CN111673742A - Industrial robot trajectory tracking control algorithm - Google Patents

Industrial robot trajectory tracking control algorithm Download PDF

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CN111673742A
CN111673742A CN202010439921.3A CN202010439921A CN111673742A CN 111673742 A CN111673742 A CN 111673742A CN 202010439921 A CN202010439921 A CN 202010439921A CN 111673742 A CN111673742 A CN 111673742A
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郑雪芳
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Jiangsu Vocational College of Information Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

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Abstract

The invention relates to a track tracking control algorithm of an industrial robot, which is based on a rapid continuous nonsingular terminal sliding mode control strategy optimized by a cuckoo algorithm, and utilizes a cuckoo algorithm optimizing mechanism to plan a reference track of a robot end effector pose; the control strategy adopts a continuous nonsingular terminal sliding mode surface to compensate and inhibit the uncertainty and the external disturbance of the system under the support of the Lyapunov stability theory, introduces a fast terminal sliding mode approach law to accelerate the response speed of the system, and compensates other nonlinear factors such as dead zones in the system by combining the Anti-Windup technology. The control method can effectively improve the precision of the track tracking control of the SCARA robot.

Description

Industrial robot trajectory tracking control algorithm
Technical Field
The invention relates to the technical field of industrial robots, in particular to an industrial robot trajectory tracking control algorithm.
Background
With the development of the disciplines of robotics, informatization technology, Control theory and the like, Industrial robots are widely applied to intelligent manufacturing, intelligent equipment and intelligent factories and are important carriers and means for realizing industry 4.0 (Zhang et al. ASensorless Hand Guiding Scheme Based on Model Identification and Control for Industrial Robot [ J ]. IEEE Transactions on Industrial information 2019,15(9): 5204-. As a four-axis serial mechanical arm common in the industry, the SCARA robot is provided with 3 rotating joints and 1 moving joint, can realize the stability of operation in the vertical direction and the flexibility of operation in the horizontal direction, and is very suitable for vertical operation tasks. In recent years, the track tracking control of the SCARA robot has been a hot point of research of scholars at home and abroad (Zhang Fe, etc.. the track tracking control of the SCARA robot is adaptively and iteratively learned [ J ] China mechanical engineering, 2018,29(14): 1724-1729.).
On one hand, the kinetic model of the tandem robot is a strongly coupled, highly nonlinear and multivariable system, and the high-precision trajectory tracking control is difficult to obtain. On the other hand, the difficulty in designing the trajectory tracking controller is further aggravated by the existence of factors such as unmodeled characteristics of the system, joint friction gaps, external interference and unknown loads at the tail end. In addition, the design of the pose reference track of the robot end effector is also important, and the accuracy of the tracking control of the robot track can be directly determined by the quality of the track design.
The sliding mode surface in the sliding mode control is irrelevant to the uncertainty of system parameters and external disturbance, and has the advantage of insensitivity to the change of the system parameters and the external disturbance. However, the conventional sliding mode control is easy to cause a buffeting phenomenon of the system, and the control performance of the system is reduced to a certain extent, so that the control precision of the system is reduced, and the energy dissipation of the system is increased. In addition, the discontinuity of the sliding mode surface can also cause the discontinuity of the tracking control moment of the robot track, which can cause the damage of elements such as a robot motor, a speed reducer, a sensor and the like.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the adverse consequences caused by factors such as the unmodeled characteristic, the joint friction clearance and the unknown load of an industrial robot system, thereby providing an industrial robot trajectory tracking control algorithm, in particular to a nonsingular terminal sliding mode trajectory tracking control algorithm of the industrial robot, which comprises the following steps:
step 1: obtaining a dynamic model of the SCARA four-axis industrial robot by utilizing a Lagrange equation:
Figure BDA0002503706790000011
in the formula, q,
Figure BDA0002503706790000021
And
Figure BDA0002503706790000022
respectively representing joint variable, joint variable speed and joint variable acceleration vector of 4 × 1, M is an inertia matrix of 4 × 1, C is a matrix of Coriolis force and centrifugal force of 4 × 4, tau is joint moment of 4 × 1, and tau isd4 × 1, which contains joint load, external disturbance, friction torque and unmodeled characteristics;
step 2: designing a fast nonsingular terminal sliding mode control law:
Figure BDA0002503706790000023
wherein the slip form surface s and its derivatives
Figure BDA0002503706790000024
Comprises the following steps:
Figure BDA0002503706790000025
Figure BDA0002503706790000026
wherein e is qr-q，
Figure BDA0002503706790000027
The method comprises the following steps that (1) joint variable tracking errors of the SCARA robot in a joint space and first derivatives and second derivatives of the joint variable tracking errors are obtained; q. q.sr、
Figure BDA0002503706790000028
And
Figure BDA0002503706790000029
is a reference joint variable and a first derivative thereof, the second reciprocal, s is a sliding mode surface, β, k1And k is2The control gain matrixes to be adjusted respectively meet the conditions that gamma is more than 1 and less than 2 and p is more than 0 and less than 1.
Figure BDA00025037067900000210
Substitution of saturation function sat for sliding mode controlThe common piecewise function sign can effectively weaken the buffeting phenomenon of the control input.
And step 3: the effectiveness of the control strategy is tested and verified in the Matlab/xPC environment.
Furthermore, due to the existence of nonlinear factors such as joint friction clearance and actuator saturation in the robot system, the Windup problem is easily caused by the designed control law, and the tracking performance of the system when a large signal is input and the stability of the whole system are further affected. Aiming at the problem, the invention uses the Windup technology to inhibit the Windup phenomenon of the system, and simultaneously designs a compensation mechanism to compensate other nonlinear characteristics such as dead zones in the controller. Therefore, the control law of the final design of the robot system in step 2 is as follows:
τ＝τa+Kwsign(τa)
in the formula, τaThe control law is the control moment K after the Anti-Windup technology and the first-order inertial filter 1/(Ts +1)wTo compensate for the gain matrix.
Further, an optimized end effector pose reference track is designed in the step 2, and an optimal joint variable track of the robot is obtained by adopting a cuckoo algorithm;
assuming that the pose matrix of each joint of the SCARA robot is X, the forward kinematic equation can be described as:
X＝f(q)
the derivative with respect to time is obtained by solving the above equation, and the differential kinematic equation of the robot can be obtained as follows:
Figure BDA0002503706790000031
in the formula (I), the compound is shown in the specification,
Figure BDA0002503706790000032
is a velocity matrix of linear velocity combined with angular velocity,
Figure BDA0002503706790000033
is a Jacobian matrix.
The joint variable velocity can be solved inversely according to equation (7), i.e.:
Figure BDA0002503706790000034
in the formula (I), the compound is shown in the specification,
Figure BDA0002503706790000035
is the generalized inverse of the jacobian matrix. The solution of the above equation allows the mode of the joint velocity to take a local minimum.
Furthermore, joint variables are acquired using a closed-loop pseudo-inverse method:
Figure BDA0002503706790000036
the joint variables are thus obtained by integrating the above equations, i.e. by means of the position matrix X of the given path pointsrTo calculate a reference joint variable qr。
Further, for the trajectory planning of the SCARA robot, a cuckoo algorithm is adopted for optimization. Let the current position of the robot end effector be Pc＝(xc,yc,zc) Target position is Pf＝(xf,yf,zf) Then its position error PeComprises the following steps:
Figure BDA0002503706790000037
furthermore, the following constraints are chosen so that the change of each joint variable in the time domain is minimal:
f1＝max{[q(t+1)-q(t)]2}
wherein t is a time step, f1Are constraints.
Therefore, the objective function of SCARA robot trajectory planning is:
F＝αPe+(1-α)f1
wherein α is a weighting factor.
Has the advantages that:
and (3) a rapid continuous nonsingular terminal sliding mode control strategy based on cuckoo algorithm optimization. The method utilizes a cuckoo algorithm optimizing mechanism to plan a reference track of the pose of the robot end effector; the control strategy adopts a continuous nonsingular terminal sliding mode surface to compensate and inhibit the uncertainty and the external disturbance of the system under the support of the Lyapunov stability theory, introduces a fast terminal sliding mode approach law to accelerate the response speed of the system, and compensates other nonlinear factors such as dead zones in the system by combining the Anti-Windup technology. The control method can effectively improve the precision of the track tracking control of the SCARA robot.
Drawings
FIG. 1 is a structural block diagram of a nonsingular terminal sliding mode trajectory tracking control method according to the present invention;
FIG. 2 is a schematic view of the structure of the SCARA robot according to the present invention;
FIG. 3 is a design diagram of an end effector pose reference trajectory based on cuckoo algorithm optimization according to the present invention;
FIG. 4 is a schematic diagram of a test platform constructed to implement the present invention;
FIG. 5 is an iterative graph of the cuckoo algorithm of the present invention;
FIG. 6 is a pose trajectory of an end effector of a SCARA robot optimized by a cuckoo algorithm of the present invention;
FIG. 7 is a graph comparing the response of the robot tracking control (FNTSMC) based on the control method proposed herein with the conventional Sliding Mode Control (SMC) according to the present invention;
FIG. 8 is a graph of the output torque response of the joint of the present invention.
Detailed Description
In order to make the technical means, the original characteristics, the achieved purposes and the effects of the invention easy to understand, the invention is further explained by combining the specific embodiments and the drawings.
The invention provides an industrial robot trajectory tracking control algorithm, in particular to a nonsingular terminal sliding mode trajectory tracking control algorithm adopted by an industrial robot, which comprises the following steps:
step 1: obtaining a dynamic model of the SCARA four-axis industrial robot by utilizing a Lagrange equation:
Figure BDA0002503706790000041
in the formula, q,
Figure BDA0002503706790000042
And
Figure BDA0002503706790000043
respectively representing joint variable, joint variable speed and joint variable acceleration vector of 4 × 1, M is an inertia matrix of 4 × 1, C is a matrix of Coriolis force and centrifugal force of 4 × 4, tau is joint moment of 4 × 1, and tau isdIs 4 × 1, and comprises joint load, external disturbance, friction torque and unmodeled characteristic1And a2Is the link length.
Step 2: designing a fast nonsingular terminal sliding mode control law:
Figure BDA0002503706790000044
wherein the slip form surface s and its derivatives
Figure BDA0002503706790000045
Comprises the following steps:
Figure BDA0002503706790000046
Figure BDA0002503706790000047
wherein e is qr-q，
Figure BDA0002503706790000048
The method comprises the following steps that (1) joint variable tracking errors of the SCARA robot in a joint space and first derivatives and second derivatives of the joint variable tracking errors are obtained; q. q.sr、
Figure BDA0002503706790000051
And
Figure BDA0002503706790000052
is a reference joint variable and a first derivative thereof, the second reciprocal, s is a sliding mode surface, β, k1And k is2The control gain matrixes to be adjusted respectively meet the conditions that gamma is more than 1 and less than 2 and p is more than 0 and less than 1.
Figure BDA0002503706790000053
The common sectional function sign in sliding mode control is replaced by the saturation function sat, so that the buffeting phenomenon of control input can be effectively weakened.
Due to the fact that nonlinear factors such as joint friction clearance and actuator saturation exist in the robot system, the Windup problem of the designed control law is easily caused, and the tracking performance of the system when large signals are input and the stability of the whole system are further influenced. Aiming at the problem, the invention uses the Windup technology to inhibit the Windup phenomenon of the system, and simultaneously designs a compensation mechanism to compensate other nonlinear characteristics such as dead zones in the controller. Therefore, the control law of the final design of the robot system in step 2 is as follows:
τ＝τa+Kwsign(τa)
in the formula, τaThe control law is the control moment K after the Anti-Windup technology and the first-order inertial filter 1/(Ts +1)wTo compensate for the gain matrix.
Assuming that the pose matrix of each joint of the SCARA robot is X, the forward kinematic equation can be described as:
X＝f(q)
the derivative with respect to time is obtained by solving the above equation, and the differential kinematic equation of the robot can be obtained as follows:
Figure BDA0002503706790000054
in the formula (I), the compound is shown in the specification,
Figure BDA0002503706790000055
linear and angular velocitiesThe speed matrix of the combination is then,
Figure BDA0002503706790000056
is a Jacobian matrix.
The joint variable velocity can be solved inversely according to equation (7), i.e.:
Figure BDA0002503706790000057
in the formula (I), the compound is shown in the specification,
Figure BDA0002503706790000058
is the generalized inverse of the jacobian matrix. The solution of the above equation allows the mode of the joint velocity to take a local minimum.
Furthermore, joint variables are acquired using a closed-loop pseudo-inverse method:
Figure BDA0002503706790000059
the joint variables are thus obtained by integrating the above equations, i.e. by means of the position matrix X of the given path pointsrTo calculate a reference joint variable qr。
For the trajectory planning of the SCARA robot, a cuckoo algorithm is adopted for optimization. Let the current position of the robot end effector be Pc＝(xc,yc,zc) Target position is Pf＝(xf,yf,zf) Then its position error PeComprises the following steps:
Figure BDA00025037067900000510
furthermore, the following constraints are chosen so that the change of each joint variable in the time domain is minimal:
f1＝max{[q(t+1)-q(t)]2}
wherein t is a time step, f1Are constraints.
Therefore, the objective function of SCARA robot trajectory planning is:
F＝αPe+(1-α)f1
wherein α is a weighting factor.
And step 3: the effectiveness of the control strategy is tested and verified in the Matlab/xPC environment.
In order to support research and test verification of the method, a robot test platform is built in the section, and comprises a host machine, a target machine, an SCARA robot and a load. As shown in fig. 4, the SCARA robot is a new reach AR4215-SCARA four-axis robot selected, and the robot comprises 4 NIDEC-MX-201 servo motors, 4 RukingSEA3-02NR drivers and 4 encoders; the host machine is provided with a Maltab/Simulink 2019a for operating the designed FNTSMC control law; the target machine is integrated with an NIPCIe-6251 board card for collecting test data. In the test, an unknown load is additionally arranged at the tail end of the SCARA robot, and an initial pose matrix X of the robot is setIAnd end pose matrix XsComprises the following steps:
Figure BDA0002503706790000061
Figure BDA0002503706790000062
then, the initial joint variable and the final joint variable can be obtained by inverse kinematics of the robot. And planning the track of the SCARA robot by using a cuckoo algorithm according to the target function, and solving the position track and the joint angle track in the motion process. The number of iterations of the cuckoo algorithm was 50, the calculation time was 1.6s, and the convergence curve is shown in fig. 5. Fig. 6 shows the pose trajectory of the SCARA robot end effector optimized by the cuckoo algorithm.
Finally, the FNTSMC algorithm as set forth herein is used to track the planned joint angle trajectory. The FNTSMC built on the host machine sends a control instruction to the SCARA robot through the target machine, the joint angular speed of the robot is collected through an encoder on a servo motor, the sampling period is 10kHz, and the joint angular speed and the angular acceleration are calculated through a difference method. Here, it is necessary toIt is noted that the test only analyzes the response of the revolute joint, since the joint variable q is3Is a moving joint and does not take into account its dynamic response. The selected control parameters for FNTSMC are shown in table 1.
TABLE 1 parameters of FNTSMC
Figure BDA0002503706790000071
In order to further verify the performance of the FNTSMC, SMC is selected as a comparison object. The relevant test results are shown in fig. 7. The result shows that the two control algorithms can enable the SCARA robot to obtain a satisfactory track tracking effect, but the FNTSMC can effectively inhibit system buffeting, so that the joint angle response track is flatter. Then, the absolute value of the Maximum Error (ME) and the Root Mean Square Error (RMSE) are used to quantify the steady-state tracking error in the joint space, and the calculation results are shown in table 2.
TABLE 2 evaluation of Steady-State tracking error
Figure BDA0002503706790000072
As can be seen from Table 2, FNTSMC shows higher trace tracking accuracy on ME or RSME than SMC, and is improved by an order of magnitude. With q1For example, FNTSMC has an ME value and an RSME value which are 87.5% and 93.55% higher than SMC, respectively. This fully verifies the superior control performance and interference immunity of the control algorithm presented herein.
Fig. 8 shows the control moments for the three joints.
In this embodiment, the dimension in the step 1 dynamical model is 4, and the generalization to any dimension is feasible.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (5)

1. The track tracking control algorithm of the industrial robot is characterized by adopting a nonsingular terminal sliding mode track tracking control algorithm of the industrial robot, and comprises the following steps:
step 1: obtaining a dynamic model of the SCARA four-axis industrial robot by utilizing a Lagrange equation:
Figure FDA0002503706780000011
in the formula, q,
Figure FDA0002503706780000012
And
Figure FDA0002503706780000013
respectively representing joint variable, joint variable speed and joint variable acceleration vector of 4 × 1, M is an inertia matrix of 4 × 1, C is a matrix of Coriolis force and centrifugal force of 4 × 4, tau is joint moment of 4 × 1, and tau isd4 × 1, which contains joint load, external disturbance, friction torque and unmodeled characteristics;
step 2, designing a fast nonsingular terminal sliding mode control law:
Figure FDA0002503706780000014
wherein the slip form surface s is:
Figure FDA0002503706780000015
slide film surface derivative
Figure FDA0002503706780000016
Is as follows;
Figure FDA0002503706780000017
wherein e is qr-q，
Figure FDA0002503706780000018
The method comprises the following steps that (1) joint variable tracking errors of the SCARA robot in a joint space and first derivatives and second derivatives of the joint variable tracking errors are obtained; q. q.sr、
Figure FDA0002503706780000019
And
Figure FDA00025037067800000110
is the reference joint variable and its first derivative, β, k1And k is2Respectively control gain matrixes to be adjusted, wherein each index coefficient respectively meets the conditions that gamma is more than 1 and less than 2 and p is more than 0 and less than 1;
Figure FDA00025037067800000111
replacing a common piecewise function sign in sliding mode control with a saturation function sat;
and step 3: the effectiveness of the control strategy is tested and verified in the Matlab/xPC environment.
2. The industrial robot trajectory tracking control algorithm of claim 1, wherein-Windup technology is used in step 2 to suppress Windup phenomenon of the robot system, and the control law of the final design of the robot system is as follows:
τ＝τa+Kwsign(τa) (5)
in the formula, τaThe control law is the control moment K after the Anti-Windup technology and the first-order inertial filter 1/(Ts +1)wTo compensate for the gain matrix.
3. The industrial robot trajectory tracking control algorithm according to claim 1 or 2, wherein an optimized end effector pose reference trajectory is further designed in step 2, and an optimal joint variable trajectory of the robot is obtained by adopting a cuckoo algorithm;
assuming that the pose matrix of each joint of the SCARA robot is X, the forward kinematic equation can be described as:
X＝f(q) (6)
the derivative with respect to time is obtained by solving the above equation, and the differential kinematic equation of the robot can be obtained as follows:
Figure FDA0002503706780000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002503706780000022
is a velocity matrix of linear velocity combined with angular velocity,
Figure FDA0002503706780000023
is a Jacobian matrix;
the joint variable velocity can be solved inversely according to equation (7), i.e.:
Figure FDA0002503706780000027
in the formula (I), the compound is shown in the specification,
Figure FDA0002503706780000024
is the generalized inverse of the Jacobian matrix; the solution of the above formula can make the mode of the joint velocity obtain the local minimum value;
furthermore, joint variables are acquired using a closed-loop pseudo-inverse method:
Figure FDA0002503706780000025
the joint variables are thus obtained by integrating the above equations, i.e. by means of the position matrix X of the given path pointsrTo calculate a reference joint variable qr。
4. The industrial robot trajectory tracking control algorithm of claim 3, wherein the cuckoo algorithm optimizes the trajectory of the joint variables by the specific steps of:
let the current position of the robot end effector be Pc＝(xc,yc,zc) Target position is Pf＝(xf,yf,zf) Then its position error PeComprises the following steps:
Figure FDA0002503706780000026
furthermore, the following constraints are chosen so that the change of each joint variable in the time domain is minimal:
f1＝max{[q(t+1)-q(t)]2} (11)
wherein t is a time step, f1Is a constraint condition;
therefore, the objective function of SCARA robot trajectory planning is:
F＝αPe+(1-α)f1(12)
wherein α is a weighting factor.
5. An industrial robot trajectory tracking control algorithm according to claim 1, characterized in that the dimension 4 in the step 1 dynamical model can be generalized to any dimension.
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CN114643584B (en) * 2022-05-17 2022-09-30 中国科学技术大学 Rapid terminal sliding mode synchronous control method for rope traction parallel robot
CN117706910A (en) * 2023-12-27 2024-03-15 哈尔滨工业大学 Robot cluster coverage method and system based on sliding mode control and with different maximum speeds
CN117706910B (en) * 2023-12-27 2024-06-07 哈尔滨工业大学 Robot cluster coverage method and system based on sliding mode control and with different maximum speeds

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Application publication date: 20200918