CN117733860A - Sliding mode control method of tail end track of double-arm robot based on position dynamics - Google Patents

Abstract

The invention belongs to the technical field of mechanical arm motion planning algorithms, and particularly relates to a sliding mode control method of a tail end track of a double-arm robot based on position dynamics, which perfects the limitation that the track tracking algorithm based on sliding mode control is applied to a two-link mechanical arm or a non-deterministic mechanical arm dynamics model at present, and designs a double-arm tail end track sliding mode control simulation system based on position dynamics; meanwhile, a hyperbolic tangent function is introduced as a sliding mode switching function, so that buffeting caused by a traditional sliding mode control algorithm is effectively restrained, and the terminal track precision of an operator in the moving process is improved; the simulation result proves the effectiveness and superiority of the force/position hybrid control algorithm based on the improved sliding mode controller, and the method can be successfully applied to the condition with a determined mechanical arm dynamics model, and has stable output moment and good track tracking effect.

Description

Sliding mode control method for end trajectory of dual-arm robot based on position dynamics

Technical field

The invention belongs to the technical field of robotic arm motion planning algorithms, and specifically relates to a sliding mode control method for the end trajectory of a two-arm robot based on position dynamics.

Background technique

At present, tracking and controlling the trajectory of dual-arm robots in university scientific research rooms or industrial factories is an important robotic technology research. The selection of control methods and the stability of the control design are the prerequisites for ensuring its efficient work. Several types of research are currently being extensively studied. Robotic arm trajectory control methods include: PID control, neural network control and fuzzy control, robust control, adaptive control, model-based control method and sliding mode control method, etc.

Sliding mode control is a special category of variable structure control. It is a discontinuous nonlinear control method. It has the advantages of fast response, strong resistance to external disturbances, and limited time convergence. It is widely used in robotic arm control methods.

However, due to the discontinuous switching of sliding mode control, system buffeting is inevitable, which has a greater impact on the control and even causes system instability. At the same time, some parameters and non-parameter uncertainties of the manipulator model itself and in the task Due to environmental disturbance factors, it is a difficult problem to achieve high-precision tracking of the end trajectory of a dual-arm robot during a tight coordination task. High-precision tracking of the end trajectory of a dual-arm robot is an important part of motion planning for a dual-arm robot, which is of great significance for completing the main tasks attached to the robotic arm.

Contents of the invention

The present invention considers that the trajectory tracking algorithm of sliding mode control is mostly used in the case of two-link or undetermined manipulator dynamics models. Based on this, a sliding mode control method of the end trajectory of a two-arm robot based on position dynamics is proposed. It can be successfully applied to situations with a certain robot arm dynamics model, the output torque is stable, and the trajectory tracking effect is good. The simulation results verify the effectiveness and superiority of the proposed method.

In order to achieve the above technical objectives and achieve the above technical effects, the present invention is implemented through the following technical solutions:

The invention provides a sliding mode control method for the end trajectory of a dual-arm robot based on position dynamics, which includes the following steps:

1) Model the coordinated motion constraints of the two-arm robot; model the pose constraints and speed constraints that exist between the robotic arm J1 as the master arm, the robotic arm J2 as the slave arm, the world coordinate system, and the objects being transported. ;

2) Dynamic modeling of the dual-arm robot in the workspace;

3) Modeling of a double-arm robot closed-chain system;

4) Design a sliding mode controller based on the position dynamics model.

Further, in step 1), the modeling of pose constraints is specifically:

The pose constraint relationship is:

in, is the homogeneous transformation matrix between the object center of mass coordinate system and the world coordinate system;/> and/> are the homogeneous transformation matrices of the base coordinate system of the master arm and the slave arm relative to the world coordinate system,/> and/> are the homogeneous transformation matrices of the master arm and slave arm end effector coordinate systems relative to their own base coordinate systems respectively,/> and/> is the homogeneous transformation matrix of the object center of mass coordinate system relative to the master arm and slave arm end effector coordinate systems.

Further, in step 1), the modeling of speed constraints is specifically:

The speed constraint relationship is:

Among them: J _l (q) is the joint velocity mapped to the linear velocity Jacobian matrix of the end link; q _J1 and q _J2 are the joint displacement vectors of the master arm and the slave arm respectively; and/> are the joint velocity vectors of the master arm and slave arm respectively.

Further, in step 2), the dynamics modeling in the workspace is specifically:

The closed dynamics model of the dual-arm coordinated operation robot is:

Among them: q＝(q _J1 , q _J2 )∈R ^1×12 , H(q)＝diag[H _J1 (q _J1 )H _J2 (q _J2 )]∈R ^12×12 is the generalized inertial component of the double-arm combination block matrix; is the centrifugal force and Coriolis force matrix of the combination of both arms;/> Represents the centrifugal force and Coriolis force terms of the two-arm combination; G(q)=[G _J1 (q _J1 ),G _J2 (q _J2 )]∈R ^12×1 , the gravity matrix of the two-arm combination; τ _m =[τ _{m ,J1} ,τ _m,J2 ]∈R ^12×1 represents the generalized moment of interaction between the master arm, the slave arm and the object; τ _d =[τ _d,J1 ,τ _d,J2 ]∈R ^12×1 represents the external force Interference torque in both arms; τ=[τ _J1 ,τ _J2 ]∈R ^12×1 represents the control torque of the two arms.

Furthermore, in step 3), the modeling of the dual-arm robot closed-chain system is specifically as follows:

When a two-arm robot carries a target object and performs motion planning in the operating space, in order to prevent the possibility of the object falling off, it is necessary to perform closed-chain constraints on the two-arm system, and apply a generalized driving force to the clamped object through the end effectors of the two arms. force constraint control;

The motion of an object is described by the motion of its center of mass m. The Euler moment balance equation and Newtonian force balance equation are established as follows:

Among them: I is the inertia tensor of the transported object; ω and are respectively the angular velocity and angular acceleration of the object being transported around its center of mass; M is the mass of the object being transported;/> is the acceleration vector at the center of mass of the transported object; g is the gravitational vector.

Further, in step 4), the sliding mode controller design is specifically:

Since the dual-arm robot system is a typical nonlinear control system, during the actual movement process, it has the disadvantages of low position accuracy and unstable control. Considering that the steepness of the hyperbolic tangent function is better than the symbolic function, continuous hyperbolic tangent is used function Replace the sign switching function sign(x) in the traditional sliding mode controller, combine it with the closed dynamics model of the dual-arm coordinated operation robot, and design a sliding mode controller based on the position loop:

in: is the angular acceleration control input quantity under the position control loop; K = diag (k ₁ , k ₂ ,..., k ₁₂ ) is the gain matrix of the controller; eta is the switching gain value of the hyperbolic tangent function; ε>0, where The value determines the slope of the hyperbolic tangent function, and all other scalars are greater than 0.

Further, by Simplifying the above equation, we get the following closed-loop control system equation:

When the global motion reaches the equilibrium point That is, there are always/> Therefore, a globally stable terminal trajectory tracking effect can be obtained.

Furthermore, after completing the above-mentioned closed-loop control of position control and force control, to realize the double-arm handling operation, the end effector needs to be in contact with the object and remain stable during the handling process. It is necessary to carry out motion planning and stable operation of both arms. Force/torque control realizes the operation task of the dual-arm robot force-coordinated handling of objects; based on the above analysis, the sliding mode control rate based on the position dynamics model in the closed-chain constraint coordinate system can be obtained:

The beneficial effects of the present invention are:

1. The sliding mode control method for the end trajectory of a two-arm robot proposed by the present invention improves the limitations of the current sliding mode control-based trajectory tracking algorithm that is mostly used in two-link manipulators or non-deterministic manipulator dynamics models.

2. The present invention designs a sliding mode control simulation system for the trajectory of the end of both arms based on position dynamics. At the same time, the hyperbolic tangent function is introduced as the sliding mode switching function, which effectively suppresses the chattering caused by the traditional sliding mode control algorithm and improves the performance of the operating object. Terminal trajectory accuracy during motion.

3. The simulation results verify that the force/position hybrid control algorithm based on the improved sliding mode controller can be successfully applied to situations with a certain mechanical arm dynamics model, the output torque is stable, and the trajectory tracking effect is good, verifying the method of the present invention. effectiveness and superiority.

Of course, any product implementing the present invention does not necessarily need to achieve all the above advantages at the same time.

Description of drawings

In order to explain the technical solutions of the embodiments of the present invention more clearly, the drawings needed to describe the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without exerting creative efforts.

Figure 1 is a flow chart of the method of the present invention;

Figure 2 is a schematic diagram of the coordinate system for coordinated handling by a two-arm robot;

Figure 3 is a schematic diagram of the dimension chain of coordinated operation of a two-arm robot;

Figure 4 is a schematic diagram of the force on the target object under the support of both arms;

Figure 5 is the torque output block diagram of the sliding mode controller based on the position dynamics model;

Figure 6 shows the angular velocity error of each joint-sign function;

Figure 7 shows the angular velocity error of each joint-hyperbolic tangent function;

Figure 8 shows the output torque-sign function of each joint;

Figure 9 shows the output torque of each joint-hyperbolic tangent function.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

The invention provides a sliding mode control method for the end trajectory of a two-arm robot based on position dynamics. It improves the limitations of the current trajectory tracking algorithm based on sliding mode control, which is mostly used in two-link manipulator or non-deterministic manipulator dynamics models. A sliding mode control simulation system for the trajectory of the arms' ends based on position dynamics is designed. At the same time, the hyperbolic tangent function is introduced as the sliding mode switching function, which effectively suppresses the chattering caused by the traditional sliding mode control algorithm and improves the performance of the operating object during movement. The terminal trajectory accuracy. The simulation results verify that the force/position hybrid control algorithm based on the improved sliding mode controller can be successfully applied to situations with a certain mechanical arm dynamics model, the output torque is stable, and the trajectory tracking effect is good, verifying the effectiveness of the method of the present invention. sex and superiority.

Specific embodiments of the present invention are as follows:

This embodiment provides a sliding mode control method for the end trajectory of a dual-arm robot based on position dynamics, which includes the following steps:

(1) Establish the posture and speed constraint relationship of the coordinated movement of the two-arm robot

The cooperative grasping motion model of the two-arm robot is shown in Figure 2, including the base, the object and the two arm parts. The definition and meaning of the coordinate system in the figure are explained as follows: {O _wor } represents the world coordinate constrained by the entire closed size chain system (that is, the base coordinate system of the entire dual-arm robot system), the left robotic arm is the master arm, and its base coordinate system is {L ₀ }; the right robotic arm is the slave arm, and its base coordinate system is {R ₀ }; {L _end } is the coordinate system of the end effector of the master arm, and {R _end } is the coordinate system of the end effector of the slave arm. {M ₀ } in the figure represents the reference coordinate system of the center of mass m ₀ of the transported object. Therefore, the arms and the object form a complete closed kinematic chain constraint system.

From the dimensional chain shown in Figure 3, it can be seen that the pose constraint relationship between the robotic arm J1 (the master arm described later), the robotic arm J2 (slave arm), the world coordinate system and the transported object is:

In the above formula, is the homogeneous transformation matrix between the object center of mass coordinate system and the world coordinate system. Homogeneous transformation matrices of the master arm and slave arm end effector coordinate systems. /> and/> are the homogeneous transformation matrices of the base coordinate system of the master arm and the slave arm relative to the world coordinate system,/> and/> are the homogeneous transformation matrices of the master arm and slave arm end effector coordinate systems relative to their own base coordinate systems respectively,/> and/> is the homogeneous transformation matrix of the object center of mass coordinate system relative to the master arm and slave arm end effector coordinate systems. Considering that during the transportation of the object, there is no relative movement between the ends of the arms and the object, so/> and/> It can be obtained based on the initial pose of the main arm and the object in the world coordinate system.

(2) Establish a coordinated moving speed constraint relationship for the dual-arm robot

In addition to posture constraints, the coordinated operation movement of both arms should also satisfy joint velocity and acceleration constraints. The end of the two robotic arms and the object can be regarded as a relatively static state. Therefore, in order to simplify the calculation during the actual operation, the speed and acceleration of the object are omitted from planning, so only the speed of the master and slave arms need to be calculated. and acceleration constraint equation modeling

Slave arm joint speed:

Among them, J _l (q) is the joint velocity mapped to the linear velocity Jacobian matrix of the end link, q _J1 and q _J2 are the joint displacement vectors of the master arm and the slave arm respectively, and/> are the joint velocity vectors of the master arm and slave arm respectively.

Angular velocity of the end links of both arms:

ω _end,J1 =ω _end,J2

In the formula: J _a (q) is the joint velocity mapped to the angular velocity Jacobian matrix of the end link.

(3) Dynamic modeling of dual-arm robot in work space

The closed dynamics model of the dual-arm coordinated operation robot is expressed as:

In the formula: H(q)=diag[H _J1 (q _J1 )H _J2 (q _J2 )]∈R ^12×12 is the generalized inertia block matrix of the two-arm combination, is the centrifugal force and Coriolis force matrix of the combination of both arms,/> Represents the centrifugal force and Coriolis force terms of the two-arm combination, G(q)=[G _J1 (q _J1 ),G _J2 (q _J2 )]∈R ^12×1 , and the two-arm combination gravity matrix, τ _m =[τ _{m ,J1} ,τ _m,J2 ]∈R ^12×1 represents the generalized moment of interaction between the main arm, the slave arm and the object, τ _d =[τ _d,J1 ,τ _d,J2 ]∈R ^12×1 represents the external force Disturbance moments in both arms. τ=[τ _J1 ,τ _J2 ]∈R ^12×1 represents the control torque of the two arms.

(4) Modeling of closed-chain system of dual-arm robot

When a two-arm robot carries a target object and performs motion planning in the operating space, in order to prevent the possibility of the object falling off, it is necessary to perform closed-chain constraints on the two-arm system, and apply a generalized driving force to the clamped object through the end effectors of the two arms. Force constraint control ^[71] , the force diagram of the target object under the support of both arms is shown in Figure 4.

The motion of an object is described by the motion of its center of mass m. The Euler moment balance equation and Newtonian force balance equation are established as follows:

In the formula: I is the inertia tensor of the transported object, ω and are respectively the angular velocity and angular acceleration of the object being transported around its center of mass. M is the mass of the object being transported,/> is the acceleration vector at the center of mass of the transported object, and g is the gravity vector.

(5) Design of sliding mode controller based on position dynamics model

When the robotic arm performs a position control loop, the robotic arm remains relatively stationary between its arms and the object in the operating space. In position control, combined with the generalized forces and moments between the three, the combined arms The dynamic model is rewritten as:

The expected joint angle q _d and joint angular velocity during the process of carrying objects with both arms are obtained from the kinematic constraint equations of both arms. And joint angular acceleration/> In order to improve the trajectory tracking effect of the control algorithm and reduce the chattering caused by the traditional sliding mode controller, the sliding mode control algorithm is used to adjust and optimize the desired angular acceleration value in position dynamics:

definition: Take the sliding mode function as:

Where s=[s ₁ , s ₂ , s ₃ , s ₄ , s ₅ , s ₆ ] ^T , Λ _p is a constant gain matrix.

Since the dual-arm robot system studied in this embodiment is a typical nonlinear control system, during the actual movement process, it has shortcomings such as low position accuracy and unstable control. Considering that the steepness of the hyperbolic tangent function is better than the sign function , where a continuous hyperbolic tangent function is used Replace the sign switching function (sign(x)) in the traditional sliding mode controller and combine the above dynamic equations to design a sliding mode controller based on the position loop:

In the formula: is the angular acceleration control input quantity under the position control loop, K=diag(k ₁ ,k ₂ ,…,k ₁₂ ) is the gain matrix of the controller; eta is the switching gain value of the hyperbolic tangent function; ε>0, where The value determines the slope of the hyperbolic tangent function, and all other scalars are greater than 0.

Simplifying the above equation, the following closed-loop control system equation can be obtained:

When the global motion reaches the equilibrium point That is, there are always/> Therefore, a globally stable terminal trajectory tracking effect can be obtained.

After completing the above closed-loop control of position control and force control, to realize the double-arm handling operation, the end effector needs to be in contact with the object and remain stable during the handling process. It requires motion planning and stable force/torque for both arms. Control to realize the operation task of the dual-arm robot force-coordinated handling of objects. Based on the above analysis, the sliding mode control rate based on the position dynamics model in the closed-chain constraint coordinate system can be obtained:

In the control rate of the above formula, through the terminal trajectory sliding mode control and force/torque control based on the position dynamics model, the hyperbolic tangent switching function In position control, it effectively suppresses the chattering caused by the traditional sliding mode control algorithm and improves the end trajectory accuracy of the operating object during movement.

The torque output block diagram of the sliding mode controller based on the position dynamics model designed based on the sliding mode control rate is shown in Figure 5.

The entire torque output block diagram shows the input and output methods of the kinematics and dynamic characteristics of the manipulator under position dynamics control. The Simscape module in Matlab/Simulink builds the equation block diagram of the control rate. The relevant matrix parameters are input in the block diagram. Run to the workspace in advance to provide corresponding data for subsequent block diagram runs and improve the running efficiency of the simulation. Next, plan the desired trajectory and end position of the transported object, and input the corresponding position/force control law in the control system according to the planning results (i.e., the obtained position and torque in the joint space of the manipulator), and add improvements The sliding mode controller obtains the corresponding position control torque and force control torque and inputs them into the dual-arm robot system, and feeds the results back to the corresponding system through the two sub-modules of Position Sensors (position sensor) and Force/Torque Sensors (force/torque sensor). The adder at the input end forms a closed-loop control, and the dual-arm carrying task is realized based on the control method of this embodiment.

Simulation experiments and analysis

In order to verify the feasibility and effectiveness of the sliding mode control method for the end trajectory of the dual-arm robot proposed in this embodiment based on position dynamics, Matlab R2021b is used to establish the kinematics model of the dual-arm robot, and the Robots Toolbox ( 10.3 version) combined with the control flow block diagram built by Simscape/MultibodyModel in Simulink, and finally realized the visual simulation of double-arm coordinated handling control in Mechanics Explorer.

Test: Compare the traditional sliding mode control algorithm (using the symbolic function as the sliding mode switching function) and the improved control algorithm based on position dynamics of the present invention (using the hyperbolic tangent function as the sliding mode switching function), and analyze the results and discuss.

Experimental preset conditions: Taking a single robotic arm as an example, the expected angle of each joint is q _d = sin (t), that is, the angular velocity is The initial joint angle of the robotic arm is:

q ₀ =[0.5650,2.1767,1.4251,0,2.3900,-0.5650]

The relevant parameters of the controller are selected as follows: constant η = 10, and denominator coefficient ε of the hyperbolic tangent function = 2. The gain matrix of the sliding mode is: K=diag[0.5,0.5,0.5,0.5,0.5,0.5].

It can be seen from Figures 6 to 7 that the joint angular velocity errors of both algorithms converge to 0rad, but the smoothness of Figure 7 is better than that of Figure 6, that is, the angular velocity tracking effect of sliding mode control based on hyperbolic tangent is more accurate. It can be seen from the partial diagram method diagrams in Figures 6 to 9 that the joint angular velocity error amplitude of sliding mode control based on traditional symbolic functions is within 0.08rad/s, and the maximum output torque amplitude of the joint is 2N/m; while in this embodiment The maximum error amplitude of the joint angular velocity of the improved hyperbolic tangent sliding mode control is about 0.01rad/s, and the maximum output torque amplitude of the joint is 0.05N/m. Based on the above result analysis, based on the sliding mode control suppression of the hyperbolic tangent function in this embodiment The buffeting effect is much higher than that of traditional symbolic functions, and it can be seen from the error results that high-precision trajectory tracking can be achieved.

The preferred embodiments of the invention disclosed above are only intended to help illustrate the invention. The preferred embodiments do not describe all details, nor do they limit the invention to specific implementations. Obviously, many modifications and variations are possible in light of the contents of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, so that those skilled in the art can better understand and utilize the present invention. The invention is limited only by the claims and their full scope and equivalents.

Claims (8)

1. A sliding mode control method for the end trajectory of a dual-arm robot based on position dynamics, which is characterized by including the following steps: 1) Model the coordinated motion constraints of the two-arm robot; model the pose constraints and speed constraints that exist between the robotic arm J1 as the master arm, the robotic arm J2 as the slave arm, the world coordinate system, and the objects being transported. ; 2) Dynamic modeling of the dual-arm robot in the work space; 3) Modeling of a double-arm robot closed-chain system; 4) Design a sliding mode controller based on the position dynamics model. 2. The sliding mode control method of the end trajectory of the dual-arm robot based on position dynamics according to claim 1, characterized in that in step 1), the modeling of pose constraints is specifically: The pose constraint relationship is: in, is the homogeneous transformation matrix between the object center of mass coordinate system and the world coordinate system;/> and/> are the homogeneous transformation matrices of the base coordinate system of the master arm and the slave arm relative to the world coordinate system,/> and/> are the homogeneous transformation matrices of the master arm and slave arm end effector coordinate systems relative to their own base coordinate systems respectively,/> and/> is the homogeneous transformation matrix of the object center of mass coordinate system relative to the master arm and slave arm end effector coordinate systems. 3. The sliding mode control method of the end trajectory of the dual-arm robot based on position dynamics according to claim 2, characterized in that in step 1), the modeling of the speed constraint is specifically: The speed constraint relationship is: Among them: Jl(q) is the joint velocity mapped to the linear velocity Jacobian matrix of the end link; q _J1 and q _J2 are the joint displacement vectors of the master arm and the slave arm respectively; and/> are the joint velocity vectors of the master arm and slave arm respectively. 4. The sliding mode control method of the end trajectory of the dual-arm robot based on position dynamics according to claim 3, characterized in that in step 2), the dynamics modeling in the work space is specifically: The closed dynamics model of the dual-arm coordinated operation robot is: Among them: q＝(q _J1 , q _J2 )∈R ^1×12 , H(q)＝diag[H _J1 (q _J1 )H _J2 (q _J2 )]∈R ^12×12 is the generalized inertial component of the double-arm combination block matrix; is the centrifugal force and Coriolis force matrix of the combination of both arms;/> Represents the centrifugal force and Coriolis force terms of the two-arm combination; G(q)=[G _J1 (q _J1 ),G _J2 (q _J2 )]∈R ^12×1 , the gravity matrix of the two-arm combination; τ _m =[τ _{m ,J1} ,τ _m,J2 ]∈R ^12×1 represents the generalized moment of interaction between the master arm, the slave arm and the object; τ _d =[τ _d,J1 ,τ _d,J2 ]∈R ^12×1 represents the external force Interference torque in both arms; τ=[τ _J1 ,τ _J2 ]∈R ^12×1 represents the control torque of the two arms. 5. The sliding mode control method of the end trajectory of the dual-arm robot based on position dynamics according to claim 4, characterized in that in step 3), the modeling of the closed-chain system of the dual-arm robot is specifically: Perform closed-chain constraints on the two-arm system, and perform force constraint control through the generalized driving force exerted on the clamped object through the end effectors of the two arms; The motion of an object is described by the motion of its center of mass m. The Euler moment balance equation and Newtonian force balance equation are established as follows: Among them: I is the inertia tensor of the transported object; ω and are respectively the angular velocity and angular acceleration of the object being transported around its center of mass; M is the mass of the object being transported;/> is the acceleration vector at the center of mass of the transported object; g is the gravitational vector. 6. The sliding mode control method of the end trajectory of the dual-arm robot based on position dynamics according to claim 5, characterized in that in step 4), the sliding mode controller design is specifically: Use a continuous hyperbolic tangent function Replace the sign switching function sign(x) in the traditional sliding mode controller, combine it with the closed dynamics model of the dual-arm coordinated operation robot, and design a sliding mode controller based on the position loop: in: is the angular acceleration control input quantity under the position control loop; K = diag (k ₁ , k ₂ ,..., k ₁₂ ) is the gain matrix of the controller; eta is the switching gain value of the hyperbolic tangent function; ε>0, where The value determines the slope of the hyperbolic tangent function, and all other scalars are greater than 0. 7. The sliding mode control method of the end trajectory of the dual-arm robot based on position dynamics according to claim 6, characterized in that: Simplifying the above equation, we get the following closed-loop control system equation: When the global motion reaches the equilibrium point That is, there are always/> Therefore, a globally stable terminal trajectory tracking effect can be obtained. 8. The sliding mode control method of the end trajectory of the dual-arm robot based on position dynamics according to claim 7, characterized in that, after completing the closed-loop control of the above-mentioned position control and force control, the dual-arm handling operation to be realized, During the handling process, the end effector needs to be in contact with the object and remain stable. It is necessary to carry out motion planning and stable force/torque control of both arms to realize the operation task of the two-arm robot force-coordinated handling of objects; based on the analysis of the above content, it can The sliding mode control rate based on the position dynamics model in the closed-chain constraint coordinate system is obtained: