Parameter Adaptive Sliding Mode Trajectory Tracking Strategy With Initial Value Identication For Swing In A Hydraulic Construction Robot

 Abstract: A novel trajectory tracking strategy is developed for the swing DOF with double actuated cylinder in a hydraulic construct robot. When the work object is grabbed and unload, the inertia parameter of swing varies greatly and the estimation algorithm is commonly insufficient. Aiming at this feature, a novel nonlinear hydraulic dynamics model is established for the double actuated hydraulic cylinder in the system and a robust adaptive control strategy with parameter adaptive estimation is designed to improve the trajectory tracking performance. Aiming at the problem of insufficient convergence speed of the identification algorithm, a method of robotic gravity identification combined with stereo vision information is proposed to obtain the mass and moment of inertia parameters of the working object so that the initial value is close to the real value. Simulations and experiments are presented to validate the effect of the novel strategy.


Introduction
Due to the risks of operating error and dynamic has been demonstrated, although automatic control has been widely used with the advantaged of precision and efficiency for controlling various types of machines [1,2].
For a robotic construction machine, to improve the environmental perception and provide intelligent assistance with automatic control to novice operators is a more practical way [3][4][5]. By optimizing the values of proportional-integral-derivative (PID) controller, an improved ant colony optimization algorithm (IACO) is proposed in [6] to improve the tracking accuracy of a hydraulic system. [7] designed a robust controller by means of µ-synthesis to guarantee robust stability and performance of a hydraulic excavator. A construction robot system with PHRI (physical human-robot interaction) is developed by Zhao etc., which is used for carry task at the earthquake disaster site [8,9]. In such a system, as the end effector may bring danger to the operator, a novel force reflect master-slave control schematic is adopted.
Most actual engineering robot systems are actuated by hydraulic servo systems which suffer from heavy Parameter Adaptive Sliding Mode Trajectory Tracking Strategy with Initial Value Identification for Swing in A Hydraulic Construct Robot ·3· disturbances including uncertainties and unknown disturbances. In order to attain high performance tracking control in the uncertain nonlinear systems, the robust adaptive control method [10] has been widely used recently because of its flexibility and robustness. A fuzzy logic controller was designed in [11] to track the given trajectory for a 2 DOF industrial robot. The controller parameters were optimized by using the particle swarm optimization with three different cost functions. The fuzzy logic in the algorithm reduces the complexity of mathematical modeling which is commonly a complex and time-consuming process, but the lack of comprehensive analysis leads to the problem of generality on multi situations, even good results have been obtained in the specified experiments. Among the methods, adaptive sliding mode control is a very important one [13,14].
Adaptive sliding mode control is a new type of control strategy for a nonlinear system, which combines the advantages of adaptive control and sliding mode control by introducing adaptive control in sliding mode controller.
According to the information uncertainty obtained by adaptive controller, the sliding mode controller can be adjusted to reduce the uncertainty of the system and reduce the conservativeness of the sliding mode control.
In this way, the system not only maintains the robustness of sliding mode control to external disturbances and unmodeled dynamics, but also uses adaptive control to eliminate the shortcomings of sliding mode control [15][16][17][18]. In order to suppress actuator's motion disturbance, a nonlinear robust dual-loop control scheme is developed in [19]. Besides actuator's motion disturbance, both the nonlinearity characteristics and friction problem of the proposed in [20].
Although sliding mode control has strong robustness, it is still a control method based on the precise mathematical model of the object strictly speaking [21].
The "rough" mathematical model of the system must be predicted before the system sliding mode surface parameters and controller parameters can be determined.
For nonlinear systems, we must know the dynamics of the nonlinear function of the system before we can design a sliding mode controller.

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Then relatively accurate initial values of controller parameters can be obtained, and the convergence and trajectory tracking accuracy of the controller are also improved. This is the motion of this article.
This paper is organized as follows: The background and related research are introduced in Section 1. In Section 2, the system overview of the teleoperation system and the problem description is proposed. In Section 3, the sliding mode adaptive robust controller for Swing is given. The Identification of the system initial value is presented in Section 4. The simulation experiment is given in Section 5, and a comparison experiment carrying object between two points by three controllers is performed in Section 6.

System description
The system in this paper is a teleoperation system consists of the following two parts: a pair of two-DOF hydraulic PHRI as the master part, a robot reconstructed from a hydraulic excavator as the slave part and the control PC of each part, as is shown in Figure 1.

Figure 1
The teleoperate system Four asymmetric hydraulic cylinders are driven by a servo valve. The working pressures can be measured by pressure sensors which are added to the rod and rodless chambers of the hydraulic cylinders. The displacements of the working device can be gained by the displacement sensors which are installed outside the hydraulic cylinders.
The system uses cameras for monitoring, but considering the limitations of camera viewing angle and clarity, a 3D vision device is used to construct a virtual scene and the work object. The general shape of the object can be obtained through the 3D camera, but the volume and shape are of low accuracy due to the limitation of the camera's resolution.

Problem description
The moment of inertia parameter of Swing varies greatly when the work object is carried and unload. But it is a constant value during one procedure. This article designs a sliding adaptive robust trajectory tracking controller for the Swing of the hydraulic construction robot. But the strategy suffers from the convergence speed when the moment of inertia parameter varies. A moment of inertia identification algorithm is effective to the problem.
Summarizing, the main problem can be split into the following subproblems.
①According to the dynamic characteristics of the robot, the gravity compensation algorithm is used to obtain the weight of the object according to the information of the arm and boom force sensors. The shape and size information of the working object is obtained by computer vision, combined with the weight information, the inertia of the object relative to the swing is obtained. ② In order to improve the ability to suppress uncertainty and disturbance, a sliding mode adaptive controller is designed for the hydraulic servo system of Swing. Combining the controller and the initial value obtained by the identification of the moment of inertia, the convergence effect of the parameter and trajectory tracking performance are improved.

The mathematic model of the hydraulic system
For the hydraulic system shown in Figure 2, its dynamic model is where m is the mass of the cylinder rod， I is the equivalate mass of the robotic arm and the cylinders，F 1 and F 2 are load force of the cylinders, C is the damp coefficient. Then, where, n, A 1 and A 2 are the area of the two sides of the piston, P 1 and P 2 are the pressures inside the two chambers of the cylinder, C is the coefficient of viscous friction.   Figure 3, the length l 1 and l 2 are small value and with almost the similar amplitude when the swing DOF moves from center position to the 60°p osition, it can be considered that To eq. (3), taking leakage and compressibility into consideration, the dynamics of cylinder oil flow can be written as follows [17] 11 where β e is the bulk modulus of the fluid, C t is the internal leakage coefficient, V 1 and V 2 are the total fluid volumes of the two sides of the cylinder. Q 1 and Q 2 are the fluid flow rate of the two chambers of the cylinder. They are related to the spool valve displacement of the servo valve x v and given as where k q is the flow gain coefficients of the servo valve.
Defining the state variables as x x x x y y P P = = x (6) The entire dynamics can be expressed in a state-space where M is the Equivalent load mass obtained from Eq.
(3), V 0 is the total fluid volumes of the two cylinders, A s is the total area of the cylinders.
The time derivative of the second eq. in (7) is In (8), the third term minus the fourth ( ) Thus, 2 12 0 0

Controller design
Define the unknown parameter set as  - Function f is not completely known but can be written asf f f = +  ， where f is the nominal part and Δf is the uncertain part, which is bounded by a known function The control gain g is unknown but confined to a certain constant range. i.e.
The estimated value of g is given as The control objective is to make the system state x L track a desired trajectory x Ld asymptotically.
The control input u is where k is the control gain, f is the boundary layer of sliding mode, and sat(Δ) is the saturation function, which can be formally defined as 1, 1, In order to obtain the adaptation laws of parameters, the following Lyapunov function is defined as where ˆi  is the estimation value of i  .
Parameter Adaptive Sliding Mode Trajectory Tracking Strategy with Initial Value Identification for Swing in A Hydraulic Construct Robot

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The estimation error given as =- The time derivative of V 1 is To make sure that 1 0 V  , the adaptation laws are chosen as It can be shown that for any adaptation function, the projection mapping guarantees The controller (20) and the adaptation laws (26) guarantee asymptotic convergence to zero of the tracking errors, i.e., ( ) 0 xt → as time t →.

Identification of the moment of inertia
The swing DOF during the carrying procedure is a robot arm system with constant parameter which cannot be identified offline. As is descripted in section 3, the main parameters in (10)  Assuming that the density, approximate shape and the volume of the work object is known as However, since the shape and volume obtained by the vision system are far from the work object, if it is directly used for estimation, the accuracy will be too low. The force obtained by the force sensor is more accurate. If the mass of the work object can be obtained with the force of arm and boom, the moment of inertia can be corrected to obtain more accurate moment of inertia parameters.
To the system constituted by boom, arm and folkglove, the dynamic model is [29] Jing-Wei Hou et al.

Figure 4
The boom and arm parameter where, τ a and τ b are the torques of arm and boom, as is shown in Figure 4. The boom angle θ b is The arm angle θ a is Where, L go is the distance from the center of the object to the Swing, which is obtained by Digiclops. where, l omin is the minimum distance of the object from swing, l omax is the max distance of the object from swing.
Here the object is supposed to be evenly distributed, the volume V 1 is obtained by the vision information.
I o1 can be used as the initial value of the parameter identification.

5.Simulation experiment
To verify the effect of the proposed scheme, the proposed control laws were simulated using Matlab's Parameter Adaptive Sliding Mode Trajectory Tracking Strategy with Initial Value Identification for Swing in A Hydraulic Construct Robot ·9· Simulink package. Three methods including compound PID control (CPID), common sliding mode control(SM) and the sliding mode control with initial value (SMI) proposed in this paper are used for compare experiment.
The schematics of the controllers are shown as the following Figure 5 The compound PID controller (CPID) The CPID controller is shown in Figure 5. This is a practical controller in a linear system. The zero and pole points are optimized through the feedforward and feedback PID controller, and the PID parameters can be adjusted in conjunction with the Routh stability criterion.

Figure 6
The sliding mode controller (SM) Figure 7 The sliding mode controller with initial value identification (SMI) The sliding mode controller is shown in Figure 6, the input modules in both Figure 4 and Figure 5 functions on desired trajectory output. Including position, velocity and acceleration. The trajectory is y=sin(πt).

Figure 8
The SimMechanics plant Plant built by SimMechanics is applied in the simulation program. As is shown in Figure 6. the load features can be adjusted by setting the mass and gravity center. Taking into account the work scenario in this article, the load parameter is a constant value after it is determined, and no disturbance force is contained. Only a commonly used friction force with LuGre model is added. The reference trajectory is chosen to be θ d =sinπt.
Positions and angles are expressed in meters and degrees, respectively. Nonlinear control with force sensors (NCFS), and compound PID control strategies with well-tuned parameter are compared in the reference trajectory given by Eq. (44).

Figure 9
The trajectory tracking result Through simulation experiment result, it can be seen that the CPID method has a certain effect. Since CPID does not have the parameter estimation function, its initial tracking error is not much different from the final tracking error. The trajectory tracking error of the SM is much smaller than the steady-state error of the CPID. But due to the parameter coupling [14], the parameters of the SM method cannot approach the parameters well, so the capability of the controller has not been fully exerted. The SMI trajectory tracking results in the later stage is the best among the three methods because of the better parameter estimation caused by initial value. But the parameter identification results are a little different from the real value because of the limit of the estimation algorithm.

Experiment
This section demonstrates the moment of inertia identification experiment and the validation experiment of SMI. The system setup and implementation issues are outlined in 6.1. The process and result of the identification experiment are presented in 6.2, and control effect verification experiment in 6.3.

Experiment setup and implementation issues
The contact setup for the experiment is shown in Figure   5.

Figure 11
Carrying the stone

The moment of inertia identification experiment
To test the effect of the vision combined with the gravity recognition algorithm of moment of inertia in Section 3.2, the three-dimensional vision and gravity compensation method are used to grasp the stone and wood.
In the experiment, the object stone was caught by folkglove at the center position and left 20cm. The position was measured by hand to ensure accuracy. Then another experiment to grab a wood object was repeated.
The Moment of inertia result is I sum .
It can be seen from the    The experiment process is closer to the real working conditions.
The experimental results show that for the carrying process, due to the uncertainty of the object. The convergence effect of SM algorithm is not very good. But after using SMI which combined with visual and gravity parameter identification, the control performance has been greatly improved. Since the initial value with higher accuracy is set in advance, this method of identification and visual assistance has higher accuracy at the initial moment. Due to the relatively short working time of Swing degree of freedom handling, its performance is often determined in the initial period of time, so this method is more practical.
Most importantly, the experimental results show that in the process of grasping and handling, due to the uncertainty of the characteristics of the object's weight, it is not easy to obtain good enough results from the simple identification algorithm, and the identification algorithm combined with vision is increased. SMI can effectively shorten the convergence time. The experimental results show the importance of the initial value identification method to the sliding mode control strategy during the handling process. In addition to trajectory tracking, this identification method can be used in other fields such as energy-saving control.

Conclusion
This study addresses the adaptive robust control scheme for trajectory tracking of the swing with the double actuated hydraulic cylinder in a hydraulic construction robot.
A novel control scheme which obtains the controller parameter initial value of sliding mode controller according to robot gravity identification algorithm and stereo vision information is proposed. The scheme can be used to solve the contradiction caused by the slow convergence speed of the parameter identification algorithm and the large change of the controller parameter caused by the change of the work object. Simulation experiment and online experiment are performed to validate the effect of the novel scheme. The simulation experiment proved the superiority of the SM algorithm over the CPID algorithm and the necessity of obtaining the initial value of the parameter adaptive sliding mode algorithm. The moment of inertia estimation experiments have proved that the moment of inertia deviation obtained by using Digiclops combined with gravity identification method reaches more than 20%, indicating the necessity of using parameter adaptive algorithm in the algorithm. The comparison experiment of grabbing stones using SMI and SM shows that the SMI method proposed in this paper has a greater accuracy than the SM method and the CPID control algorithm. The work in this manuscript may bring new topics on robot and parameter estimation-based control.