Elsevier

ISA Transactions

Volume 111, May 2021, Pages 35-46
ISA Transactions

Research article
Robust adaptive control for spacecraft final proximity maneuvers with safety constraint and input quantization

https://doi.org/10.1016/j.isatra.2020.10.064Get rights and content

Highlights

  • A combined nonconvex forbidden zone composed of a cylinder and a ellipsoid is developed around the target.

  • A novel safety controller is proposed by combining the repulsive potential function with sliding mode control methodology.

  • The proposed control scheme is capable of simultaneously tackling unknown model parameters, motion constraints, input saturation and quantization.

Abstract

In this paper, we tackled the robust quantized proximity control problem for spacecraft with uncertain system parameters, external disturbances and safety constraint. As a stepping stone, a nonconvex forbidden zone composed of a cylinder and an ellipsoid is established around the target spacecraft. Then, a novel repulsive potential function is employed to encode the collision-avoidance requirement. Furthermore, an adaptive safety controller is proposed for spacecraft rendezvous and docking by combining the artificial potential function with sliding mode methodology. Within the Lyapunov framework, rigorous stability analysis indicates that the presented controller guarantees the ultimate boundedness of all system signals, whilst providing a real-time safety trajectory for the chaser spacecraft. Finally, simulation results validates the theoretical analysis.

Introduction

With the burgeoning role of aerospace technology, autonomous spacecraft proximity and docking has drawn considerable attention from space community owing to its potential in various engineering missions, such as spacecraft servicing and assembly, space debris removal, deep space exploration, to name a few [1], [2], [3]. To fulfill these missions successfully, concurrent coupled pose control must be taken into consideration [4]. However, the nonlinearity and coupling feature arising from the kinematics and dynamics of spacecraft in the presence of uncertain system parameters and unknown disturbances would make it much more difficult to design control scheme [5], [6].

For the spacecraft nonlinear concurrent pose control problem, numerous advanced control schemes have been investigated in recent decades [7], [8]. Xu et al. [9] studied the velocity-free consensus control of multiple spacecraft attitude tracking. Owing to the inherent robustness against uncertainties and disturbances, sliding mode control technique was widely adopted in relative pose control law design of spacecraft [10], [11], [12]. By virtue of super twisting technique, Zhang and Duan [10] proposed an output-feedback line-of-sight control scheme for attitude tracking of tumbling spacecraft. Sun et al. [12] addressed the robust pose synchronization control problem for spacecraft subject to uncertain parameters and input saturation. Xia and Huo [13], [14] designed a robust backstepping control algorithm for the final proximity maneuvers by utilizing the radial basis function neural networks. With application of the minimum-learning-parameter approach, Liu et al. [15] designed a novel state-feedback control scheme for spacecraft proximity operations. Jia et al. [16] addressed the concurrent pose control problem for close-range proximity-around mission, and two nonlinear sliding mode controllers were proposed. Gaudet et al. [17] tackled the reinforcement meta-learning based pose control problem for spacecraft with time-varying dynamics and sensor distortion. Jiang et al. [18] presented an adaptive fixed-time rendezvous control law for close-range proximity maneuvers. Gao et al. [19] designed a nonlinear suboptimal solution for spacecraft capture of a floating target. By virtue of dual quaternions, an adaptive concurrent attitude and orbit control scheme was put forward for satellite rendezvous maneuvers [20]. In view of the active disturbance rejection control framework, Zhang et al. [21] proposed a disturbance-observer based control strategy for spacecraft proximity maneuver by employing exponential coordinates on the Lie group SE(3).

Besides the concurrent relative position tracking and attitude synchronization, another practical issue is the forbidden zone in the proximity process [22]. So far, various effective approaches have been adopted to achieve collision-avoidance requirement [23], [24], [25]. Hu et al. [26] tackled the dynamic trajectory planning and tracking issue for spacecraft proximity operations by employing the three dimensional B-spline technique and model predictive control methodology. Li et al. [27] developed a receding horizon guidance algorithm for rendezvous and docking with a malfunctional spacecraft with motion constraint and input saturation. Hu et al. [28] tackled the adaptive collision-free control problem for spacecraft in close-range rendezvous and docking process. By employing artificial potential function, Liu et al. [29] developed a neuroadaptive distributed formation flying control strategy for a group of second-order multiagent systems under motion constraints. Badway and McInnes [30] presented a superquadric potential function based algorithm for autonomous on-orbit assembly of large structure. By introducing the null-space based concept, Zhou et al. [31] designed a task-priority based algorithm for multiple autonomous agents. Zhang et al. [32] developed a optimal collision-avoidance path planning algorithm for a active chaser in order to approach a spinning target by using the Gauss pseudospectral method. Zong and Emami. [33] studied the optimal coordinated control problem of space manipulator rendezvous operations with thrust limitations. Huang and Jia [34] presented an integrated relative pose algorithm for spacecraft proximity-around mission under input limitations and state constraints. With resort to barrier Lyapunov function, Yang et al. [35] studied the path tracking control problem of robot manipulator subject to output error constraints and input saturation. Li and Wang [36] investigated the position tracking problem for a group of autonomous underwater vehicles under safety constraints and connectivity maintenance. Nevertheless, most of the aforementioned works assumed that the forbidden zone around the target was described by a single convex and/or axisymmetric motion constraint, which is usually too conservative in practical proximity maneuvers. In addition, few of previous studies have considered input saturation and quantization [37].

Motivated by the above discussions, this study is devoted to the final approaching control problem of close-range proximity maneuvers subject to external disturbances, unknown dynamics, and input saturation and quantization. To ensure the safety requirement, a nonconvex forbidden zone is encoded in the body-fixed frame of the target to represent the motion constraints during the proximity process. By employing repulsive potential function and sliding mode control methodology, a collision-free control scheme is introduced for autonomous rendezvous maneuvers, and two adaptive algorithms are applied to compensate for the unknown model parameters and external disturbances. It is provided that the developed scheme ensures the ultimate boundedness of all signals in the six-degree-of-freedom system, whilst providing a safety proximity trajectory for the chaser spacecraft. The main novelties of this study are stated as follows.

(1) Compared with the existing collision-free control algorithms, such as [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], a combined nonconvex forbidden zone composed of a superquadrics based cylinder and a slender ellipsoid is developed around the target spacecraft, which is much closer to the practical geometric envelope of the target, and increases the rendezvous corridor.

(2) Unlike the existing artificial potential function based control strategies, such as [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], only repulsive potential function is involved in this paper, and the objectives of relative pose tracking and collision avoidance are achieved by enabling the convergence of the well-designed sliding mode manifold. Therefore, there is no need to guarantee the potential function converges to the whole minimum eventually, which implies that the local minimum problem is avoided.

(3) Compared with the existing proximity and docking control methods, such as [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], the proposed robust safety control scheme is capable of tackling model uncertainties, disturbances, motion constraints, and input saturation and quantization simultaneously.

The remainder of this study is arranged as follows. Section 2 illustrates system model and mathematical preliminaries. The main results including control schemes development and stability analysis are formalized in Section 3. Section 4, performs simulation studies to illustrate the validity of the designed control schemes. Section 5 draws conclusions.

Section snippets

Coordinate reference frames and notations

Before proceeding, the relevant coordinate reference frames are stated, as provided in Fig. 1.

(1) Fi{OiXiYiZi} denotes the Earth-center inertial (ECI) frame. Its origin is located at the mass center of the Earth, OiXi axis points toward the vernal equinox, OiZi axis is parallel to the north pole, and OiYi axis completes the right-handed frame.

(2) Fc{OcXcYcZc} denotes the chaser body-fixed coordinate frame. Its origin is located at the mass center of the chaser, OcXc axis is parallel to the

Controller development

In this section, two quantized control algorithms are proposed for relative rotational dynamics and relative translational dynamics, respectively.

Simulation results

In this section, simulation results are applied to verify the performance the proposed method. In order to illustrate the collision-avoidance ability of the proposed scheme (Proposed), the disturbance observer based control method (DOC) [4] is employed for comparison purpose. Moreover, the cardioid-based forbidden zone, formulated as h3=(xe5)2+ye2+ze2+13(xe5)2(xe5)2+ye2+ze2 [39], is introduced to demonstrate the merit of the proposed combined forbidden zone. Suppose that the target orbit

Conclusions

This paper addresses the six degree-of-freedom proximity control problem for spacecraft rendezvous and docking in the presence of uncertain system parameters, external disturbances, safety constraints, and input limitations. A combined nonconvex forbidden zone composed of a superquadrics based cylinder and a slender ellipsoid is developed around the target spacecraft to describe the collision-avoidance requirement in the proximity operations. By integrating potential function technique with

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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