Finite time robust trajectory tracking control method for wheeled mobile robot

Abstract

The invention discloses a robust trajectory tracking control method for a wheeled mobile robot in finite time, belongs to the technical field of robots, and aims to solve the problems that the wheeled mobile robot is inevitably influenced by model uncertainty and external disturbance in a task execution process due to a complex working environment, and the robot is difficult to track. The design difficulty of a wheeled mobile robot control system is greatly increased due to the factors. The method comprises the following steps: 1, establishing kinematics and dynamics models of a wheeled mobile robot; the invention discloses a wheeled mobile robot finite time robust trajectory tracking control method based on a nonlinear extended state observer, and the method consists of a kinematics controller and a dynamics controller, the kinematics controller can guarantee that the position and attitude tracking error of a wheeled mobile robot is gradually converged to zero, and the kinematics controller can guarantee that the position and attitude tracking error of the wheeled mobile robot is gradually converged to zero. The dynamic controller can ensure that the speed and angular speed tracking errors of the wheeled mobile robot converge to zero within finite time.

Description

Technical Field

[0001] The invention belongs to the technical field of robots, and in particular relates to a finite-time robust trajectory tracking control method for a wheeled mobile robot. Background Art

[0002] Wheeled mobile robots have the advantages of good flexibility, high reliability, strong load capacity, and simple structure. In recent years, they have been widely used in logistics, power grid inspection, disaster relief and other fields. However, the dynamic model of wheeled mobile robots has the characteristics of high nonlinearity, strong coupling, multiple inputs and multiple outputs, and non-holonomic constraints. In addition, due to the complex working environment, wheeled mobile robots are inevitably affected by model uncertainty and external disturbances during the execution of tasks. These factors greatly increase the difficulty of designing the control system of wheeled mobile robots.

[0003] The control method based on extended state observer is widely used in the design of trajectory tracking controller for wheeled mobile robots. The extended state observer is used to estimate and feedforward compensate the lumped uncertainty. The control method based on extended state observer is very robust to model uncertainty and external disturbances. However, the traditional control method based on extended state observer can only achieve asymptotically stable trajectory tracking, which means that the convergence time of the controller is theoretically infinite. The prior art [1] (see: Wang Liling, Dong Liyuan, Ma Dong, Liu Xiuling, Wang Hongrui. Self-disturbance rejection tracking control of wheeled mobile robots under sliding and slipping conditions [J]. Control Theory and Applications, 2020, 37(2): 431-438.) designed a robust control method based on linear extended state observer for the trajectory tracking problem of wheeled mobile robots. This control method can only achieve asymptotically stable trajectory tracking for wheeled mobile robots.

[0004] Therefore, in order to overcome the shortcomings of the existing technology, we propose a finite-time robust trajectory tracking control method for a wheeled mobile robot. Summary of the invention

[0005] The technical problem to be solved by a finite-time robust trajectory tracking control method for a wheeled mobile robot based on a nonlinear extended state observer disclosed in the present invention is to realize high-precision trajectory tracking control of the wheeled mobile robot under the condition of considering model uncertainty and external disturbance;

[0006] It has the following advantages:

[0007] (1) The control method consists of two parts: a kinematic controller and a dynamic controller. The kinematic controller can ensure that the position and posture tracking errors of the wheeled mobile robot converge to zero asymptotically, and the dynamic controller can ensure that the speed and angular velocity tracking errors of the wheeled mobile robot converge to zero within a finite time.

[0008] (2) In the design process of the dynamic controller, a nonlinear extended state observer is used to estimate the lumped uncertainties including model uncertainty and external disturbances. The nonlinear extended state observer can accurately estimate the lumped uncertainties within a finite time.

[0009] (3) Thanks to the use of the nonlinear extended state observer, the controller is highly robust to model uncertainties and external disturbances.

[0010] To achieve the above object, the present invention provides the following technical solution: a finite-time robust trajectory tracking control method for a wheeled mobile robot, comprising the following steps:

[0011] Step 1: Establish the kinematic and dynamic models of the mobile robot.

[0012] The structure of a wheeled mobile robot is as follows Figure 1 As shown, its front wheels are auxiliary wheels, and the two rear wheels are driving wheels, and the driving wheel radius is r. Assuming that the center of mass of the wheeled mobile robot coincides with the geometric center, an inertial coordinate system O is established. r X r Y r and the body coordinate system O b X b Y b Describe the planar motion of a wheeled mobile robot. The mass and moment of inertia of the wheeled mobile robot are m and I respectively, and the distance between the driving wheel and the geometric center is l. Ignoring slip and sideslip, the kinematic equation of the wheeled mobile robot is:

[0013]

[0014] Where q = [x, y, θ] T is the position and posture of the wheeled mobile robot, ζ=[v,ω] T is the speed and angular velocity of the wheeled mobile robot, J(q)∈ 3×2 is the velocity conversion matrix, and the nonholonomic constraints of the wheeled mobile robot can be described as The dynamic equation of the wheeled mobile robot is:

[0015]

[0016] Where M(q)∈ 3×3 is the inertia matrix, is the centripetal force and Coriolis force matrix, G(q)∈ 3 is the gravity vector, B(q)∈ 3×2 is the input transformation matrix, τ∈ 2 is the control torque, d∈ 3 is the external disturbance, A T (q)∈3 is the nonholonomic constraint vector, λ is the Lagrange multiplier, and their specific expressions are

[0017]

[0018] Model uncertainty is considered as M(q)=M 0 (q)+M Δ (q), where M 0 (q) and M Δ (q) represent the nominal part and the uncertain part respectively. By taking the derivative of (1) with respect to time, we can get

[0019]

[0020] Substituting equation (3) into equation (2) and applying the relation J T (q)A T (q) = 0 2 Can get

[0021]

[0022] In the formula, represents the lumped uncertainty.

[0023] Step 2: Design a kinematic controller based on the kinematic model of the wheeled mobile robot.

[0024] First, a kinematic controller is designed so that the position and posture of the wheeled mobile robot can track the desired position and posture. The desired trajectory of the wheeled mobile robot is given as

[0025]

[0026] Define the position and attitude tracking error of a wheeled mobile robot:

[0027]

[0028] Then the kinematic error equation of the wheeled mobile robot can be expressed as

[0029]

[0030] The kinematic controller of the wheeled mobile robot is designed as

[0031]

[0032] In the formula, h 1 >0,h 2 >0,h 3 >0, v c and ω c are the virtual speed and angular velocity.

[0033] Considering the wheeled mobile robot system described by equations (1) and (2), under the action of the kinematic controller, the position and posture tracking errors of the wheeled mobile robot can converge to zero asymptotically.

[0034] Step 3: Design a dynamic controller based on the dynamic model of the wheeled mobile robot.

[0035] Then, a dynamic controller is designed to enable the speed and angular velocity of the wheeled mobile robot to track the virtual speed and angular velocity. Define the state variable x 1 =ζ,x 2 =δ. The dynamic model (4) of the wheeled mobile robot can be expressed in the form of the following state space:

[0036]

[0037] The nonlinear extended state observer is designed as

[0038]

[0039] In the formula, l 1 >0,l 2 >0,l 3 >0,l 3 >0, and For x 1 and x 2 The estimated value of .

[0040] For the differential wheeled robot system, a nonlinear extended state observer (10) is used to accurately estimate the lumped uncertainty term δ within a finite time.

[0041] Define the velocity and angular velocity tracking error of a wheeled mobile robot:

[0042]

[0043] Then the dynamic error equation of the wheeled mobile robot can be expressed as

[0044]

[0045] The dynamic controller of the wheeled mobile robot is designed as

[0046]

[0047] In the formula, 0<α<1, k>0, for a given vector x∈ n and scalar p∈, symbol sig p (·) is defined as sig p (x) = [sigp (x 1 ),sig p (x 2 ),…,sig p (x n )] T , where sig p (x i )=|x i | p sgn(x i ).

[0048] Considering the wheeled mobile robot system described by equations (1) and (2), under the action of the dynamic controller (13), the position and posture tracking errors of the wheeled mobile robot can converge to zero in a finite time.

[0049] Compared with the prior art, the finite-time robust trajectory tracking control method for a wheeled mobile robot provided by the present invention has at least the following beneficial effects:

[0050] 1. The present invention discloses a finite-time robust trajectory tracking control method for a wheeled mobile robot based on a nonlinear extended state observer, which consists of two parts: a kinematic controller and a dynamic controller. The kinematic controller can ensure that the position and posture tracking errors of the wheeled mobile robot converge to zero asymptotically, and the dynamic controller can ensure that the speed and angular velocity tracking errors of the wheeled mobile robot converge to zero within a finite time.

[0051] 2. The present invention discloses a finite-time robust trajectory tracking control method for a wheeled mobile robot based on a nonlinear extended state observer. During the design process of the dynamic controller, a nonlinear extended state observer is used to estimate the lumped uncertainties including model uncertainties and external disturbances. The nonlinear extended state observer can accurately estimate the lumped uncertainties within a finite time.

[0052] 3. The present invention discloses a finite-time robust trajectory tracking control method for a wheeled mobile robot based on a nonlinear extended state observer. Thanks to the use of the nonlinear extended state observer, the controller has strong robustness to model uncertainty and external disturbances.

[0053] 4. The present invention discloses a finite-time robust trajectory tracking control method for a wheeled mobile robot based on a nonlinear extended state observer. The controller has a simple structure, good tracking performance, and strong robustness. The method is suitable for tasks such as logistics transportation, power grid inspection, and disaster relief, and has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a schematic structural diagram of a wheeled mobile robot in an embodiment of the present invention;

[0055] Figure 2 It is a control block diagram of a finite-time robust trajectory tracking control method for a wheeled mobile robot based on a nonlinear extended state observer disclosed by the present invention in an embodiment of the present invention;

[0056] Figure 3 is a schematic diagram of simulation results of planar trajectory tracking of a wheeled mobile robot in an embodiment of the present invention;

[0057] Figure 4 is a schematic diagram of simulation results of x-direction position tracking of a wheeled mobile robot in an embodiment of the present invention;

[0058] Figure 5 is a schematic diagram of simulation results of the y-direction position tracking of the wheeled mobile robot in an embodiment of the present invention;

[0059] Figure 6 is a schematic diagram of simulation results of posture tracking of a wheeled mobile robot in an embodiment of the present invention;

[0060] Figure 7 is a schematic diagram of simulation results of the control torque of the wheeled mobile robot in an embodiment of the present invention;

[0061] Figure 8 It is a schematic diagram of simulation results of lumped uncertainty observation by a nonlinear extended state observer in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The following is a detailed description of a wheeled mobile robot finite time robust trajectory tracking control method provided by the present invention in conjunction with the accompanying drawings and specific embodiments. At the same time, it is explained here that in order to make the embodiments more detailed, the following embodiments are the best and preferred embodiments, and those skilled in the art may also adopt other alternatives to implement some known technologies; and the accompanying drawings are only for a more specific description of the embodiments, and are not intended to specifically limit the present invention.

[0063] It should be noted that the references to "one embodiment", "an embodiment", "an exemplary embodiment", "some embodiments" and the like in the specification indicate that the embodiments described may include specific features, structures or characteristics, but not every embodiment may include the specific features, structures or characteristics. In addition, when a specific feature, structure or characteristic is described in conjunction with an embodiment, it should be within the knowledge of a person skilled in the art to implement such feature, structure or characteristic in conjunction with other embodiments (whether or not explicitly described).

[0064] In general, a term can be understood, at least in part, from its use in context. For example, depending, at least in part, on the context, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in the singular sense, or can be used to describe a combination of features, structures, or characteristics in the plural sense. Additionally, the term "based on" can be understood as not necessarily intended to convey an exclusive set of factors, but can instead, depending, at least in part, on the context, allow for the presence of other factors that are not necessarily explicitly described.

[0065] It will be understood that the meanings of “on,” “over,” and “above” in the present invention should be interpreted in the broadest manner, so that “on” not only means “directly on” something, but also includes the meaning of being “on” something with intervening features or layers therebetween, and “on” or “over” not only means “on” or “above” something, but also includes the meaning of being “on” or “above” something with no intervening features or layers therebetween.

[0066] In addition, spatially relative terms such as "under," "beneath," "lower," "above," "upper," etc. may be used herein for descriptive convenience to describe the relationship of one element or feature to another element or features, as shown in the accompanying drawings. The spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the accompanying drawings. The device may be oriented in other ways, and the spatially relative descriptors used herein may be similarly interpreted accordingly.

[0067] The following examples are used to illustrate the present invention, but they cannot be used to limit the scope of protection of the present invention. The conditions in the examples can be further adjusted according to specific conditions. Simple improvements to the method of the present invention under the premise of the concept of the present invention belong to the scope of protection claimed in the present invention.

[0068] See also Figure 1-8 The present invention provides a finite-time robust trajectory tracking control method for a wheeled mobile robot. The present embodiment discloses an event-triggered adaptive trajectory tracking control method for a wheeled mobile robot, comprising the following steps:

[0069] Step 1: Establish the kinematic and dynamic models of the mobile robot.

[0070] The structure of a wheeled mobile robot is as follows Figure 1 As shown in the figure, the front wheel is an auxiliary wheel, the two rear wheels are driving wheels, and the driving wheel radius is r = 0.05m. Assuming that the center of mass of the wheeled mobile robot coincides with the geometric center, the inertial coordinate system O is established. r X r Y r and the body coordinate system Ob X b Y b Describe the planar motion of a wheeled mobile robot. The mass and moment of inertia of the wheeled mobile robot are m = 3kg and I = 2kgm respectively. 2 , the distance between the driving wheel and the geometric center is l = 0.15m, and skidding and side slipping are not considered. The kinematic equation of the wheeled mobile robot is:

[0071]

[0072] Where q = [x, y, θ] T is the position and posture of the wheeled mobile robot, ζ=[v,ω] T is the speed and angular velocity of the wheeled mobile robot, J(q)∈ 3×2 is the velocity conversion matrix, and the nonholonomic constraints of the wheeled mobile robot can be described as The dynamic equation of the wheeled mobile robot is:

[0073]

[0074] Where M(q)∈ 3×3 is the inertia matrix, is the centripetal force and Coriolis force matrix, G(q)∈ 3 is the gravity vector, B(q)∈ 3×2 is the input transformation matrix, τ∈ 2 is the control torque, d = [0.4sin(0.6t), 0.3sin(0.4t), 0.1sin(0.5t)] T is the external disturbance, A T (q)∈ 3 is the nonholonomic constraint vector, λ is the Lagrange multiplier, and their specific expressions are G(q)=0 3 ,

[0075] Model uncertainty is considered as M(q)=M 0 (q)+M Δ (q), where M 0 (q) = 0.95M(q) and M Δ (q) = 0.05M(q) represents the nominal part and the uncertain part respectively. By taking the derivative of equation (1) with respect to time, we can get

[0076]

[0077] Substituting equation (3) into equation (2) and applying the relation J T (q)A T (q) = 0 2Can get

[0078]

[0079] In the formula, H = (J T (q)M 0 (q)J(q)) -1 J T (q)B(q), represents the lumped uncertainty.

[0080] Step 2: Design a kinematic controller based on the kinematic model of the wheeled mobile robot.

[0081] First, a kinematic controller is designed so that the position and posture of the wheeled mobile robot can track the desired position and posture. The desired trajectory of the wheeled mobile robot is given as x r = sin(t)m,y r = -cos(t)m,θ r =trad,v r =1m / s,ω r =1rad / s, satisfying the relationship:

[0082]

[0083] Define the position and attitude tracking error of a wheeled mobile robot:

[0084]

[0085] Then the kinematic error equation of the wheeled mobile robot can be expressed as

[0086]

[0087] The kinematic controller of the wheeled mobile robot is designed as

[0088]

[0089] In the formula, h 1 =10,h 2 =10,h 3 =10, v c and ω c are the virtual speed and angular velocity.

[0090] Considering the wheeled mobile robot system described by equations (1) and (2), under the action of the kinematic controller (8), the position and posture tracking errors of the wheeled mobile robot can converge to zero asymptotically.

[0091] Step 3: Design a dynamic controller based on the dynamic model of the wheeled mobile robot.

[0092] Then, a dynamic controller is designed to enable the speed and angular velocity of the wheeled mobile robot to track the virtual speed and angular velocity. Define the state variable x 1 =ζ,x 2 =δ. The dynamic model (4) of the wheeled mobile robot can be expressed in the form of the following state space:

[0093]

[0094] The nonlinear extended state observer is designed as

[0095]

[0096] In the formula, l 1 =2, l 2 =1,l 3 =1,l 3 =10, and For x 1 and x 2 The estimated value of .

[0097] For the differential wheeled robot system, a nonlinear extended state observer (10) is used to accurately estimate the lumped uncertainty term δ within a finite time.

[0098] Define the velocity and angular velocity tracking error of a wheeled mobile robot:

[0099]

[0100] Then the dynamic error equation of the wheeled mobile robot can be expressed as

[0101]

[0102] The dynamic controller of the wheeled mobile robot is designed as

[0103]

[0104] In the formula, α = 99 / 101, k = 20, for a given vector x∈ n and scalar p∈, symbol sig p (·) is defined as sig p (x) = [sig p (x 1 ),sig p (x 2 ),…,sig p (x n )] T , where sig p (x i )=|xi | p sgn(x i ).

[0105] Considering the wheeled mobile robot system described by equations (1) and (2), under the action of the dynamic controller (13), the position and posture tracking errors of the wheeled mobile robot can converge to zero in a finite time. According to the above steps, refer to Figure 2 , a control block diagram of a finite-time robust trajectory tracking control method for a wheeled mobile robot based on a nonlinear extended state observer is given.

[0106] The simulation results of the designed finite-time robust trajectory tracking control method for wheeled mobile robots based on nonlinear extended state observer are shown in Figures 3 to 8 As shown in the figure, set the total simulation time to 20s and the sampling time interval to 0.01s.

[0107] Figure 3 The simulation results of the planar trajectory tracking of a wheeled mobile robot are given. Figure 3 It can be seen that, considering the model uncertainty and external disturbances, the proposed finite-time controller can well track the desired circular trajectory.

[0108] Figure 4 and Figure 5 The schematic diagram of the simulation results of the wheeled mobile robot position tracking is given. Figure 6 A schematic diagram of the simulation results of the wheeled mobile robot posture tracking is given.

[0109] from Figures 4 to 6 It can be seen that the proposed finite-time controller can ensure that the position and posture tracking errors of the wheeled mobile robot converge to zero, and it is highly robust to model uncertainty and external disturbances.

[0110] Figure 7 The simulation results of the control torque of the wheeled mobile robot are given. During the entire trajectory tracking process, the control torque amplitude is always kept within the engineering allowable range.

[0111] Figure 8 The simulation results of the nonlinear extended state observer for observing lumped uncertainties are given. Figure 8 It can be seen that the proposed nonlinear extended state observer can accurately estimate the lumped uncertainties including model uncertainty and external disturbances within a finite time.

[0112] The designed controller has a simple structure, good tracking performance and strong robustness. It is suitable for tasks such as logistics transportation, power grid inspection, emergency rescue and disaster relief, and has a wide range of applications.

[0113] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons with ordinary skills in the field to which the present invention belongs. The words "including" or "comprising" and the like used in the present invention mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, but do not exclude other elements or objects. The words "connect" or "connected" and the like are not limited to physical or mechanical connections, but may also include electrical connections, whether direct or indirect. "Up", "down", "left", "right", etc. are only used to indicate relative position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0114] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A finite-time robust trajectory tracking control method for a wheeled mobile robot, characterized in that: The following steps are involved: Step 1: Establish the kinematic and dynamic model of the wheeled mobile robot; Step 2: Design a kinematic controller based on the kinematic model of the wheeled mobile robot; Step 3: Design a dynamic controller based on the dynamic model of the wheeled mobile robot.

2. The finite-time robust trajectory tracking control method for a wheeled mobile robot according to claim 1, characterized in that: In step 1, the front wheels of the wheeled mobile robot are auxiliary wheels, the two rear wheels are driving wheels, and the radius of the driving wheel is r. Assuming that the center of mass of the wheeled mobile robot coincides with the geometric center, an inertial coordinate system O is established. r X r Y r and the body coordinate system O b X b Y b Describing the planar motion of a wheeled mobile robot, the mass and moment of inertia of the wheeled mobile robot are m and I respectively, the distance between the driving wheel and the geometric center is l, and skidding and side slipping are not considered. The kinematic equation of the wheeled mobile robot is: Where q = [x, y, θ] T is the position and posture of the wheeled mobile robot, ζ=[v,ω] T is the speed and angular velocity of the wheeled mobile robot, J(q)∈ 3×2 is the velocity conversion matrix, and the nonholonomic constraints of the wheeled mobile robot can be described as 3. The finite-time robust trajectory tracking control method for a wheeled mobile robot according to claim 2, characterized in that: The dynamic equation of the wheeled mobile robot is: Where M(q)∈ 3×3 is the inertia matrix, is the centripetal force and Coriolis force matrix, G(q)∈ 3 is the gravity vector, B(q)∈ 3×2 is the input transformation matrix, τ∈ 2 is the control torque, d∈ 3 is the external disturbance, A T (q)∈ 3 is the nonholonomic constraint vector, λ is the Lagrange multiplier, and their specific expressions are 4. The finite-time robust trajectory tracking control method for a wheeled mobile robot according to claim 3, characterized in that: The model uncertainty is considered as M(q)=M0(q)+M Δ (q), where M0(q) and M Δ (q) represent the nominal part and the uncertain part respectively. By taking the derivative of (1) with respect to time, we can get Substituting equation (3) into equation (2) and applying the relation J T (q)A T (q)=02, we can get In the formula, H = (J T (q)M0(q)J(q)) -1 J T (q)B(q), represents the lumped uncertainty.

5. The finite-time robust trajectory tracking control method for a wheeled mobile robot according to claim 1, characterized in that: In step 2, a kinematic controller is designed so that the position and posture of the wheeled mobile robot can track the desired position and posture. The desired trajectory of the wheeled mobile robot is given as Define the position and attitude tracking error of a wheeled mobile robot: Then the kinematic error equation of the wheeled mobile robot can be expressed as 6. The finite-time robust trajectory tracking control method for a wheeled mobile robot according to claim 5, characterized in that: The kinematic controller of the wheeled mobile robot is designed as In the formula, h1>0, h2>0, h3>0, v c and ω c are the virtual speed and angular velocity.

7. The finite-time robust trajectory tracking control method for a wheeled mobile robot according to claim 1, characterized in that: In step 3, a dynamic controller is designed to enable the speed and angular velocity of the wheeled mobile robot to track the virtual speed and angular velocity, and the state variables x1 = ζ, x2 = δ are defined. The dynamic model (4) of the wheeled mobile robot can be expressed in the form of the following state space: The nonlinear extended state observer is designed as In the formula, l1>0, l2>0, l3>0, l3>0, and are the estimated values ​​of x1 and x2.

8. The finite-time robust trajectory tracking control method for a wheeled mobile robot according to claim 7, characterized in that: For the differential wheeled robot system, a nonlinear extended state observer (10) is used to accurately estimate the lumped uncertainty term δ within a finite time. Define the velocity and angular velocity tracking error of a wheeled mobile robot: Then the dynamic error equation of the wheeled mobile robot can be expressed as The dynamic controller of the wheeled mobile robot is designed as In the formula, 0<α<1, k>0, for a given vector x∈ n and scalar p∈, symbol sig p (·) is defined as sig p (x) = [sig p (x1),sig p (x2),…,sig p (x n )] T , where sig p (x i )=|x i | p sgn(x i ).

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