Delta parallel robot trajectory tracking control method based on fuzzy adaptive sliding mode

Abstract

The present invention discloses a trajectory tracking control method for a delta parallel robot based on a fuzzy adaptive sliding mode, comprising the following steps: S1, obtaining a dynamic model and a reference motion trajectory; S2, establishing a mapping to obtain a joint rotation angle; S3, obtaining the tracking error of the joint angle, designing a sliding mode, selecting a convergence rate, and making the angle tracking error reach the sliding mode; designing a control law for the robot trajectory tracking controller based on the robot model and the control target of trajectory tracking, and determining control parameters; S4, introducing a fuzzy adaptive control system; S5, analyzing the stability and convergence of the fuzzy adaptive control system, adjusting the control parameters of the controller, and outputting a trajectory tracking result. The present invention introduces fuzzy adaptive control on the basis of a sliding mode controller, replacing the discontinuous switching function in the sliding mode control law with the output of the fuzzy system, thereby achieving smooth output of the robot control torque and maintaining the robustness of the robot system during trajectory tracking.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of robot system trajectory tracking, and particularly relates to a trajectory tracking control method based on fuzzy adaptive sliding mode for a Delta parallel robot. BACKGROUND

[0002] With the progress of science and technology and the development of the times, the degree of industrial automation of a country also keeps pace with the times. A robot is a comprehensive system that can realize autonomous movement towards a target and complete corresponding tasks under the action of a controller according to its own state and sensing information. Motion control is the most basic problem in the study of robot autonomy, because any task that a robot wants to complete autonomously is based on movement. Due to the uncertainty of the working environment of a robot, the robot is usually required to track a feasible trajectory that has been planned. This kind of problem is called trajectory tracking problem, and is a hot issue in the field of robot motion control.

[0003] For the research on robot trajectory tracking technology, the commonly used method is to use linear feedback control or nonlinear feedback control, which has the main disadvantage that it cannot be applied to motion planning problems in complex environments, and the robustness of the system and the control effect are not ideal. With the development of robot technology, the dynamic and static requirements such as rapidity, accuracy and anti-interference ability of the robot system motion trajectory tracking are also getting higher and higher. In reality, the system may be disturbed by the external environment during operation, and the sliding mode control has the characteristics of being insensitive to system uncertainty factors and external disturbances, that is, it can maintain good robustness for linear systems and nonlinear systems. Moreover, the sliding mode control method can also obtain satisfactory dynamic quality through the design of sliding mode, and the control algorithm is simple and easy to implement. Considering the trajectory tracking control of the Delta parallel robot, and the system is affected by external disturbances, using the sliding mode control strategy is a good choice. However, the discontinuous switching function contained in the reaching rate of the sliding mode controller will cause the rapid switching of the brake responsible for driving, causing chattering. In the robot system, the control input of the system is torque, and severe chattering will increase the energy loss of the system and affect the accuracy and stability of the trajectory tracking of the system. SUMMARY

[0004] To solve the technical problems existing in the prior art, the present application provides a trajectory tracking control method based on fuzzy adaptive sliding mode for a Delta parallel robot, which introduces fuzzy adaptive control on the basis of the sliding mode controller, replaces the discontinuous switching function in the sliding mode control law with the output of the fuzzy system, realizes the smooth output of the control torque of the robot, and maintains the robustness of the robot system trajectory tracking.

[0005] The application adopts the following technical scheme to realize the method: a trajectory tracking control method based on fuzzy self-adaptive sliding mode for a Delta parallel robot, comprising the following steps:

[0006] S1, a dynamics model of the robot and a reference motion trajectory Xr are given according to the structure of the Delta parallel robot;

[0007] S2, a mapping between the reference motion trajectory Xr of the robot and the driving joint angle is established according to the inverse kinematics of the Delta parallel robot, so as to obtain the expected joint rotation angle qd corresponding to the reference motion trajectory;

[0008] S3, the actual rotation angle of the driving joint of the robot is measured and fed back to the controller, and the difference between the expected joint angle in step S2 is obtained, so as to obtain the tracking error of the joint angle; according to the angle tracking error information, a sliding mode is designed, a reaching rate is selected, and the angle tracking error reaches the sliding mode; according to the robot model and the control target of trajectory tracking, the control law of the robot trajectory tracking controller is designed, and the control parameters are determined;

[0009] S4, a fuzzy self-adaptive control system is introduced, and the smooth output of the fuzzy self-adaptive control system is used to replace the discontinuous switching function in the sliding mode control rate;

[0010] S5, the stability and convergence of the fuzzy self-adaptive control system are analyzed, the control parameters of the controller are adjusted, and the trajectory tracking result is output.

[0011] Compared with the prior art, the application has the following advantages and beneficial effects:

[0012] 1, the fuzzy self-adaptive control is introduced on the basis of the sliding mode controller, the output of the fuzzy system is used to replace the discontinuous switching function in the sliding mode control law, the smooth output of the robot control torque is realized, and the robustness of the robot system trajectory tracking is maintained.

[0013] 2, the output of the fuzzy function contains the information of the system modeling error and the disturbance error, and the online estimation can be performed, so that the adaptive ability of the system is enhanced. DETAILED DESCRIPTION

[0014] Figure 1 is a method flowchart of the application;

[0015] Figure 2 is a three-dimensional perspective view of a reference trajectory in an embodiment of the application;

[0016] Figure 3 is a schematic diagram of an expected joint rotation angle in an embodiment of the application;

[0017] Figure 4is a schematic diagram of torque output under the action of a simple sliding mode controller in step S53 in the embodiment of the application;

[0018] Figure 5 is a schematic diagram of torque output under the action of a fuzzy adaptive sliding mode controller in step S53 in the embodiment of the application;

[0019] Figure 6 is a schematic diagram of trajectory tracking error of each joint under the action of a fuzzy adaptive sliding mode controller in the embodiment of the application. DETAILED DESCRIPTION

[0020] The application will be further described in conjunction with the embodiments and the accompanying drawings, but the embodiments of the application are not limited thereto.

[0021] EMBODIMENT

[0022] As shown in the figure, the trajectory tracking control method based on fuzzy adaptive sliding mode for a Delta parallel robot in the embodiment includes the following steps: Figure 1

[0023] S1, a dynamics model of the robot and a reference motion trajectory Xr are given according to the structure of the Delta parallel robot;

[0024] S2, a mapping between the reference motion trajectory Xr of the robot and the driving joint angle is established according to the inverse kinematics of the Delta parallel robot, so as to obtain the expected joint rotation angle qd corresponding to the reference motion trajectory, as shown in the figure; Figure 3

[0025] S3, the actual rotation angle of the driving joint of the robot is measured and fed back to the controller, and the tracking error of the joint angle is obtained by subtracting the expected joint angle in step S2; according to the angle tracking error information, a sliding mode is designed, a reaching rate is selected, and the angle tracking error reaches the sliding mode; according to the robot model and the control target of trajectory tracking, the control law of the robot trajectory tracking controller is designed, and the control parameters are determined;

[0026] S4, a fuzzy adaptive control system is introduced, and the smooth output of the fuzzy adaptive control system is used to replace the discontinuous switching function in the sliding film control rate;

[0027] S5, the stability and convergence of the fuzzy adaptive control system are analyzed, the control parameters of the controller are adjusted, and the trajectory tracking result is output.

[0028] Specifically, in the embodiment, the dynamics model of the robot in step S1 is as follows:

[0029]

[0030] wherein τ is the joint driving torque, τ​​d is the external disturbance, q, represent the driving joint angle, angular velocity and angular acceleration, respectively, M(q) is the mass matrix, is the Coriolis force and centrifugal force matrix, G(q) is the gravity vector;

[0031] a given reference motion trajectory X r = [x y z] T m; wherein x is the x-axis value, and x = 0.3sin5t; y is the y-axis value, and y = 0.3cos5t; z is the z-axis value, and z = -0.5;

[0032] As Figure 2 shown, the Delta parallel robot has three kinematic chains, each of which is driven by a motor and can translate in three-dimensional space; a given reference motion trajectory X r = [0.3sin5t 0.3cos5t -0.5] T .

[0033] Specifically, in this embodiment, the specific process of step S3 is as follows:

[0034] S31, measure the joint rotation angle q = [q1 q2 q3] T and the joint rotation angular velocity of the Delta parallel robot through the sensors installed in the driving motor; assume that the parameters of the robot dynamics model are unknown, and the external disturbance τ d acting on the system is unknown; estimate these unknown items, and take the control law as u, to obtain the following control system:

[0035]

[0036] wherein, are the estimated values of M(q), G(q) and τ d , and further obtain:

[0037]

[0038] wherein, is the product of the estimated value of the mass matrix and the joint rotation angular acceleration; is the linear regression form of , which includes the modeling error of the system and the disturbance estimation error; represent the estimation errors of M(q), G(q) and τ d respectively; thus, the relationship between the driving joint angle angular velocity and the control law u is obtained:

[0039]

[0040] where, is the angular acceleration, is all the disturbance information the system receives;

[0041] S32, the desired joint rotation angle is q d , the actual joint rotation angle of the Delta parallel robot is q, and the tracking error e = q d -q is defined; then the sliding mode surface is designed:

[0042]

[0043] where e is the tracking error; is the derivative of the tracking error; λ is a tunable parameter;

[0044] When s = 0, the tracking error of the system enters the sliding mode, at which time The solution of the tracking error of the system is an exponential function, which gradually converges to 0 as time changes;

[0045] S33, in order to make the tracking error e of the system eventually converge to 0, it is required to move on the sliding mode, that is, t→∞, s = 0; in order to meet this condition, the reaching rate The first derivative of the sliding mode surface is:

[0046]

[0047] where, is the derivative of the sliding mode surface; is the second derivative of the error; is the desired angular acceleration; is the actual angular acceleration;

[0048] The reaching rate contains the control law of the sliding mode controller, at which time the design of the reaching rate is related to the control law of the controller; to design a reaching rate that meets the control requirements, the essence becomes to design a control law u that meets the gradual convergence of the tracking error and eventually stays in the sliding mode;

[0049] S34, in order to make the tracking error e of the system eventually converge to 0, the control law is designed as:

[0050]

[0051] where, is the upper bound of the norm; λ and η are tunable parameters, and always satisfy λ > 0, η > 0; sgn(s) is the sign operation result of s; substituting the control law into the first derivative of the sliding mode surface can obtain when s > 0, When s < 0, This ensures that the tracking error of the system can always tend to the sliding mode.

[0052] Specifically, in the embodiment, the specific process of step S4 is as follows:

[0053] S41, replace the discontinuous term contained in the control law u obtained in step S3 with the smooth output of the fuzzy adaptive system The fuzzy function is defined as follows:

[0054] K = Θ T ψ(s) (21)

[0055] Wherein, K = [k1, k2, k3] T represents the output of the fuzzy adaptive system; Θ = [θ1, θ2, …, θ N ] T represents the free parameters of the fuzzy adaptive system, which are automatically updated by designing the adaptive law; Ψ(s) = [ψ1(s), ψ2(s), …, ψ N (s)] is the fuzzy basis function, N represents the number of fuzzy logic rules, s is the sliding surface, and T is the matrix transpose symbol; the fuzzy basis function is represented as:

[0056]

[0057] Wherein, is the membership function; l is the number of elements of s; n is any integer from 1 to N; i is any integer from 1 to l;

[0058] S42, fuzzy logic rule definition; specifically, the fuzzy logic rule definition is shown in Table 1; wherein, the IF column lists all the cases, and the THEN column lists the rules corresponding to the cases; NB represents a large negative number; NS represents a small negative number; ZO represents 0; PB represents a large positive number; PS represents a small positive number.

[0059] Table 1

[0060]

[0061] S43, using Gaussian membership function, fuzzy logic rule, using product inference machine and center average defuzzifier to obtain smooth fuzzy function output K; specifically, the membership function is i = 1, 2, 3; M = n = 1, 2, 3, 4, 5, and each fuzzy function output is:

[0062]

[0063] Wherein, θ Mis the free parameter of the Mth fuzzy system; M is the number of free parameters; j is any integer from 1 to M; a i is the ith adjustable parameter, and a i ∈(0, 1]; s i is the ith sliding surface;

[0064] Substitute K into formula (7) and replace its discontinuous term The control law of the fuzzy adaptive sliding mode controller is obtained:

[0065]

[0066] Specifically, in this embodiment, the specific process of step S5 is as follows:

[0067] S51, select the Lyapunov function as follows:

[0068]

[0069] where V is the Lyapunov function; is the estimated deviation value, and θ ki represents a free parameter; θ kid is the estimated value of θ ki , and the adaptive law is selected as:

[0070]

[0071] where, is the adaptive law; ψ ki (s i ) is the fuzzy base function;

[0072] S52, find the first derivative of the Lyapunov function, and get:

[0073]

[0074] where, is the first derivative of the Lyapunov function; s i is the sliding surface; is the disturbance information received by the system; ψ ki (s i ) is the fuzzy base function; η is the adjustable parameter;

[0075] Under the action of the control law, the system is stable, and the trajectory tracking error of the system is convergent. The convergence speed of the trajectory tracking error of the system is related to the parameter η. The larger η is, the faster the convergence speed of the trajectory tracking error of the system is.

[0076] S53, combining the control law and the analysis of steps S51 and S52, select the adjustable parameter λ = diag (10, 10, 10), η=60, and the output torque of the Delta parallel robot under the action of the sliding mode controller is obtained, as Figure 4 As shown. Figure 5 It can be seen that without the introduction of the fuzzy adaptive system, the output torque of the robot system will vibrate. Severe vibration will increase the energy loss of the system and affect the accuracy and stability of the system trajectory tracking.

[0077] After introducing the fuzzy adaptive control system, combined with the step control law and the analysis of steps S51 and S52, the adjustable parameters are selected as λ = diag(10,10,10), η = 100, and the output torque of the Delta parallel robot under the fuzzy adaptive sliding mode controller is obtained, as shown in the figure. Figure 5 As shown. Figure 5 It can be seen that after the introduction of the fuzzy adaptive control system, the output torque of the robot system is smooth, and the upper bound of the system modeling error and external disturbance is estimated online through the fuzzy system, which reduces the difficulty of parameter adjustment and enhances the adaptive ability of the system.

[0078] S54, the Delta parallel robot outputs a smooth torque under the action of the fuzzy sliding mode controller to drive the movement of each joint of the robot. The actual rotation angle of each joint of the Delta parallel robot is measured by the sensor, and the tracking error of each joint angle is calculated, such as Figure 6 shown.

[0079] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A trajectory tracking control method for a delta parallel robot based on fuzzy adaptive sliding mode, characterized in that: The following steps are involved: S1. According to the structure of the Delta parallel robot, the robot's dynamic model and reference motion trajectory X are given. r ; S2. According to the inverse kinematics of the Delta parallel robot, establish the robot reference motion trajectory X r The mapping between the angles of the driven joints and the desired joint rotation angle q of the robot corresponding to the reference motion trajectory is obtained d ; S3: Measure the actual rotation angle of the robot's driving joint, feed it back to the controller, and subtract it from the expected joint angle in step S2 to obtain the tracking error of the joint angle; Based on the angle tracking error information, the sliding mode is designed and the approach rate is selected to make the angle tracking error reach the sliding mode. Based on the robot model and the control objectives of trajectory tracking, the control law of the robot trajectory tracking controller is designed and the control parameters are determined. The details are as follows: Let the desired joint rotation angle be q d , the actual joint rotation angle of the Delta parallel robot is q, and the tracking error is defined as e = q d -q; then design the sliding surface: Where, e is the tracking error; is the derivative of the tracking error; λ is an adjustable parameter; When s=0, the tracking error of the system enters the sliding mode. The tracking error of the solved system is an exponential function that converges to 0 asymptotically over time; In order to make the tracking error e of the system converge to 0, it is necessary to make it move on the sliding mode, that is, t→∞, s=0; in order to meet this condition, it is necessary to design the approach rate Take the first-order derivative of the sliding surface: in, is the derivative of the sliding surface; is the second derivative of the error; is the desired angular acceleration; is the actual angular acceleration; In order to make the tracking error e of the system converge to 0, the control law is designed as follows: in, yes The upper bound of the norm; λ and η are adjustable parameters, and always satisfy λ>0, η>0; sgn(s) is the result of the symbolic operation of s; Substituting the control law into the first-order derivative of the sliding surface, we can get When s>0, When s<0, This ensures that the tracking error of the system always tends towards the sliding mode; S4. Introduce a fuzzy adaptive control system and use the smooth output of the fuzzy adaptive control system to replace the discontinuous switching function in the sliding mode control rate; S5. Analyze the stability and convergence of the fuzzy adaptive control system, adjust the control parameters of the controller, and output the trajectory tracking results.

2. The trajectory tracking control method of a delta parallel robot based on fuzzy adaptive sliding mode according to claim 1 is characterized in that: The dynamic model of the robot in step S1 is as follows: Where τ is the joint driving torque, τ d is the external disturbance, q, Represent the driving joint angle, angular velocity and angular acceleration respectively, M(q) is the mass matrix, are the Coriolis and centrifugal force matrices, G(q) is the gravity vector; Given a reference motion trajectory X r =[xyz] T m; wherein, x is the x-axis value, and x=0.3sin5t; y is the y-axis value, and y=0.3cos5t; z is the z-axis value, and z=-0.

5.

3. The trajectory tracking control method of a delta parallel robot based on fuzzy adaptive sliding mode according to claim 1, characterized in that: The specific process of step S3 also includes: The rotation angle of each joint of the Delta parallel robot is measured by sensors installed in the drive motors: q = [q1 q2q3] T and joint rotation angular velocity Assume that the parameters of the robot dynamics model are unknown and the external disturbance τ acting on the system is d unknown; estimate these unknowns and take the control law as u, and get the following control system: in, They are M(q), G(q) and τ d The estimated value of , thus obtaining: in, is the product of the estimated value of the mass matrix and the joint rotation angular acceleration; yes The linear regression form of , which includes the system modeling error and disturbance estimation error; Represent M(q), G(q) and τ d The estimation error is: in, is the angular acceleration, is the information of all disturbances received by the system.

4. The trajectory tracking control method of a delta parallel robot based on fuzzy adaptive sliding mode according to claim 1, characterized in that: The specific process of step S4 is as follows: S41. Use the smooth output of the fuzzy adaptive system to replace the discontinuous term dsgn(s) contained in the control law u obtained in step S3, and define the following fuzzy function: K=Θ T Ψ(s) (8) Where K = [k1, k2, k3] T represents the output of the fuzzy adaptive system; Θ=[θ1,θ2,…,θ N ] T represents the free parameters of the fuzzy adaptive system, which are automatically updated by the designed adaptive law; Ψ(s)=[ψ1(s),ψ2(s),…,ψ N (s)] is the fuzzy basis function, N represents the number of fuzzy logic rules, s is the sliding surface, and T is the matrix transpose symbol; the fuzzy basis function is expressed as: in, is the membership function; l is the number of elements in s; n is any integer from 1 to N; i is any integer from 1 to l; S42, defining fuzzy logic rules; S43, using Gaussian membership function, fuzzy logic rules, product inference engine and central average defuzzifier to obtain smooth fuzzy function output K; membership function is M=n=1,2,3,4,5, the output of each fuzzy function is: Among them, θ M is the free parameter of the Mth fuzzy system; M is the number of free parameters; j is any integer from 1 to M; a i is the ith adjustable parameter, and a i ∈(0,1];s i is the i-th sliding surface; Substitute K into formula (7) and replace its discontinuous terms The control law of the fuzzy adaptive sliding mode controller is obtained:

5. The trajectory tracking control method of a delta parallel robot based on fuzzy adaptive sliding mode according to claim 4 is characterized in that: The specific process of step S5 is as follows: S51. Select the Lyapunov function as follows: Where V is the Lyapunov function; is the estimated deviation value, and θ ki represents a free parameter; θ kid is θ ki The estimated value of , the adaptive law is selected as: in, is the adaptive law; ψ ki (s i ) is the fuzzy basis function; S52. Find the first-order derivative of the Lyapunov function and we get: in, is the first-order derivative of the Lyapunov function; s i is the sliding surface; is the disturbance information of the system; ψ ki (s i ) is the fuzzy basis function; η is an adjustable parameter; S53, combining the control law and the analysis of steps S51 and S52, select the adjustable parameter λ = diag (10, 10, 10), η = 60, the output torque of the Delta parallel robot under the action of the sliding mode controller is obtained; After introducing the fuzzy adaptive control system, combined with the step control law and the analysis of steps S51 and S52, the adjustable parameters are selected as λ = diag(10,10,10), η = 100, and the output torque of the delta parallel robot under the action of the fuzzy adaptive sliding mode controller is obtained; S54, the Delta parallel robot outputs a smooth torque under the action of the fuzzy sliding mode controller to drive the movement of each joint of the robot. The actual rotation angle of each joint of the Delta parallel robot is measured by the sensor, and the tracking error of each joint angle is calculated.

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