one of the most popular techniques to handle the control problem of nonlinear systems in recent years. It has been widely studied in control engineering [27]. The defect of complexity explosion when differentiating the signals of the virtual control law has been thoughtfully solved by command filter [28] or DSC technique [29]. Compared with command filter, DSC has the advantage that it does not need any information about control systems. This makes it ideal for situations where system dynamics is difficult to utilize. A lot of meaningful research related to DSC has been developed during the past two decades [23], [24], [25]. For instance, Lu et al. [30] used the backstepping technique combined with DSC to design an adaptive controller with prescribed performance for the stabilization control of the post-capture tethered combination.

In this paper, the prescribed performance tracking control problem is addressed for a FFSR simultaneously affected by actuators constraints and unknown time-varying disturbances. The main contributions are as follows:

• Input saturation and unknown time-varying disturbances are simultaneously considered for the prescribed performance control design of a FFSR system. In addition, the actuators whose physical constraints lead to input saturation include not only the control moment gyroscopes (CMG) of the base spacecraft but also the motors of the manipulator.

• A composite robust controller that combines backstepping technique with prescribed performance and DSC technique is proposed for the FFSR. Furthermore, two auxiliary dynamic systems are designed to deal with input saturation. We also construct a nonlinear disturbance observer to estimate the external unknown time-varying disturbances and enhance the robustness for the FFSR control system.

The remainder of this paper is organized as follows: Section 2 introduces the dynamic model of a FFSR with two rigid links and the related preliminaries. The robust controller with prescribed performance is designed in Section 3, where the stability of the controller is also analyzed. In Section 4, the results of numerical simulation are presented to demonstrate the effectiveness of the proposed control strategy. Finally, the conclusions are given in Section 5.