A fast and continuous sliding mode control method for a hybrid mechanism of automobile electrophoretic coating conveying

Abstract

The present invention discloses a new comprehensive error fast continuous sliding mode control method for the task space of a hybrid mechanism for automobile electrophoretic coating transportation, and belongs to the technical field of automobile electrophoretic coating. Firstly, a posture contour error is designed in the task space for the hybrid mechanism for automobile electrophoretic coating transportation, which can reflect the terminal position of the hybrid mechanism and indirectly reflect the terminal posture of the mechanism, and then the integral of the posture contour error and the terminal tracking error are integrated to establish a new comprehensive error; secondly, the new comprehensive error is introduced, and a new comprehensive error fast continuous sliding mode control algorithm for the task space is designed, and finally, the control quantities of each branch obtained by Jacobian matrix conversion are sent to the motor driver to realize the new comprehensive error fast continuous sliding mode control in the task space of the hybrid mechanism for automobile electrophoretic coating transportation. The present invention can ensure the convergence speed, contour accuracy, and tracking accuracy of the hybrid mechanism system, and weaken the sliding mode control chattering.

Description

Technical Field

[0001] The invention relates to automobile electrophoretic coating technology, and in particular to a novel comprehensive error rapid continuous sliding mode control method for a task space of an automobile electrophoretic coating conveying hybrid mechanism. Background Art

[0002] The hybrid mechanism for automobile electrophoretic coating conveying combines series and parallel mechanisms reasonably, and has the advantages of flexible movement and large working space of the series mechanism, strong load-bearing capacity and high flexibility of the parallel mechanism. It can solve the problems of poor heavy load bearing capacity and low flexibility of the existing electrophoretic coating conveying equipment due to the cantilever beam series structure. However, the hybrid mechanism system for automobile electrophoretic coating conveying will inevitably be affected by uncertain factors such as joint friction, modeling error, and external interference during actual operation, which is specifically manifested as the friction of each active joint of the mechanism; modeling errors caused by the gap of the lead screw, the tilt of the connecting rod and the load changes of different vehicle bodies. Secondly, there is a coupling effect between the kinematic chains of each branch of the hybrid mechanism, that is, when a single branch moves, it will affect other branches, but the actuators of each branch can only correct the motion error of its own control loop, and do not respond to the motion error from other coupled branches. Therefore, it is easy for the actuators of each branch to produce uncoordinated motion. These problems can easily lead to inaccurate movement of the hybrid mechanism for automobile electrophoretic coating conveying, increase the contour error of the end of the mechanism, and even cause instability of the entire system in severe cases.

[0003] In the paper "Neural Network Super-helical Sliding Mode Control of Multi-joint Robot Arm" (Zhang Runmei, Xia Xu, Journal of Ordnance Equipment Engineering, 2022, No. 43, pp. 258-264), a non-singular fast terminal sliding surface is designed to address the uncertainty factors of the multi-joint robot control system, and a second-order non-singular fast terminal sliding surface is designed by combining the non-singular fast terminal sliding surface with the super-helical switching term to improve the convergence speed of the sliding surface and make the control law continuous. However, the control in the paper is in the joint space, which cannot guarantee the tracking accuracy of the end effector. In addition, the super-helical switching term has the problem of slow convergence speed.

[0004] In the paper "Research on Synchronous Coordination Control of Conveying Mechanism Based on Contour Error" (Lv Guitao, Gao Guoqin, Information Technology, 2017, Issue 12, Pages 18-21), a synchronous coordination control method based on contour error is designed for the hybrid mechanism of automobile electrophoretic coating conveying. In this paper, a terminal contour error based on tangent estimation is designed to further improve the synchronous coordination and tracking accuracy of the system. However, the contour error design only includes the contour error of the terminal position component of the parallel / hybrid mechanism, and does not consider the contour error of the posture component. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention proposes a new comprehensive error fast continuous sliding mode control method in the task space for the hybrid mechanism of automobile electrophoretic coating conveying. Since the posture component of the contour error is difficult to express quantitatively in the terminal coordinate system, the existing contour error only contains the position direction component, and the posture direction component is not considered. To address this problem, the present invention uses the posture component of the active joint synchronization error of the hybrid mechanism mapped to the task space and the posture component of the terminal tracking error to design an indirect posture contour error that can reflect the posture component of the contour error of the hybrid mechanism in a cross-coupling manner, and then expands the existing position contour error that can only reflect the terminal position through the dimension into a posture contour error that can reflect both the terminal position of the hybrid mechanism and the posture of the terminal of the mechanism indirectly. Furthermore, the integral of the terminal posture contour error and the terminal tracking error are integrated to establish a new comprehensive error in the task space to more accurately characterize the tracking accuracy and contour accuracy of the terminal actuator of the hybrid mechanism; secondly, the designed new comprehensive error is introduced into a fast nonlinear sliding control method. The hybrid mechanism system is designed with a fast nonlinear sliding mode variable to construct a new comprehensive error fast nonlinear sliding mode surface; then, based on the designed new comprehensive error and fast nonlinear sliding mode variable of the hybrid mechanism system, a fast continuous reaching law design is introduced to construct the fast continuous sliding mode control switching term of the hybrid mechanism system; further, based on the designed new comprehensive error, fast nonlinear sliding mode variable and fast continuous sliding mode control switching term of the hybrid mechanism system, combined with the uncertain dynamic model of the hybrid mechanism, a fast continuous sliding mode controller based on the new comprehensive error is designed, and then a new comprehensive error fast continuous sliding mode control method for the task space of the hybrid mechanism is proposed to improve the convergence speed, contour accuracy and tracking accuracy of the hybrid mechanism system, and weaken the sliding mode control chattering.

[0006] The technical solution of the present invention is: a new comprehensive error fast continuous sliding mode control method for the task space of a hybrid mechanism for automobile electrophoretic coating conveying, comprising the following steps:

[0007] 1) Taking the automobile electrophoretic coating conveying hybrid mechanism as the controlled object, the analytical method is used to analyze the kinematic inverse solution of the hybrid mechanism, and the kinematic positive solution and Jacobian matrix of the hybrid mechanism are further obtained;

[0008] 2) The Lagrangian method is used to establish the standard dynamic model of the hybrid mechanism and the dynamic model including uncertainties such as joint friction, modeling error, and external interference;

[0009] 3) Aiming at the problem that the posture component of the contour error of the hybrid mechanism is difficult to be quantitatively expressed in the terminal coordinate system of the hybrid mechanism, an indirect posture contour error that can reflect the posture component of the contour error of the hybrid mechanism is designed in a cross-coupling manner by using the posture component of the active joint synchronization error of the hybrid mechanism and the posture component of the terminal tracking error mapped to the terminal of the task space, and then the existing position contour error that can only reflect the terminal position is expanded through the dimension into a posture contour error that can reflect both the terminal position of the hybrid mechanism and the posture of the terminal of the mechanism indirectly; further, the integral of the posture contour error and the terminal tracking error are integrated to establish a new type of comprehensive error in the task space;

[0010] 4) Based on the new comprehensive error of the hybrid mechanism system designed in step 3), the new comprehensive error is introduced into a fast nonlinear sliding mode variable design to construct a fast nonlinear sliding mode surface of the new comprehensive error of the hybrid mechanism system;

[0011] 5) Based on the new comprehensive error and fast nonlinear sliding mode variable of the hybrid mechanism system designed in steps 3 and 4), the new comprehensive error and fast nonlinear sliding mode variable are introduced into a fast continuous reaching law design to construct a fast continuous sliding mode control switching term of the hybrid mechanism system;

[0012] 6) Based on the uncertain hybrid mechanism dynamics model designed in steps 2, 4, and 5), the new comprehensive error fast nonlinear sliding surface and the fast continuous sliding control switching term, a new comprehensive error fast continuous sliding controller of the hybrid mechanism task space is designed in the task space;

[0013] 7) Through software programming, a new type of comprehensive error fast continuous sliding mode control of the task space of the hybrid mechanism is realized.

[0014] Further, the specific process of step 3) is as follows:

[0015] According to the synchronization error of the active joint of the hybrid mechanism and the positive kinematics definition, the synchronization error attitude component ε in the β direction of the hybrid mechanism is designed. tβ (t) is

[0016] ε tβ (t) = ΑJ + H1e xi (t) (12)

[0017] In the formula, ε tβ (t) is the synchronization error attitude component in the β direction, J + is the inverse of the Jacobi matrix, Α is the row vector [0,0,1], H1 is the conversion matrix from active joint tracking error to active joint synchronization error, and e xi (t) is the active joint tracking error, e xi (t) = Xid (t)-X i (t),i∈[1,6], is the expected displacement vector of the active joint of the hybrid mechanism, is the actual displacement vector of the active joint of the hybrid mechanism, x 1d ,x 2d ,x 3d ,x 4d , are the expected displacements of the six active joints of the mechanism, x1, x2, x3, x4, are the actual displacements of the six active joints of the mechanism;

[0018] The attitude component ε of the active joint synchronization error of the hybrid mechanism at the end of the task space to (t) is

[0019] ε to (t) = [ε tα (t),ε tβ (t),ε tγ (t)] T (13)

[0020] In the formula, ε tα (t), ε tβ (t) and ε tγ (t) are the components of the task space synchronization error attitude in the α direction, β direction and γ direction respectively. Since the end of this hybrid mechanism has only the β direction attitude component, ε tα (t) = ε tγ (t) = 0, and ε tβ (t) is as shown in formula (1);

[0021] Further, the synchronization error attitude component ε of the active joint of the hybrid mechanism at the end of the task space is to (t) and the terminal tracking error attitude component e to (t) Cross-coupling, designing the indirect posture profile error e that can reflect the posture component of the hybrid mechanism profile error co (t) is

[0022]

[0023] In the formula, e to (t) = [e tα (t),e tβ (t),e tγ (t)] T , e tα (t) = e tγ (t) = 0, e to (t) = q do (t)-q o(t), where q do (t) and q o (t) are the desired posture vector and actual posture vector of the end of the hybrid mechanism, respectively, do (t) = (α d ,β d ,γ d ) T ,q o (t) = (α, β, γ) T , α d , β d , γ d are the components of the three directions of the desired posture vector of the terminal, α, β, γ are the components of the three directions of the actual posture vector of the terminal, and λ is an adjustable parameter;

[0024] According to the geometric definition of the end of the hybrid mechanism, the tangent estimated position contour error e is calculated cp (t) is

[0025]

[0026] In the formula, e cx (t), e cz (t) is the position profile error e of the end effector of the hybrid mechanism reflecting the end position cp (t) is the position component in the x and z directions. Since the end of this hybrid mechanism only has position components in the x and z directions, e cy (t) = 0; e tx (t), e tz (t) is the position tracking error of the end effector of the hybrid mechanism e tp (t) is the x and z position component, e tp (t) = [e tx ,e ty ,e tz ] T , e tp (t) = q dp (t)-q p (t), e ty (t) = 0, where q dp (t) and q p (t) are the desired position vector and actual position vector of the end of the hybrid mechanism, q dp (t) = (x d ,y d ,z d ) T ,q p (t)=(x,y,z) T , x d ,y d 、z dare the components of the three directions of the terminal's expected position vector, x, y, z are the position components of the three directions of the terminal's actual position vector, and θ is the inclination angle of the tangent corresponding to the expected position;

[0027] Furthermore, the existing position profile error e that can only reflect the end position cp (t) is expanded by dimension to reflect the position and posture profile error e of the end position of the hybrid mechanism and indirectly reflect the end posture of the mechanism c (t)

[0028] e c (t) = [e cp (t),e co (t)] T (16)

[0029] In the formula, e cp (t) is the position component of the contour error, e co (t) is the posture component of the contour error;

[0030] The new comprehensive error e established in the task space * (t) is

[0031]

[0032] In the formula, e t (t) is the tracking error of the terminal position of the hybrid mechanism, e t (t) = [e tp (t),e to (t)] T =q d (t)-q(t),q d (t) and q(t) are the expected pose vector and actual pose vector of the end of the hybrid mechanism respectively, and ξ is an adjustable parameter.

[0033] Further, the specific process of step 4) is as follows:

[0034] Based on the new comprehensive error of the hybrid mechanism system, a new comprehensive error fast nonlinear sliding mode variable s=[s1,s2,s3,s4,s5,s6] is designed T for

[0035]

[0036] Where, α = diag(α1, α2, α3, α4, α5, α6), β = diag(β1, β2, β3, β4, β5, β6), α and β are parameter matrices, of which α1, α2, α3, α4, α5 and α6 are non-negative adjustable parameters, β1, β2, β3, β4, β5 and β6 are non-negative adjustable parameters, e *(t) is the new comprehensive error, is the derivative of the new comprehensive error, p, q are odd numbers, r>1;

[0037] Taking the derivative of the above formula, we can get

[0038]

[0039] Further, the specific process of step 5) is as follows:

[0040] Based on the designed new comprehensive error and fast nonlinear sliding mode variable of the hybrid mechanism system, the new comprehensive error and fast nonlinear sliding mode variable are introduced into a fast continuous reaching law design to construct a fast continuous switching term.

[0041]

[0042] Where ρ1, ρ2, and k are adjustable parameters, where ρ1 and ρ2 are positive numbers, 0<k<1, and the sign term sgn(s)=[sgn(s1),sgn(s2),sgn(s3),sgn(s4),sgn(s5),sgn(s6)] T , sgn(s1), sgn(s2), sgn(s3), sgn(s4), sgn(s5) and sgn(s6) are the six components of the sliding mode variables;

[0043] The dynamic model of the uncertain hybrid mechanism is introduced as

[0044]

[0045] Where H(t) is the lumped disturbance, the unit of H(t) is N·m, and M(q) is the inertia matrix; are the Coriolis force and centrifugal force terms; G(q) is the gravity term, Q is the generalized control torque, and the unit of Q is N·m; q(t) is the actual posture vector of the end of the hybrid mechanism, is the actual velocity vector at the end of the hybrid mechanism, is the actual acceleration vector at the end of the hybrid mechanism.

[0046] Further, in step 6), based on the designed uncertain hybrid mechanism dynamics model, the new comprehensive error fast nonlinear sliding surface and the fast continuous sliding control switching term, a new comprehensive error fast continuous sliding controller in the task space is designed.

[0047]

[0048] In the formula, is the desired acceleration vector at the end of the hybrid mechanism, is the actual velocity vector of the end of the hybrid mechanism, H(t) is the lumped disturbance, the unit of H(t) is N·m, and M(q) is the inertia matrix; are the Coriolis force and centrifugal force terms; G(q) is the gravity term, and Q is the generalized control torque, with the unit of Q being N·m.

[0049] The present invention proposes for the first time a novel comprehensive error fast continuous sliding mode control method for the task space of a hybrid mechanism for electrophoretic coating conveying of an automobile, which is applied to realize the motion control of the hybrid mechanism for electrophoretic coating conveying of an automobile, and its characteristics and beneficial effects are:

[0050] 1. Design a posture contour error in the task space that can reflect the end position of the hybrid mechanism and indirectly reflect the end posture of the mechanism, and then integrate the integral of the end posture contour error and the end tracking error to establish a new type of comprehensive error to more accurately characterize the tracking accuracy and contour accuracy of the end effector of the hybrid mechanism;

[0051] 2. Based on the new comprehensive error of the hybrid mechanism system, a new comprehensive error fast nonlinear sliding mode variable is designed to ensure the convergence speed, contour accuracy and tracking accuracy of the state error in the sliding stage of the system;

[0052] 3. Based on the designed new comprehensive error and fast nonlinear sliding mode variable of the hybrid mechanism system, the new comprehensive error and fast nonlinear sliding mode variable are introduced into a fast continuous reaching law design, and the new comprehensive error fast continuous sliding mode control law of the task space of the automobile electrophoretic coating conveying hybrid mechanism is designed, so that the switching term in the control law can be hidden to suppress the chattering problem in the sliding mode control system and improve the convergence speed, contour accuracy and tracking accuracy of the hybrid mechanism system. Therefore, this method can effectively improve the motion tracking control performance of the automobile electrophoretic coating conveying hybrid mechanism in practical application. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a structural diagram of the hybrid mechanism for conveying automobile electrophoretic coating. In the figure: 1. Guide rail 2. Base 3. Travel drive motor 4. Reducer 5. Moving slide block 6. Lifting drive motor 7. Connecting rod 8. Driven wheel 9. Driving wheel 10. Connecting rod 11. Car body 12. Flipping drive motor 13. Electric cylinder.

[0054] Figure 2 It is the schematic diagram of a new type of comprehensive error fast continuous sliding mode control system in task space.

[0055] Figure 3 It is a simplified diagram of the lifting and flipping mechanism structure.

[0056] Figure 4 It is the overall structure diagram of the control system of the automobile electrophoretic coating conveying hybrid mechanism.

[0057] Figure 5 It is the expected motion posture and actual motion posture diagram of each component of the terminal motion posture of the hybrid mechanism.

[0058] (a) is the trajectory tracking curve of the posture component of the midpoint of the connecting rod in the z direction;

[0059] (b) is the trajectory tracking curve of the midpoint of the connecting rod moving counterclockwise around the y-axis.

[0060] Figure 6 It is the trajectory tracking error diagram of each component of the terminal motion posture of the hybrid mechanism.

[0061] (a) is the trajectory tracking error diagram of the posture component of the midpoint of the connecting rod in the z direction;

[0062] (b) is the trajectory tracking error diagram of the midpoint of the connecting rod moving counterclockwise around the y-axis.

[0063] Figure 7 It is a simulation diagram of the control force / torque of each active joint of the lifting and flipping mechanism.

[0064] (a) is the control force diagram of the first and third sliders;

[0065] (b) is the control force diagram of the third and fourth sliders;

[0066] (c) is the control torque diagram of the first and second driving wheels. DETAILED DESCRIPTION

[0067] The specific implementation manner of the present invention is further described below with reference to the accompanying drawings.

[0068] Firstly, the analytical method is used to analyze the kinematic inverse solution of the hybrid mechanism of automobile electrophoretic coating, and then the kinematic positive solution and Jacobian matrix J of the hybrid mechanism are obtained; secondly, the Lagrangian method is used to establish the standard dynamic model of the hybrid mechanism and the dynamic model containing uncertainties such as modeling error, friction and external interference; then, by using the active joint synchronization error posture component and the terminal tracking error posture component of the hybrid mechanism mapped to the task space, an indirect posture contour error that can reflect the posture component of the hybrid mechanism contour error is designed in a cross-coupling manner, and then the existing position contour error that can only reflect the terminal position is expanded through dimension into an indirect posture contour error that can reflect both the terminal position of the hybrid mechanism and the posture component of the terminal tracking error. The posture contour error of the terminal posture; further, the integral of the terminal posture contour error and the terminal tracking error are integrated to establish a new comprehensive error in the task space; then, based on the new comprehensive error of the hybrid mechanism, a new comprehensive error fast nonlinear sliding mode variable is designed; further, the designed new comprehensive error of the hybrid mechanism and the fast nonlinear sliding mode variable are introduced into a fast continuous reaching law design, and a fast continuous sliding mode controller based on the new comprehensive error is designed, and then a new comprehensive error fast continuous sliding mode control method for the task space of the hybrid mechanism is proposed; finally, through software programming, the new comprehensive error fast continuous sliding mode control of the task space of the hybrid mechanism of automobile electrophoretic coating conveying is realized. The specific method is as follows:

[0069] 1) The analytical method is used to perform inverse kinematic analysis on the hybrid mechanism of automobile electrophoretic coating conveying, and then the kinematic positive solution and Jacobian matrix J of the hybrid mechanism are obtained.

[0070] Usually the end pose vector of the mechanism is q(t) = (x, y, z, α, β, γ) T , x, y, z, α, β, γ are the postures of the six dimensions of the mechanism respectively. In the hybrid mechanism studied in the present invention, the end effector of the mechanism is the midpoint of the connecting rod, x is the displacement of the midpoint of the connecting rod of the mechanism in the x-axis direction (in m), z is the displacement of the midpoint of the connecting rod in the z-axis direction (in m); β is the angle of the midpoint of the connecting rod rotating counterclockwise around the y-axis (in rad), and the postures in other directions are all zero. The analytical method is used to perform inverse kinematic analysis on the hybrid mechanism to obtain the inverse position equation. Further, the two ends of the inverse kinematic equation are differentiated to obtain:

[0071]

[0072] In the formula, is the velocity vector of the end of the mechanism; is the velocity vector of the active joint of the mechanism, are the velocity variables of the six active joints of the mechanism, and J is the Jacobian matrix.

[0073] 2) The Lagrangian method is used to establish the standard dynamic model of the hybrid mechanism and the dynamic model including uncertainties such as modeling error, friction and external interference.

[0074] According to the definition of Lagrangian function, the standard dynamic equation is sorted out and established as follows:

[0075]

[0076] Where, M(q) is the inertia matrix; are the Coriolis force and centrifugal force terms; G(q) is the gravity term, and Q is the generalized control torque (in N·m); is the actual acceleration vector at the end of the hybrid mechanism, is the actual velocity vector at the end of the hybrid mechanism;

[0077] Considering the uncertainties such as modeling error, friction and external interference in the hybrid mechanism control system, the dynamic model of the hybrid mechanism including uncertainty is established as follows:

[0078]

[0079] In the formula, the lumped disturbance (Unit: N·m). ΔM(q), and ΔG(q) is the modeling error term, is the friction term (in N·m), and D(t) is the external interference term (in N·m).

[0080] 3) By using the hybrid mechanism active joint synchronization error posture component and the terminal tracking error posture component mapped to the task space, an indirect posture profile error that can reflect the hybrid mechanism contour error posture component is designed in a cross-coupling manner, and then the existing position profile error that can only reflect the terminal position is expanded through dimensions into a posture profile error that can reflect both the hybrid mechanism terminal position and the terminal posture of the mechanism indirectly; further, the integral of the terminal posture profile error and the terminal tracking error are integrated to establish a new type of comprehensive error in the task space;

[0081] Firstly, according to the active joint synchronization error and forward kinematics definition of the hybrid mechanism, the attitude direction component ε of the task space synchronization error β of the hybrid mechanism is designed. tβ (t) is

[0082] ε tβ (t) = AJ + H1e xi (t) (26)

[0083] In the formula, J +is the inverse of the Jacobi matrix, Α is the row vector [0,0,1], H1 is the conversion matrix from active joint tracking error to active joint synchronization error, and e xi (t) is the active joint tracking error, e xi (t) = X id (t)-X i (t),i∈[1,6], is the expected displacement vector of the active joint of the hybrid mechanism, is the actual displacement vector of the active joint of the hybrid mechanism, x 1d ,x 2d ,x 3d ,x 4d , are the expected displacements of the six active joints of the mechanism, x1, x2, x3, x4, are the actual displacements of the six active joints of the mechanism;

[0084] Task space synchronization error attitude component ε to (t) is

[0085] ε to (t) = [ε tα (t),ε tβ (t),ε tγ (t)] T (27)

[0086] In the formula, ε tα (t), ε tβ (t) and ε tγ (t) are the components of the task space synchronization error attitude in the α direction, β direction and γ direction respectively. Since the end of this hybrid mechanism has only the β direction attitude component, ε tα (t) = ε tγ (t) = 0, and ε tβ (t) is as shown in formula 14;

[0087] Further, the task space terminal synchronization error attitude component ε to (t) and the end attitude tracking error e to (t) Cross-coupling, designing the indirect posture profile error e that can reflect the posture component of the hybrid mechanism profile error co (t) is

[0088]

[0089] In the formula, e to (t) is the posture tracking error of the end effector of the hybrid mechanism, e to (t) = [e tα (t),e tβ(t),e tγ (t)] T , e tα (t) = e tγ (t) = 0, e to (t) = q do (t)-q o (t), where q do (t) and q o (t) are the desired posture vector and actual posture vector of the end of the hybrid mechanism, respectively, do (t) = (α d ,β d ,γ d ) T ,q o (t) = (α, β, γ) T , α d , β d , γ d are the components of the three directions of the desired posture vector of the terminal, α, β, γ are the components of the three directions of the actual posture vector of the terminal, and λ is an adjustable parameter;

[0090] According to the geometric definition, the tangent line estimated position contour error is calculated as

[0091]

[0092] In the formula, e cx (t), e cz (t) is the position contour error e of the end of the hybrid mechanism cp (t) is the xz position direction component. Since the end of this hybrid mechanism only has x and z direction position components, e cy (t) = 0; e tx (t), e tz (t) is the end position tracking error of the hybrid mechanism e tp (t) is the x and z position component, e tp (t) = [e tx ,e ty ,e tz ] T , e tp (t) = q dp (t)-q p (t), e ty (t) = 0, where q dp (t) and q p (t) are the desired position vector and actual position vector of the end of the hybrid mechanism, q dp (t) = (x d ,y d ,z d ) T ,qp (t)=(x,y,z) T , x d ,y d 、z d are the components of the three directions of the terminal's expected position vector, x, y, z are the components of the three directions of the terminal's actual position vector, and θ is the inclination angle of the tangent corresponding to the expected position;

[0093] Furthermore, the existing position profile error that can only reflect the end position is expanded through dimension into a posture profile error e that can reflect both the end position of the hybrid mechanism and the end posture of the mechanism indirectly. c (t)

[0094] e c (t) = [e cp (t),e co (t)] T (30)

[0095] In the formula, e cp (t) is the position component of the contour error, e co (t) is the posture component of the contour error;

[0096] The new comprehensive error in the designed task space * (t) is

[0097]

[0098] In the formula, e t (t) is the tracking error vector e of the terminal position of the hybrid mechanism t (t) = [e tp (t),e to (t)] T =q d (t)-q(t),q d (t) and q(t) are the desired pose vector and actual pose vector of the end of the hybrid mechanism, respectively. d (t) = [q dp ,q do ] T , q(t)=[q p ,q o ] T , ξ is an adjustable parameter.

[0099] 4) Based on the designed new comprehensive error of the hybrid mechanism, a new comprehensive error fast nonlinear sliding mode variable is designed, and a fast nonlinear sliding mode surface s = [s1, s2, s3, s4, s5, s6] is constructed. T for

[0100]

[0101] Where, α = diag(α1, α2, α3, α4, α5, α6), β = diag(β1, β2, β3, β4, β5, β6), α and β are parameter matrices, of which α1, α2, α3, α4, α5 and α6 are non-negative adjustable parameters, β1, β2, β3, β4, β5 and β6 are non-negative adjustable parameters, e * (t) is the new comprehensive error, is the derivative of the new comprehensive error, p, q are odd numbers, r>1;

[0102] Taking the derivative of the above formula, we can get

[0103]

[0104] 5) Based on the designed new comprehensive error and fast nonlinear sliding mode variable of the hybrid mechanism, the new comprehensive error and fast nonlinear sliding mode variable are introduced into a fast continuous reaching law design, and the fast continuous switching term is constructed as

[0105]

[0106] Where ρ1, ρ2, and k are adjustable parameters, where ρ1 and ρ2 are positive numbers, 0<k<1, and the sign term sgn(s)=[sgn(s1),sgn(s2),sgn(s3),sgn(s4),sgn(s5),sgn(s6)] T , where sgn(s1), sgn(s2), sgn(s3), sgn(s4), sgn(s5) and sgn(s6) are the six components of the sliding mode variables.

[0107] 6) For the hybrid mechanism system considering uncertainty, based on the uncertainty dynamic model designed by Equations 13, 20 and 22, the new comprehensive error fast nonlinear sliding surface and the fast continuous sliding mode control switching term, a new comprehensive error fast continuous sliding mode controller for the hybrid mechanism task space is designed as

[0108]

[0109] In the formula, is the expected acceleration vector at the end of the hybrid mechanism.

[0110] 7) Through software programming, a new type of comprehensive error fast continuous sliding mode control of the task space of the automobile electrophoretic coating conveying hybrid mechanism is realized

[0111] In order to facilitate the actual control of the hybrid mechanism, the generalized torque is converted into the joint driving torque, and the following transformation is required:

[0112] Q=J T τ (36)

[0113] Where τ is the joint driving torque (in Nm).

[0114] According to formula (24), the driving control quantity of each active joint of the automobile electrophoretic coating hybrid mechanism is obtained, and by writing a new comprehensive error fast continuous sliding mode control algorithm software program in the task space, the voltage analog quantity obtained by the digital / analog conversion of the numerical control system is sent to the servo driver corresponding to the motor, and each motor is controlled to drive the corresponding active joint, thereby driving the end effector of the automobile electrophoretic coating conveying hybrid mechanism to achieve the desired movement.

[0115] The following provides embodiments of the present invention:

[0116] Example 1

[0117] like Figure 1 As shown, 1. guide rail 2. base 3. travel drive motor 4. reducer 5. moving slider 6. lifting drive motor 7. connecting rod 8. driven wheel 9. driving wheel 10. connecting rod 11. vehicle body 12. flip drive motor 13. electric cylinder.

[0118] The present invention mainly focuses on improving the motion control performance of the automobile electrophoretic coating conveying hybrid mechanism by using a new task space comprehensive error fast continuous sliding mode control technology. The principle block diagram of the new task space comprehensive error fast continuous sliding mode control of the automobile electrophoretic coating conveying hybrid mechanism is as follows Figure 2 As shown, the specific implementation of the control method is as follows:

[0119] 1) The analytical method is used to analyze the kinematic inverse solution of the hybrid mechanism for automobile electrophoretic coating, and the kinematic positive solution and Jacobian matrix J of the hybrid mechanism are further obtained.

[0120] Usually the actual pose vector of the end of the mechanism is q(t) = (x, y, z, α, β, γ) T , x, y, z, α, β, γ are the six-dimensional postures of the mechanism. In the hybrid mechanism studied in this invention, the end effector of the mechanism is the midpoint of the connecting rod, x is the displacement of the midpoint of the connecting rod in the x-axis direction (in m), z is the displacement of the midpoint of the connecting rod in the z-axis direction (in m); β is the angle of the midpoint of the connecting rod rotating counterclockwise around the y-axis (in rad), and the postures in other directions are all zero.

[0121] exist Figure 3 In the equation, the rod length constraint equation is adopted, and the kinematic equation of the mechanism can be obtained according to the structure of the lifting and flipping mechanism:

[0122]

[0123] Where, L1 is the length of the connecting rod (in meters); z i (i=1,2)(unit: m), βi (i=1,2)(unit is rad) respectively Figure 1 The z-axis positions of the two ends of the middle connecting rod 16 in the static coordinate system and the counterclockwise rotation angle around the y-axis direction, where z is the position of the midpoint of the connecting rod; x i (i=1,2,3,4)(unit is m) respectively Figure 1 The four sliders are located in the x-axis direction; (unit: rad) are Figure 1 The angle of the two driving wheels rotating counterclockwise around the y-axis, x i (i=1,2,3,4) and The six active joint variables that constitute the mechanism are R and r (both in m) are the radius of the driving wheel and the radius of the driven wheel respectively.

[0124] The inverse kinematic solution of the lifting and flipping mechanism can be obtained from equation (25) and the kinematic characteristics of the mechanism, and the Jacobian matrix of the lifting and flipping mechanism is solved by the differential transformation method, that is, the two ends of equation (23) are respectively differentiated with respect to time and rearranged to obtain:

[0125]

[0126] Formula (26) can be simplified as Then the Jacobian matrix J of the lifting and flipping mechanism is

[0127]

[0128] 2) The Lagrangian method is used to establish the standard dynamic model of the hybrid mechanism and the dynamic model including uncertainties such as modeling error, friction and external interference.

[0129] The standard dynamic equation of the automobile electrophoretic coating conveying hybrid mechanism can be expressed as:

[0130]

[0131] Where M(q) is a symmetric positive definite inertia matrix; are the Coriolis force and centrifugal force terms; G(q) is the gravity term, Q is the generalized control torque (in N·m); q(t), and They are respectively the midpoint pose vector, velocity vector and acceleration vector of the connecting rod of the hybrid mechanism.

[0132] Considering the uncertainties such as modeling error, friction and external interference in the hybrid mechanism control system, the dynamic model of the hybrid mechanism including uncertainty is established as follows:

[0133]

[0134] In the formula, the lumped disturbance (Unit: N·m).

[0135] ΔM(q), and ΔG(q) is the modeling error term, is the friction term (in N·m), and D(t) is the external interference term (in N·m).

[0136] 3) By using the hybrid mechanism active joint synchronization error posture component and the terminal tracking error posture component mapped to the task space, an indirect posture profile error that can reflect the hybrid mechanism contour error posture component is designed in a cross-coupling manner, and then the existing position profile error that can only reflect the terminal position is expanded through dimensions into a posture profile error that can reflect both the hybrid mechanism terminal position and the terminal posture of the mechanism indirectly; further, the integral of the terminal posture profile error and the terminal tracking error are integrated to establish a new type of comprehensive error in the task space;

[0137] The hybrid mechanism has six active joints, including four translational joints and two rotational joints. Its tracking error can be expressed as:

[0138] e xi (t) = X id (t)-X i (t),i∈[1,6] (42)

[0139] In the formula, is the expected displacement vector of the active joint of the hybrid mechanism, is the actual displacement vector of the active joint of the hybrid mechanism, x 1d ,x 2d ,x 3d ,x 4d , are the expected displacement variables of the six active joints of the mechanism, x1, x2, x3, x4, are the actual displacement variables of the six active joints of the mechanism;

[0140] Active joint synchronization error ε can be defined g (t) is:

[0141] ε g (t) = H1e xi (t) (43)

[0142] In the formula, e xi (t) is the active joint tracking error, H1 is the conversion matrix from the active joint tracking error to the active joint synchronization error, and

[0143] According to the positive kinematics definition, the active joint synchronization error ε g(t) Transform to task space:

[0144] ε t (t) = J + H1e xi (t) = [ε tx (t),ε tz (t),ε tβ (t)] (44)

[0145] In the formula, J + is the generalized inverse of the Jacobi matrix, ε tx (t), ε tz (t) is the synchronization error in the X and Z position directions of the task space, ε tβ (t) is the attitude direction component of the task space synchronization error β.

[0146] Furthermore, according to ε in Eq. 32 tβ (t) Design task space synchronization error attitude component ε to (t) is

[0147] ε to (t) = [ε tα (t),ε tβ (t),ε tγ (t)] T (45)

[0148] In the formula, ε tα (t), ε tβ (t) and ε tγ (t) are the components of the task space synchronization error attitude in the α direction, β direction and γ direction respectively. Since the end of this hybrid mechanism has only the β direction attitude component, ε tα (t) = ε tγ (t) = 0

[0149] Then the task space terminal synchronization error attitude component ε to (t) and the end attitude tracking error e to (t) Cross-coupling, designing the indirect posture profile error e that can reflect the posture component of the hybrid mechanism profile error co (t) is

[0150]

[0151] In the formula, e to (t) is the posture tracking error of the end effector of the hybrid mechanism, e to (t) = [e tα (t),e tβ (t),e tγ (t)] T , e tα(t) = e tγ (t) = 0, e to (t) = q do (t)-q o (t), where q do (t) and q o (t) are the desired posture vector and actual posture vector of the end of the hybrid mechanism, respectively, do (t) = (α d ,β d ,γ d ) T ,q o (t) = (α, β, γ) T , α d , β d , γ d They are the components of the three directions of the desired posture vector of the terminal, α, β, γ are the components of the three directions of the actual posture vector of the terminal, and λ is an adjustable parameter.

[0152] Calculate the tangent line estimated position contour error e according to the geometric definition cp (t) is

[0153]

[0154] In the formula, e cx (t), e cz (t) is the position profile error of the end effector of the hybrid mechanism e cp (t) is the xz position component. Since the end of this hybrid mechanism only has the xz position component, e cy (t) = 0; e tx (t), e tz (t) is the end position tracking error of the hybrid mechanism e tp (t) is the x and z position component, e tp (t) = [e tx ,e ty ,e tz ] T , e tp (t) = q dp (t)-q p (t), e ty (t) = 0, where q dp (t) and q p (t) are the desired position vector and actual position vector of the end of the hybrid mechanism, q dp (t) = (x d ,y d ,z d ) T ,q p (t)=(x,y,z)T , x d ,y d 、z d are the components of the three directions of the terminal's expected position vector, x, y, z are the components of the three directions of the terminal's actual position vector, and θ is the inclination angle of the tangent corresponding to the expected position;

[0155] Furthermore, the existing position profile error that can only reflect the end position is expanded through dimension into a posture profile error e that can reflect both the end position of the hybrid mechanism and the end posture of the mechanism indirectly. c (t)

[0156] e c (t) = [e cp (t),e co (t)] T (48)

[0157] In the formula, e cp (t) is the position component of the contour error, e co (t) is the posture component of the contour error.

[0158] The new comprehensive error in the designed task space * (t) is

[0159]

[0160] In the formula, e t (t) is the tracking error vector e of the terminal position of the hybrid mechanism t (t) = [e tp (t),e to (t)] T =q d (t)-q(t),q d (t) and q(t) are the desired pose vector and actual pose vector of the end of the hybrid mechanism, respectively. d (t) = [q dp ,q do ] T , q(t)=[q p ,q o ] T , ξ is an adjustable parameter.

[0161] 4) Based on the designed new comprehensive error of the hybrid mechanism, a new comprehensive error fast nonlinear sliding mode variable is designed, and a fast nonlinear sliding mode surface s = [s1, s2, s3, s4, s5, s6] is constructed. T for

[0162]

[0163] Where, α = diag(α1, α2, α3, α4, α5, α6), β = diag(β1, β2, β3, β4, β5, β6) are non-negative adjustable parameters, α and β are parameter matrices, among which α1, α2, α3, α4, α5 and α6 are non-negative adjustable parameters, β1, β2, β3, β4, β5 and β6 are non-negative adjustable parameters, e * (t) is the new comprehensive error, is the derivative of the new comprehensive error, p, q are odd numbers, and r>1.

[0164] Taking the derivative of the above formula, we can get

[0165]

[0166] 5) Based on the designed new comprehensive error and fast nonlinear sliding mode variable of the hybrid mechanism, the new comprehensive error and fast nonlinear sliding mode variable are introduced into a fast continuous reaching law design, and the fast continuous switching term is constructed as

[0167]

[0168] Where ρ1, ρ2, and k are adjustable parameters, where ρ1 and ρ2 are positive numbers, 0<k<1, and the sign term sgn(s)=[sgn(s1),sgn(s2),sgn(s3),sgn(s4),sgn(s5),sgn(s6)] T , where sgn(s1), sgn(s2), sgn(s3), sgn(s4), sgn(s5) and sgn(s6) are the six components of the sliding mode variables.

[0169] 6) For the hybrid mechanism system considering uncertainty, based on the uncertainty dynamic model designed by Eqs. 29, 38 and 40, the new comprehensive error fast nonlinear sliding surface and the fast continuous sliding control switching term, a new comprehensive error fast continuous sliding mode controller for the hybrid mechanism task space is designed as

[0170]

[0171] In the formula, is the expected acceleration vector at the end of the hybrid mechanism.

[0172] 7) Through software programming, a new type of comprehensive error fast continuous sliding mode control of the task space of the automobile electrophoretic coating conveying hybrid mechanism is realized.

[0173] The control system of the automobile electrophoretic coating conveying hybrid mechanism adopts a distributed structure of "upper computer PC + lower computer UMAC multi-axis motion controller". Figure 4As shown. The control system is based on the UMAC multi-axis motion controller, in which the CPU board TURBO PMAC2 CPU module of the UMAC realizes the human-machine interface communication with the host computer IPC through the Ethernet RJ45 network port; the axis channel expansion card ACC-24E2A of the UMAC multi-axis motion controller communicates with the servo driver to realize the encoder information collection and the output function of the drive control signal; the digital expansion I / O interface board ACC-65E of the UMAC multi-axis motion controller transmits information with each servo driver and the automobile electrophoretic coating conveying hybrid mechanism respectively to realize the servo start, stop and alarm functions. In addition, the control system uses a high-precision absolute position detection device to detect the absolute position of the servo driver, and the host computer realizes serial communication with the servo driver through the RS232 / RS422 interface converter to read the absolute position information.

[0174] In order to facilitate the actual control of the hybrid mechanism, the generalized torque is converted into the joint driving torque, and the following transformation is required:

[0175] Q=J T τ (54)

[0176] Where τ is the joint driving torque (in N·m).

[0177] According to formula (42), the driving control quantity of each active joint of the automobile electrophoretic coating conveying hybrid mechanism is obtained, and by writing a new comprehensive error fast continuous sliding mode control algorithm software program in the task space, the voltage analog quantity obtained by the digital / analog conversion of the driving quantity by the numerical control system is sent to the servo driver corresponding to the motor, and each motor is controlled to drive the corresponding active joint, thereby driving the end effector of the automobile electrophoretic coating conveying hybrid mechanism to achieve the desired movement.

[0178] Through MATLAB simulation and automobile electrophoretic coating conveying hybrid mechanism prototype system experiment, the control effects of the proposed task space new comprehensive error fast continuous sliding mode control (NCE-TSFCSMC), the task space fast continuous sliding mode control (PCE-TSFCSMC) that only considers the hybrid mechanism end position contour error, and the new comprehensive error approaching rate sliding mode control (NCE-SMC) are compared. Figure 5 The trajectory tracking curve of each component of the midpoint of the connecting rod of the automobile electrophoretic coating conveying hybrid mechanism shown in the figure, Figure 6 The trajectory tracking error of each component of the connecting rod midpoint is shown as well as Figure 7 The driving force / torque of each active joint of the hybrid mechanism shown.

[0179] Depend on Figure 5 and Figure 6It can be seen that the new task space comprehensive error fast continuous sliding mode control method proposed in the present invention has higher tracking accuracy on the terminal posture component of the mechanism than the task space fast continuous sliding mode control algorithm that only considers the terminal position contour error of the hybrid mechanism; it has faster trajectory tracking speed and stronger convergence performance than the new comprehensive error reaching law sliding mode control algorithm, and has stronger robustness. Figure 7 It shows that the new task space comprehensive error fast continuous sliding mode control method proposed in the present invention can effectively weaken the sliding mode control chattering.

[0180] It should be understood that the above embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent modifications of the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

Claims

1. A new type of comprehensive error fast continuous sliding mode control method for the task space of a hybrid mechanism for electrophoretic coating conveying of automobiles, characterized in that: The steps include: 1) Taking the automobile electrophoretic coating conveying hybrid mechanism as the controlled object, the analytical method is used to analyze the kinematic inverse solution of the hybrid mechanism, and the kinematic positive solution and Jacobian matrix of the hybrid mechanism are further obtained; 2) The Lagrangian method is used to establish the standard dynamic model of the hybrid mechanism and the dynamic model including uncertainties such as joint friction, modeling error, and external interference; 3) Aiming at the problem that the posture component of the contour error of the hybrid mechanism is difficult to be quantitatively expressed in the terminal coordinate system of the hybrid mechanism, an indirect posture contour error that can reflect the posture component of the contour error of the hybrid mechanism is designed in a cross-coupling manner by using the posture component of the active joint synchronization error of the hybrid mechanism and the posture component of the terminal tracking error mapped to the terminal of the task space, and then the existing position contour error that can only reflect the terminal position is expanded through the dimension into a posture contour error that can reflect both the terminal position of the hybrid mechanism and the posture of the terminal of the mechanism indirectly; further, the integral of the posture contour error and the terminal tracking error are integrated to establish a new type of comprehensive error in the task space; 4) Based on the new comprehensive error of the hybrid mechanism system designed in step 3), the new comprehensive error is introduced into a fast nonlinear sliding mode variable design to construct a fast nonlinear sliding mode surface of the new comprehensive error of the hybrid mechanism system; 5) Based on the new comprehensive error and fast nonlinear sliding mode variable of the hybrid mechanism system designed in steps 3 and 4), the new comprehensive error and fast nonlinear sliding mode variable are introduced into a fast continuous reaching law design to construct a fast continuous sliding mode control switching term of the hybrid mechanism system; 6) Based on the uncertain hybrid mechanism dynamics model designed in steps 2, 4, and 5), the new comprehensive error fast nonlinear sliding surface and the fast continuous sliding control switching term, a new comprehensive error fast continuous sliding controller of the hybrid mechanism task space is designed in the task space; 7) Through software programming, a new type of comprehensive error fast continuous sliding mode control of the task space of the hybrid mechanism is realized; The specific process of step 3) is as follows: According to the synchronization error of the active joint of the hybrid mechanism and the positive kinematics definition, the synchronization error attitude component ε in the β direction of the hybrid mechanism is designed. tβ (t) is ε tβ (t)=ΑJ + H1e xi (t) (1) In the formula, ε tβ (t) is the synchronization error attitude component in the β direction, J + is the inverse of the Jacobi matrix, Α is the row vector [0,0,1], H1 is the conversion matrix from active joint tracking error to active joint synchronization error, and e xi (t) is the active joint tracking error, e xi (t) = X id (t)-X i (t),i∈[1,6], is the expected displacement vector of the active joint of the hybrid mechanism, is the actual displacement vector of the active joint of the hybrid mechanism, x 1d ,x 2d ,x 3d ,x 4d , are the expected displacements of the six active joints of the mechanism, x1, x2, x3, x4, are the actual displacements of the six active joints of the mechanism; The attitude component ε of the active joint synchronization error of the hybrid mechanism at the end of the task space to (t) is e to (t)=[e tα (t),e tβ (t),e tγ (t)] T (2) In the formula, ε tα (t), ε tβ (t) and ε tγ (t) are the components of the task space synchronization error attitude in the α direction, β direction and γ direction respectively. Since the end of this hybrid mechanism has only the β direction attitude component, ε tα (t) = ε tγ (t) = 0, and ε tβ (t) is as shown in formula (1); Further, the synchronization error attitude component ε of the active joint of the hybrid mechanism at the end of the task space is to (t) and the terminal tracking error attitude component e to (t) Cross-coupling, designing the indirect posture profile error e that can reflect the posture component of the hybrid mechanism profile error co (t) is In the formula, e to (t) = [e tα (t),e tβ (t),e tγ (t)] T , e tα (t) = e tγ (t) = 0, e to (t) = q do (t)-q o (t), where q do (t) and q o (t) are the desired posture vector and actual posture vector of the end of the hybrid mechanism, respectively, do (t) = (α d ,β d ,γ d ) T ,q o (t) = (α, β, γ) T , α d , β d , γ d are the components of the three directions of the desired posture vector of the terminal, α, β, γ are the components of the three directions of the actual posture vector of the terminal, and λ is an adjustable parameter; According to the geometric definition of the end of the hybrid mechanism, the tangent estimated position contour error e is calculated cp (t) is In the formula, e cx (t), e cz (t) is the position profile error e of the end effector of the hybrid mechanism reflecting the end position cp (t) is the position component in the x and z directions. Since the end of this hybrid mechanism only has position components in the x and z directions, e cy (t) = 0; e tx (t), e tz (t) is the position tracking error of the end effector of the hybrid mechanism e tp (t) is the x and z position component, e tp (t) = [e tx ,e ty ,e tz ] T , e tp (t) = q dp (t)-q p (t), e ty (t) = 0, where q dp (t) and q p (t) are the desired position vector and actual position vector of the end of the hybrid mechanism, q dp (t) = (x d ,y d ,z d ) T ,q p (t)=(x,y,z) T , x d ,y d 、z d are the components of the three directions of the terminal's expected position vector, x, y, z are the position components of the three directions of the terminal's actual position vector, and θ is the inclination angle of the tangent corresponding to the expected position; Furthermore, the existing position profile error e that can only reflect the end position cp (t) is expanded by dimension to reflect the position and posture profile error e of the end position of the hybrid mechanism and indirectly reflect the end posture of the mechanism c (t) e c (t)=[e cp (t),e co (t)] T (5) In the formula, e cp (t) is the position component of the contour error, e co (t) is the posture component of the contour error; The new comprehensive error e established in the task space * (t) is In the formula, e t (t) is the tracking error of the terminal position of the hybrid mechanism, e t (t) = [e tp (t),e to (t)] T =q d (t)-q(t),q d (t) and q(t) are the expected pose vector and actual pose vector of the end of the hybrid mechanism respectively, and ξ is an adjustable parameter.

2. The method according to claim 1, characterized in that: The specific process of step 4) is as follows: Based on the new comprehensive error of the hybrid mechanism system, a new comprehensive error fast nonlinear sliding mode variable s=[s1,s2,s3,s4,s5,s6] is designed T for Where, α = diag(α1, α2, α3, α4, α5, α6), β = diag(β1, β2, β3, β4, β5, β6), α and β are parameter matrices, of which α1, α2, α3, α4, α5 and α6 are non-negative adjustable parameters, β1, β2, β3, β4, β5 and β6 are non-negative adjustable parameters, e * (t) is the new comprehensive error, is the derivative of the new comprehensive error, p, q are odd numbers, r>1; Taking the derivative of the above formula, we can get 3. The method according to claim 1, characterized in that: The specific process of step 5) is as follows: Based on the designed new comprehensive error and fast nonlinear sliding mode variable of the hybrid mechanism system, the new comprehensive error and fast nonlinear sliding mode variable are introduced into a fast continuous reaching law design to construct a fast continuous switching term. Where ρ1, ρ2, and k are adjustable parameters, where ρ1 and ρ2 are positive numbers, 0<k<1, and the sign term sgn(s)=[sgn(s1),sgn(s2),sgn(s3),sgn(s4),sgn(s5),sgn(s6)] T , sgn(s1), sgn(s2), sgn(s3), sgn(s4), sgn(s5) and sgn(s6) are the six components of the sliding mode variables; The dynamic model of the uncertain hybrid mechanism is introduced as Where H(t) is the lumped disturbance, the unit of H(t) is N·m, and M(q) is the inertia matrix; are the Coriolis force and centrifugal force terms; G(q) is the gravity term, Q is the generalized control torque, and the unit of Q is N·m; q(t) is the actual posture vector of the end of the hybrid mechanism, is the actual velocity vector at the end of the hybrid mechanism, is the actual acceleration vector at the end of the hybrid mechanism.

4. The method according to claim 1, characterized in that: In step 6), a new type of comprehensive error fast continuous sliding mode controller for the task space of the hybrid mechanism is designed in the task space: Where M(q) is the inertia matrix, is the expected acceleration vector at the end of the hybrid mechanism, and ξ is an adjustable parameter.

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