P-Rob Six-Degree-of-Freedom Robot Manipulator Dynamics Modeling and Anti-Disturbance Control

In this paper, the problem of modeling and anti-disturbance control is studied for lightweight personal robotics (P-Robs) with a six-degree-of-freedom robot manipulator to solve the movement instability phenomenon caused by time-varying uncertain disturbances during the movement of the robot manipulator. The detailed dynamical equations of the P-Rob system are solved based on the Lagrange energy equation, and the actual dynamical model of the robot manipulator system is obtained. The disturbance observer is designed to estimate the disturbance effectively, and an integral sliding mode control algorithm is proposed to realize tracking control. Stability analysis of the system is carried out using the Lyapunov function. Finally, experiments are conducted on an actual P-Rob system model, and the experimental results show that the robot manipulator system tracks the desired trajectory effectively, which validates the effectiveness of the proposed control algorithm.


I. INTRODUCTION
In recent years, service-type six-degree-of-freedom robots have been widely used. In the field of intelligent medicine, quadriplegic patients can reach and grasp imaginary objects through a neural-controlled robot manipulator [1]. In laboratory automation production, an ideal six-degree-of-freedom robot manipulator automatic synthesis platform is used to complete the unmanned compound automatic production process [2]. In the packaging industry, the use of mobile sixdegree-of-freedom robot manipulators and the design of automatic wrappers have enabled the fast and accurate packaging of objects [3]. In a complex working environment, the robot manipulator can collaborate with humans to complete the task and improve work efficiency [4].
Sliding mode control [5]- [11], which has the advantage of not relying on the precise structure of the system, has been widely used in the control of robots and has achieved more results. In [12], for a sensor-less telerobotic system, it is proposed a variable structure control with neural network and optimized fractional-order selection policy. In [13], to improve the tracking performance of wafer stages for semiconductor manufacturing. Based on sliding mode The associate editor coordinating the review of this manuscript and approving it for publication was Mohammad Alshabi . control (SMC), a practical fractional-order variable gain super-twisting algorithm (PFVSTA) is proposed. In [14], sliding mode controllers are designed for regulating the dead zone and gravity unknown behavior of the robot manipulator. In [15], effective control of a service robot manipulator is achieved using an improved sliding mode index arrival rate. Reference [16] presented a radical adaptive terminal sliding mode control method for robot manipulators with model uncertainties and external disturbances.
Robot manipulator systems are often subject to various uncertain external perturbations and modeling inaccuracy problems in practical applications, so anti-disturbance control and adaptive neural-network control has successfully been used to solve the control problems of robot manipulators. A control scheme based on a disturbance observer is proposed for robot manipulators with internal and external disturbances in [17]. In [18], a general framework is proposed for disturbed nonlinear systems using disturbance observerbased control (DOBC) techniques. It is also applied to a two-linked robot manipulator. To solve the trajectory tracking problem of the underwater manipulator for the set-total perturbation, a fractional integral sliding mode control strategy with a perturbation observer is proposed [19]. Combined with the design of the disturbance observer, in the general case, the literature [20]- [22] considered the external VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ disturbance as an unknown bounded constant, which in turn gave the anti-disturbance control of the robot manipulator. References [23] proposes an adaptive neural-network control scheme, an effective estimation of the unmodeled dynamics of the robotic manipulator system is performed. For the parameter uncertainty and model nonlinearity of the robotic arm system, an improved neural network control algorithm is proposed in the literature [24] to overcome the perturbation phenomenon of the system. Based on the above literature, good research results are obtained for the sliding mode control of the robot manipulator system and various anti-disturbance controls. However, none of the above-mentioned literature has explored the applicability of the designed control algorithm on a real six-degreeof-freedom mathematical model. For the simulation tests, a two-degree-of-freedom or three-degree-of-freedom robotic arm model with a simpler mathematical model is chosen. The same problem occurs in the literature [25]- [32]. The kinematics of lightweight robot manipulators have been studied in the literature [33]- [35]. Through extensive literature reading, it is found that the lightweight robot manipulator is mainly oriented to real-life human-robot interaction applications with small motion speed for safety reasons. Therefore, there are more studies on the kinematics of lightweight robot manipulators and fewer studies on the dynamics. However, in the custom-oriented miniaturized rapid packaging line, an intelligent emerging manufacturing scenario, the dynamics of lightweight robotic arms are essential to study. Moreover, the modeling of six-degree-of-freedom robot manipulator systems is given only a general theoretical description in much of the literature, with no or very little literature providing a complete representation of the exact dynamics model. This leads to the fact that in practice when the studied control algorithm is applied to a six-degree-of-freedom robot manipulator system, it does not achieve a better control effect similar to that in the simulation. This paper studies the dynamic modeling and antidisturbance control of a lightweight six-degree-of-freedom robot manipulator. The rate of change of the total system disturbance is considered to be nonzero, and the global asymptotically stable convergence of the disturbance estimation error to zero is ensured by the reasonable design of the observer gain. The main work is reflected in the following aspects. Since the dynamics of lightweight robot manipulators are less studied, we investigated the dynamics of lightweight robot manipulators. The lightweight robot manipulator is sensitive to the dynamical parameters, which in turn poses certain challenges for dynamics modeling. For this reason, we have made reasonable assumptions in combination with the mechanical structure of the system and a form that more closely resembles real motion. To address the problem that much of the literature does not consider the actual mathematical model of the six-degree-of-freedom robot manipulator in its theoretical and simulation analysis, an accurate modeling calculation of the P-Rob six-degreeof-freedom robot manipulator system is carried out, and the specific dynamics model expression of the P-Rob system is solved based on the Lagrange equation. Design the disturbance observer and consider a non-zero rate of change of the total system disturbance. An integral sliding mode control algorithm based on a disturbance observer is proposed to achieve effective tracking of the desired trajectory of the system. Finally, the designed control algorithm is experimentally verified on an actual P-Rob robot manipulator platform based on the Python language.

II. P-ROB SYSTEM DYNAMICS MODEL CONSTRUCTION
To solve the complexity of the analysis of the actual model of the robot manipulator, it is convenient to solve and analyze the dynamic equations of the robot manipulator and then accurately obtain a system dynamics model. The model diagram is shown in Figure 1. There are many kinds of dynamic analysis methods for manipulator systems. The Lagrange equation is used in this system to derive the dynamics equation of P-Rob. The fundamental principle of the Lagrange method is the differentiation of each state in the system and time by combining the energy equation of the system, which only needs to analyze the kinetic energy and potential energy of the system without considering other problems [36].
To obtain the dynamics equations of the system, the kinetic energy and potential energy of the system should be solved, and then the Lagrange function should be established. Then, the partial derivatives of the system variables and time can be obtained by using the Lagrange function.
where L is the Lagrange function, K and P are the system kinetic energy and potential energy respectively; τ i is the sum of the external torque that produces rotation; and θ i is the system variable.

A. SOLVING FOR KINETIC ENERGY OF SYSTEM
The kinetic energy of each link is solved separately for the P-Rob six-degree-of-freedom manipulator, and the total kinetic energy of the system is finally obtained. We establish a right-angle coordinate system from the bottom of the base, denoted as x 0 y 0 z 0 . Taking the center of each link as the center of mass position, according to the established Cartesian coordinate system, we can obtain the coordinates of the center of mass of each link. By deriving the coordinates of the center of mass of each linkage, the velocity component of the linkage on the three axes of the coordinate system is obtained and denoted asẋ i ,ẏ i ,ż i , i = 1, 2, . . . 6. From formula v i = ẋ 2 i +ẏ 2 i +ż 2 i can be obtained from the speed of the i th link, and then we get the i th link of the flat kinetic energy, plus the i th link of the kinetic energy of rotation. Then, we determine the total kinetic energy of the i th link through formula (2).
where m i is the mass of the i th joint,θ i is the angular velocity of each joint, and I i is the rotational inertia of the ith linkage. The six links are now analyzed separately for translational and rotational kinetic energies.
Assumption 1: Link 4 and link 6 are always parallel to link 1 during the movement and rotate around the same direction.
Remark 1: To facilitate the construction of the system dynamics model, it is assumed that link 4 and link 6 are always parallel to link 1 in the process of moving and only rotate in the vertical direction. This assumption is very reasonable. Combined with the mechanical structure of the system and through reasonable trajectory planning calculation, the motion of joint 2 and joint 3 can make link 4 parallel to link 1, and the motion of joint 2, joint 3, and joint 5 can make Now, we solve for the coordinates of the centroid of each link.
Link 1: Link 2: Link 3: Link 4: VOLUME 9, 2021 Link 5: Link 6: To solve for the center-of-mass velocity of each linkage, the center-of-mass coordinates of each link are derived separately, and the components of the center-of-mass velocity of each linkage in the three directions of the coordinate system can be obtained as Link 1: Link 2: Link 3: Link 6: Based on the kinetic and potential energies of each linkage obtained in Sections A and B, the detailed Lagrange function of the P-Rob six-degree-of-freedom robot manipulator can now be obtained The obtained Lagrange functions are derived separately for the system state and time, which leads to the dynamics equations for the six joints.

1) SOLUTION OF THE 1ST DYNAMICS EQUATION
Taking the partial derivative ofθ 1 in the Lagrange function yields The derivation of the above formula concerning time t can be obtained as The coefficients of each item in the formula are expressed as Taking the partial derivative of θ 1 in the Lagrange function yields According to (35) and (36) and considering the existence of disturbance d 1 in the system, the first dynamics equations can be obtained

2) SOLUTION OF THE 2ND DYNAMICS EQUATIONS
Taking the partial derivative ofθ 2 in the Lagrange function yields The coefficients of each item in the formula are expressed as Derivation of the above formula concerning time t can be obtained as The coefficients of each item in the formula are expressed as Taking the partial derivative of θ 2 in the Lagrange function yields The coefficients of each item in the formula are expressed as According to (39) and (40) and considering the existence of disturbance d 2 in the system, the second dynamics equations can be obtained:

3) SOLUTION OF THE 3RD DYNAMICS EQUATIONS
Taking the partial derivative ofθ 3 in the Lagrange function yields The coefficients of each item in the formula are expressed as Derivation of the above formula concerning time t can be obtained as d dt The coefficients of each item in the formula are expressed as According to (43) and (44) and considering the existence of disturbance d 3 in the system, the third dynamics equation can be obtained as Taking the partial derivative of θ 4 in the Lagrange function yields ∂L ∂θ 4 = 0 According to (47) and (48) and considering the existence of disturbance d 4 in the system, the fourth dynamics equation can be obtained as

5) SOLUTION OF THE 5TH DYNAMICS EQUATIONS
Taking the partial derivative ofθ 5 in the Lagrange function yields According to (51) and (52), and considering the existence of disturbance d 5 in the system, the fifth dynamics equation can be obtained as

6) SOLUTION OF THE 6TH DYNAMICS EQUATIONS
Taking the partial derivative ofθ 6 in the Lagrange function yields ∂L ∂θ 6 = I 6 θ 1 +θ 4 +θ 6 (54) Derivation of the above formula concerning time t can be obtained as d dt ∂L ∂θ 6 = I 6θ1 + I 6θ4 + I 6θ6 (55) Taking the partial derivative of θ 6 in the Lagrange function yields ∂L ∂θ 6 = 0 (56) According to (55) and (56), and considering the existence of disturbance d 6 in the system, the sixth dynamics equation can be obtained as In the text,

D. SYSTEM MODEL DESCRIPTION
Based on the above solution of the P-Rob dynamics equations, we can see that the entire solution process is very complex. We obtain detailed expressions for each matrix in the system dynamics equation as shown in (58)-(60) at the bottom of the next page.
The parameters in the above three matrices are given by Section C. By looking up the coefficients obtained in Section C, we see that q 8 = j 7 , q 9 = p 7 , and j 9 = p 8 . This result confirms that the M 0 (θ) matrix is a positive definite symmetric matrix, and the correctness of the solution to the dynamical model is further tested.
The solution provides a true understanding of the specific coupling relationships between the joint angles in the P-Rob robot manipulator system, which in turn facilitates the effective design of the control algorithm and the testing of the actual system dynamics model. The dynamics model can be described as follows In the above formula, M 0 (θ) ∈ R 6×6 is the positive definite inertia matrix of the system, C 0 θ,θ ∈ R 6×6 is the Coriolis force and centrifugal force, and G 0 (θ) ∈ R 6×1 is the gravity term vector acting on the joint. All three matrices above are precise parts of the system model. d is the total of modeling error and external disturbance of the system, and τ is the control input to the system.

III. P-ROB SYSTEM CONTROL DESIGN
A block diagram of the control system is shown in Figure 2. Figure 2 shows that θ d is the desired predetermined trajectory of the system joints, θ is the actual trajectory of the system joints, the difference between θ d and θ is used as the input of the controller, τ c is the output control law of the integral sliding mode controller, τ d is the control law of the output of the disturbance observer, τ is the actual input torque of the robot manipulator system, d is the total of modeling error and external disturbance of the system, andd is the estimated value of d.

A. DESIGN OF DISTURBANCE OBSERVER
To estimate the total disturbance of the system, in combination with (61), the nonlinear disturbance observer can be given by [37] and represented as followṡ The above equation can also be expressed aṡ In general, there is no a priori information about the derivative of the disturbance d. Designing it asḋ = 0 means that the disturbance changes slowly concerning the dynamics of the disturbance observer. In this paper, it is assumed that the derivatives of the disturbance satisfẏ where h (t) ∈ L 2 is the squared product, d ∈ L ∞ . Further combining (64) yieldṡ When the gain matrix L θ,θ is designed to be L θ,θ > 0, it is asymptotically stable for all θ ∈ R 6 . Therefore, when t → ∞, the estimation of disturbance ∧ d can approach d asymptotically, that is, lim t→∞ ∧ d = lim t→∞ d, and the estimation error of disturbance can globally and asymptotically converge to zero. At the same time, the acceleration signalθ of the robot manipulator system cannot be measured to obtain effective information, so the selection of special L θ,θ can also eliminate the acceleration nonlinear term contained in (62).
To obtain an estimate of the system disturbance d, the observer state auxiliary variable can be defined by [38] as This is set here: Combining (67) and (68) with (62) yieldṡ Here the relationship between the observed gain matrix L θ,θ and the vector P θ,θ satisfies where X is a constant invertible matrix defined as

B. SYSTEM LINEARIZATION REPRESENTATION
Transforming (61), we geẗ . Then, the above equation can be expressed as We rewrite the nonlinear dynamics equation represented by (74) in state-space form where f θ i ,θ i is the explicitly known quantity of the system, θ i = [θ i1 , θ i2 ] T is the system state, y is the system output,d i is the total disturbance estimate of the system, andτ i is the controlled object input.
We assume that the disturbance error ∇d of the system is bounded, i.e., |∇d| ≤ D. where D ∈ R + , R + is the normal real number space.
The system control is designed so that the output of the system can effectively track the desired trajectory and keep the error close to zero, where θ d is the desired motion trajectory of the system.

C. DESIGN OF NONLINEAR INTEGRAL SLIDING MODE SURFACE
The traditional integral sliding surface is where c ∈ R + , and k ∈ R + . The traditional integral sliding mode surface cannot guarantee that the initial state is located on the switching surface, so the entire integral sliding mode surface inspired by [39] is designed as follows In the formula, e (0) andė (0) respectively represent the initial values of θ i1 and θ i2 of the system state variables. It is easy to obtain s (0) = 0, which ensures that the initial moment of the system is located on the switching surface.

D. CONTROLLER DESIGN
The process of the sliding mode can be divided into two phases: the sliding phase of s = 0 andṡ = 0 and the arrival phase of s = 0. Corresponding to these two different phases, the control is divided into two parts: equivalent control and switching control. Equation (77) is derived to obtaiṅ When the above equation is equal to zero, the tracking error can be ensured to converge to zero asymptotically by selecting the appropriate gains c > 0 and k > 0 to achieve effective tracking of the trajectory.
Substituting the system model into the above formula, we haveṡ When the system output is kept on the sliding mode surface, the total set disturbance of the system is zero, i.e., d + ∇d = 0. Fromṡ = 0, we can obtain the equivalent control law asτ As external disturbances and parameter changes of the system can cause the initial output trajectory of the system to not lie on the sliding mode surface, the switching control law needs to be designed to drive the output trajectory of the system to the sliding mode. This process is called the arrival phase. For this purpose, we choose the Lyapunov function as The selection of a suitable control strategy ensures that the error trajectory is switched from the arrival phase to the sliding phase and is also called the arrival condition. Foṙ to make the sliding mode reachability condition hold, the equivalent control lawτ eq has been obtained thus far, and the control lawτ is now expanded by the switching control lawτ sw , which isτ We insert the system parameters and variables into the arrival condition (83) to obtaiṅ Simple calculations, it follows thaṫ Since the disturbance estimated i is a bounded known quantity,τ sw can be designed as where µ is a positive real number indicating the upper limit of uncertainty. µ ∈ R + (µ ≥ D), ζ ∈ R + . The derivative of Lyapunov time can be expressed as fol-lowsV Lemma 1 ( [40]): For any real numbers λ 1 > 0, λ 2 > 0, and 0 < γ < 1, an extended Lyapunov condition of finite-time stability can be given asV ( The further derivation is as follows: The system is finite-time asymptotically stable according to Lyapunov stability theorem. Therefore, the system control law can be designed as

IV. ANALYSIS OF SIMULATION RESULTS
The system dynamics equations established in this section and the validity of the controller design are further tested [41]. Using Simulink in MATLAB, the actual solved six-degreeof-freedom robot manipulator model obtained in this section is simulated and verified. And the control algorithm in the literature [42] is applied to this system, and then the comparison test of the two algorithms is realized. The inherent parameters velocityθ 0 = [0 0 0 0 0 0] T , the total system disturbance is d = 3 + sin (t) / (1 + t), µ = diag (10,10,10,10,10,10), c = diag (8,8,8,8,8,8), k = diag (5,5,5,5,5,5), ξ = diag (6,6,6,6,6,6), acceleration of gravity g = 9.8m/s 2 , and the expected trajectory of each joint is θ d = sin (πt). The control parameters are based on several simulated experiments and actual P-Rob platform experiments and finally selected in a trade-off between the best results of the two experiments.
Now the six-degree-of-freedom robot manipulator system is simulated using the control algorithm designed in this paper, and then the effectiveness of the algorithm design is verified. Since joints 1, 4, and 6 are parallel to each other and rotate in the same direction, and joints 2, 3, and 5 are parallel to each other and rotate in the same direction. Therefore, only the simulation results of trajectory tracking, velocity tracking, trajectory tracking error, control input and disturbance observation for joint 1 and joint 2 are displayed. The simulation results are shown as follows.
The control algorithm in the literature [42] is used for trajectory tracking and velocity tracking of the system, and the simulation results of joints 1 and 2 are presented.
Now consider applying constant disturbances as well as different time-varying disturbances in the system to further verify the effectiveness of the anti-disturbance integral sliding mode controller designed in this paper. These disturbances are designed as Considering the space limitation, only the simulation results of joint 1 under different disturbances are represented as follows.
In the table, d is the different disturbances, e is the tracking error under different disturbances, which is obtained by making the deviation between the actual trajectory and the desired trajectory for each data point and finally adding and averaging them, and t is the time to reach stable tracking.
Using the control algorithm designed in this paper, the simulation results obtained are shown in Figure 3-figure 7. Figure 3 - figure 5 demonstrates the tracking effect of the system trajectory and velocity on the desired value, and the tracking error of the system position. We can see that the closed-loop system can reach a steady state in a short   time. Figures 6 and 7 show the control input of the system and the state performance of the disturbance observer. It should be noted that the input signal of the closed-loop system is bounded and the disturbance observer effectively estimates the system disturbance in a short time, proving that the control algorithm designed in this paper has a good control performance. To further demonstrate the superiority of the control algorithm designed in this paper, we applied the control algorithm designed in the literature [42] to this research system and compared it with the simulation results in this paper for analysis. The simulation results of trajectory    tracking and velocity tracking for the control scheme proposed in the literature [42] are shown in figure 8 and figure 9, and we can see that the control scheme in the literature [42] is not very satisfactory for the control of the P-Rob system. The jitter vibration phenomenon is more obvious, and there is always an error in the trajectory tracking. To verify the robustness of the control algorithm designed in this paper, three different disturbances were selected to conduct numerical experiments on the system, and the experimental results are shown in Figures 10-12. Figure 10 shows the estimation effect of the system for different disturbances. Figure 11 depicts the trajectory tracking effect of the joint under the influence of different disturbances. Figure 12 depicts the tracking error of    Table 1.
The system can effectively estimate the constant disturbances or different time-varying disturbances, and achieve effective trajectory tracking in a short time, and the system can quickly reach the steady-state under the action of different types of disturbances, which indicates that the robustness of the control algorithm designed in this paper is good. The tracking control effect of the algorithm designed in this paper is more satisfactory, with smoother output, no abrupt changes, the jitter vibration phenomenon is suppressed, the tracking error converging to zero in a relatively short time, and the robustness is strong. This system locates the initial state of the system on the sliding mode surface through the selection of the integral sliding mode surface, and the total disturbance is effectively compensated, so the simulation effect is better than the control algorithm in the literature [42]. Through simulation experiments of the two control algorithms, it can be seen that the dynamic performance index and static performance index of the control algorithm designed in this paper are better and achieve the design objectives. The entire control performance is satisfactory in terms of work effectiveness.

V. P-ROB PLATFORM EXPERIMENTAL ANALYSIS
In order to further investigate the practical value of the control algorithm designed in this paper, the designed control algorithm is now experimentally analyzed on the P-Rob platform. The P-Rob experimental platform has three wrist joints and three elbow joints, and it operates with a voltage limit of 100-240V AC, 50/60Hz, and maximum power consumption of 600W. The P-Rob is powered by a builtin 24V or 48V power supply with the battery embedded in its base. It has a total weight of 20 kg and a maximum payload of 3 kg at the end. The control of P-Rob is relatively simple and is web-based via myP software, with an intuitive web browser-based graphical user interface to control and communicate with P-Rob. The P-Rob experimental platform is shown in Figure 13. Now, the P-Rob system is used to execute a series of experiments to grasp and put back a ping-pong ball. First, the path that the P-Rob system passes through in space is designed, and then the ideal motion trajectory of each joint of the P-Rob system is set according to the length of the P-Rob and the reachable range of the joints. The ideal motion trajectory of the end is formed by the motion of six joints. Finally, in the Application Editor window, the program for robot manipulator recognition is written in Python based on the designed anti-disturbance integral sliding mode control algorithm. The entire experiment is completed. The experimental results are shown in Figure 14. During the entire motion of the P-Rob system from the initial position to catching the ball, releasing it, and finally returning to the initial position, each joint moved according to the ideal trajectory that they each set, which realized the effective trajectory tracking of the P-Rob system. When an external disturbing torque is applied to the running robot manipulator, it is observed that under the action of the external torque, the robot manipulator first performs a jitter-removal pause and then puts it back into motion. This continuous process compared to the simulation results is the existence of a disturbance elimination time difference, this time difference can be understood as the system from the receipt of the external jitter signal, and then the controller issued to eliminate the disturbance command to reach the system actuator process. We perform 10 experiments, each experiment applied a different disturbance torque, and then the results of each experiment are compared with the simulation results of the same disturbance torque, the average value of the time difference is 1.273 seconds, this deviation robot manipulator system is very small in practical applications. Because this time difference is very short, the robot manipulator system quickly returns to a stable operating state. So the experimental results further confirm the effectiveness of the control scheme designed in this paper. Through experiments we observe that the entire process of catching ping-pong balls by the P-Rob system is fast and smooth, effectively tracking the desired trajectory and resisting external disturbances. This fully reflects the rationality of the control algorithm design in this paper and that the theory can be combined with practice.

VI. CONCLUSION
In this paper, based on the Lagrange energy equation, a detailed solution of the lightweight P-Rob system is carried out to obtain the inertia, Coriolis force, and gravity matrices of the actual system model. The solution to the specific coupling equation for the P-Rob six-degree-of-freedom robot manipulator deepens the understanding of the robot manipulator system model. In a system simulation, a mathematical model solved for the actual P-Rob six-degree-of-freedom robot manipulator system is used. This is a simulation of great practical value.
To improve the trajectory tracking control accuracy under possible time-varying uncertain disturbances to the robot manipulator during operation, this paper combined the disturbance observer and integral sliding mode controller and proposed an integral sliding mode control algorithm based on the disturbance observer. The algorithm reduced the large adjustment gain of the control system, solved the shortcomings of the traditional sliding mode control system oscillation, improved the response speed, reduced the tracking error, the time-varying disturbances can be effectively suppressed, and enhanced the stability of the control system. A better tracking trajectory is obtained through simulation software, and experimental analysis is carried out on an actual sixdegree-of-freedom P-Rob system. The practical value of the designed control algorithm is fully reflected by the experimental results, which provide a reference for the design of the mechanical mechanism of the robot manipulator and antidisturbance control during motion in subsequent practical work.