This paper presents a novel solution to the control problem of end-effector robust trajectory tracking for space robot. External disturbance and system uncertainties are addressed. For the considered robot operating in free-floating mode, a Chebyshev neural network is introduced to estimate system uncertainties and external disturbances. An adaptive controller is then proposed. The closed-loop system is guaranteed to be ultimately uniformly bounded. The key feature of this proposed approach is that, by choosing appropriate control gains, it can achieve any given small level of
With the development and launch of spacecraft, the function of spacecrafts is becoming more and more complex. As a result, any component failure will deteriorate spacecraft’s performance and sometimes even make the planned mission totally terminate. Aiming to decrease economic loss induced by spacecraft failures, on-orbit servicing has received considerable attentions. However, due to the harsh operating environment such as high temperature, it is very difficult for astronauts to accomplish orbital works. This makes space robot become the best option to accomplish orbital repair. Additionally, the space robot can also perform other on-orbit servicing missions such as repair, assembly, refueling, and/or upgrade of spacecraft. This leads to development of space robot techniques [
For space robot, the end-effector control in the presence of uncertain kinematics and dynamics is becoming one of the challenges that need to be addressed. In [
The preceding approaches were proposed based on the assumption that the dynamic model can be linearized. However, this assumption would not be satisfied for space robot. As a result, the above control methodologies were not applicable to space robot. Moreover, in the above nonlinear controller design, the developed controllers can only ensure the stability of the resulted system. They were not able to achieve disturbance attenuation. It greatly limits the application of those schemes. To achieve tracking control with disturbance attenuation,
Inspired by the great performance of
This paper is organized as follows. In Section
The notation adopted in this paper is fairly standard. Let
Our main results relay on the following stability definitions for a given nonlinear system:
Let
Consider
To control the plant (
The nominal Jacobian matrix
The Chebyshev neural network (CNN) [
As a result, for any continuous nonlinear function vector
The optimal weight matrix
The objective of the proposed design methodology is to construct a control input function such that the end-effector trajectory state
Because the system dynamics described in (
In the controller design, it is assumed that the trajectory of the space robot’s end-effector is always within the Path Independent Workspace (PIW). All the points in the PIW are guaranteed not to have dynamic singularities. As a result, it can ensure that
Define the trajectory tracking error as
To remove the effect of the above uncertain kinematics, CNN is used to approximate
To accomplish controller design, a virtual control input is
Additionally, define an error vector for
Introduce two new variables
Consider the space robot system described by (
For the introduced variables, applying (
Choose a Lyapunov candidate function as
Based on Assumption
Define lumped disturbance as
It should be stressed that the smaller the value of
Additionally, because the desired trajectory
To test the proposed controller, a two-link space robot operating in a free-floating mode is numerically simulated. The trajectory tracking control for its end-effector is performed. The main physical parameters, control gains, and external disturbances are listed in Table
Simulations parameters.
Physical name | Value |
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Space robot link |
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Control gains |
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The order of CNN |
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The initial value of optimal weight matrix |
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External disturbance |
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With application of the proposed approach, Figure
The desired trajectory (solid line) and the actual trajectory (dashed line) of end-effector with
The position tracking error of the end-effector with
The initial response
The steady-state behavior
The velocity tracking error of the end-effector with
The initial response
The steady-state behavior
The estimate of the optimal weight matrix (
As summarized in Theorem
The position tracking error of the end-effector with
The position tracking error of the end-effector with
The position tracking error of the end-effector with
The position tracking error of the end-effector with
In this case, an ideal condition is considered. That is, there are no external disturbances acting on the space robot. By using the proposed control law, the control performance is shown in Figures
The desired trajectory (solid line) and the actual trajectory (dashed line) of end-effector in the absence of external disturbances.
The position tracking error of end-effector in the absence of external disturbances.
The initial response
The steady-state behavior
The velocity tracking error of end-effector in the absence of external disturbances.
The initial response
The steady-state behavior
The estimate of the optimal weight matrix (
The problem of end-effector trajectory tracking control was investigated for a space robot working in free-floating mode by incorporating the criterion of a tracking performance given by
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported partially by the National Natural Science Foundation of China (Project nos. 61503035 and 61573071) and the Foundation of the National Key Laboratory of Science and Technology on Space Intelligent Control (Project no. 9140C590202140C59015). The authors highly appreciate the preceding financial supports. The authors would also like to thank the reviewers and the editor for their valuable comments and constructive suggestions that helped to improve the paper significantly.