An adaptive bilateral impedance control based on nonlinear disturbance observer for different flexible targets grasping☆
Introduction
In most contact operations, the slave manipulator in the tele-operation systems usually needs to contact with the controlled object, among which both of the trajectory control and the force control are essential to improve the working capability [1]. Safety contacts with various soft issues in different environments have become an active topic in engineering applications, such as in parts surface polishing [2], fruit and vegetable grasping [3], rehabilitation training [4], and tele-surgeries [5]. However, for the purpose of controlling tasks that involve flexible targets, the safety is often the prime thing to be considered. The trajectory tracking control strategy cannot fulfill the ideal control requirements anymore, since small trajectory planning errors may lead to permanent mechanical damages of the target. Excessive contact forces or small contact forces even make task failed of grasping soft objects due to deviations of the contact target. Many researchers have studied force control methods, such as impedance control [6], conductance control [7], hybrid force/position control [8],intelligent control [9], [10] and so on. Among them, the impedance control is widely used in practice due to its simple structure and high efficiencies. Impedance control methods apply a target impedance model [11] that establishes a dynamic relationship between the environmental contact force and the end point of the manipulator, so that these two quantities can be controlled indirectly to achieve soft objects grasping. However, traditional impedance control may achieve good effects merely by the precise environment model [12]. In practice, the external environment is usually unknown and time-varied, it is difficult to construct a specific impedance model. Therefore, the traditional impedance controller is not adaptable to the varied environment, and it is easy to create a large contact force error which may greatly affects the safety performances.
In order to reduce the contact force error, various control methods have been presented, which can be roughly divided into three categories: indirect adjustment of reference trajectory, direct adjustment of impedance position, and variable impedance control methods. The basic principle of indirectly adjusting the reference trajectory is to identify the environmental stiffness, environmental positions and other information to obtain the reference trajectory. In [13], an adaptive trajectory correction scheme based on contact force error is proposed to change the desired trajectory using adaptive law to estimate the environmental stiffness. At the same time, it adjusted the gain of the controller to compensate for the uncertain environmental stiffness. In [14], Komati et al. presented the contact information with the current environment for online estimations of the environmental stiffness and the analyze of the steady-state error. In [15], Zhang et al. investigated adaptive environmental parameter estimations via tracking the desired force by position-based impedance controller. Indirectly adjusting the reference trajectory has improved the adaptability to different environments by identifying environmental parameters with past information so as to estimate the unknown information. However, it may easily cause contact force errors. The fundamental principle of the direct adjustment of the reference trajectory is to correct the desired trajectory directly by a priori information. A controller based on model-referenced adaptive theory is used in [16], aiming to estimate the reference trajectory and to provide a stable ideal impedance for achieving the contact force tracking. The basic principle of the variable impedance control is to adjust the impedance parameters in real time by force feedback information and to adjust impedance model for the purpose of achieving high contact force tracking. In [17], Wang et al. introduced adaptive variable impedance approach to compensate for environmental uncertainty by adjusting the stiffness of the environment relative to the robotic manipulator. In [18], an impedance controller with variable stiffness is addressed based on the optimal control formulation in order to improve the contact force tracking effects using the dynamics of the system. In [19], Erol D et al. presented the neural network to adjust the coefficients of force control which reduced the requirement of the robotic manipulator for the accuracy of environmental parameters in impedance models.
In engineering applications, the control of contact forces can ensure the safety of the flexible target capture, while the stability and tracking accuracies of the robot motion control can also be adversely affected by external disturbances in the control process. Therefore, it has great theoretical and practical importance to study superior control strategies to enhance the stability of the system, the accuracy of trajectory tracking, and the resistance to disturbances [20], [21], [22]. In [23], a feedback controller based on the computational moment method and adaptive sliding mode controller is designed to decrease the influence of model. In [24], a nonlinear disturbance observer is tuned with the adaptive backstepping sliding mode controller so as to attenuate the chattering and to simultaneously estimate the effect of external disturbances. In [25], Liu et al. estimated the disturbance term consisting of time-varying parameters and the nonlinearity of the system by means of a nonlinear disturbance observer. It compensated the input and reduced the effect of the disturbance signal for the system.
From existed work, the control process of grasping soft targets not only requires the accurate force tracking to ensure the safety of soft targets, but also needs the precise trajectory tracking with strong anti-disturbance capabilities and high stabilities. Therefore, a composite control strategy combining adaptive bilateral impedance controller and sliding mode controller based on nonlinear disturbance observer is designed in this paper. Establishing a position-based impedance model, an adaptive controller is designed to online modify the desired trajectory using the error between the desired contact force and the actual contact force. Meanwhile, a nonlinear disturbance observer is applied to estimate the external uncertainties and disturbance terms. The modified desired trajectory is accurately tracked by sliding mode controller, so as to realize accurate tracking as well as to supply appropriate contact forces.
The contributions of this paper are summarized as follows.
(1) An adaptive bilateral impedance control method is designed into the bilateral teleoperation system. The desired force can be sufficiently tracked with the proposed method, which ensures the safety of various soft targets. (2) A nonlinear disturbance observer is introduced into the novel bilateral impedance control which not only accurately estimates the internal and external disturbances but also enhances the system stability during various soft targets grasping. (3) Numerical simulations and experiments are performed to verify the effectiveness of the proposed method and control.
Rest of paper is organized as follows: Section 2 describes the dynamics model of the bilateral tele-operation system with similar manipulators on both the master and slave side. Section 3 introduces our an adaptive impedance controller and a sliding mode controller based on a nonlinear disturbance observer. The stability of the proposed method is analyzed by Lyapunov functions. Numerical simulations and experiments are discussed and demonstrated in Section 4, followed by conclusions in Section 5.
Section snippets
Dynamical model of teleoperation system
A bilateral tele-operation system is generally divided into three parts: the human operator and the master manipulator located on the master side, the communication channel between the master and the slave side, and the slave manipulator located on the slave side. If the same model of n-DOF manipulator is used to both the master and the slave side, considering the existence of external disturbances and other factors in the system model, according to the Lagrange equation, the dynamics model of
Adaptive impedance bilateral tele-operation control
The impedance control system usually consists of a combination of impedance controller and a motion controller, The control structure diagram is showed in Fig. 1.
The error between the desired contact force and the actual contact force is input to the impedance controller so as to obtain the desired position modification, which converts the force error to position error. Then, the modified desired position is acquired by adding the position modification to the initial desired
Numerical simulations and experiments
For the purpose of verifying the effectiveness and the superiority of the proposed control strategy, the robotic manipulator on the master and slave sides adopt the same model and parameters. The dynamics model used in the simulation is written as follows, The parameters of the manipulator on both the master and the slave
Conclusion
In this paper, an adaptive impedance control strategy based on a nonlinear disturbance observer is proposed for solving the trajectory tracking and contact force tracking problems during the grasping of various soft targets in bilateral tele-operation systems. In order to achieve compatible grasping of various targets, a position-based impedance model is established. For different stiffness coefficients and environmental positions of the targets, an adaptive impedance controller is designed
CRediT authorship contribution statement
Yichen Zhong: Conceptualization, Methodology, Software, Writing – original draft. Ting Wang: Reviewing and editing. Yanfeng Pu: Editing.
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.
Acknowledgments
This work was supported by the National Natural Science Foundation of China [grant numbers No. 61906086] and Nanjing Customs Project [2022KJ03].
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