Constraint-following based control method for underactuated two-wheel mobile robot

Abstract

The application discloses a control method of an under-actuated two-wheel mobile robot based on constraint following, and the method comprises the following steps: a dynamics model of the under-actuated two-wheel mobile robot is established based on a Lagrange modeling method; a motion control problem of the under-actuated two-wheel mobile robot is expressed as a constraint following control problem, a constraint mathematical model is established according to expected control performance, and the constraint mathematical model is expressed in the form of servo constraint; the servo constraint is analyzed, a first-order or second-order servo constraint is obtained, and a controller not considering initial constraint deviation is designed; based on the controller not considering initial constraint deviation, an additional control action is added to process possible initial constraint deviation, a robust controller is designed, and a robust control strategy is constituted; and the complete constraint and non-complete constraint control design is constituted by taking the constraint following as a guide. The application can solve the under-actuated control design problem of the two-wheel mobile robot, the control design does not need auxiliary variables or pseudo variables, and the control efficiency and control precision are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of mechanical system dynamics and robot control technology, in particular to a control method for an underactuated two-wheel mobile robot based on constraint following. BACKGROUND

[0002] In recent years, the research on two-wheel mobile robots, especially the research on its motion control, has been widely concerned by the academic and industrial circles at home and abroad. This is mainly due to its ability to simulate a class of modern vehicles that can safely and efficiently transport personnel or cargo, and demonstrate various control strategies. From the perspective of motion control design, a significant feature of two-wheel mobile robots is that it is usually underactuated. That is, its control input is less than the degrees of freedom to be controlled. This poses a difficult problem that researchers often encounter, namely the control design of underactuated mechanical systems.

[0003] Based on the above, the present inventors have found that the control design problem of underactuated systems still needs new development and more insights. Therefore, a new constraint following is introduced to develop a control method for the underactuation problem of two-wheel mobile robots. Compared with previous constraint-following control research, the constraint is considered in a more general form, requiring wider applicability and more accurate control accuracy. Therefore, in view of the above, the existing structure is studied and improved, and a control method for an underactuated two-wheel mobile robot based on constraint following is provided, in order to achieve a more practical purpose. SUMMARY

[0004] To solve the above technical problems, the present application provides the following technical solutions:

[0005] The control method for an underactuated two-wheel mobile robot based on constraint following of the present application comprises the following steps:

[0006] Step 1: based on the Lagrange modeling method, a dynamic model of the underactuated two-wheel mobile robot is established;

[0007] Step 2: the motion control problem of the underactuated two-wheel mobile robot in step 1 is expressed as a constraint-following control problem, a constraint mathematical model is established according to the desired control performance, and is expressed in the form of servo constraint;

[0008] Step 3: the servo constraint in step 2 is analyzed to obtain a first-order or second-order servo constraint, and a controller that does not consider the initial constraint deviation is designed;

[0009] Step 4: based on the controller without initial constraint deviation, an additional control action is added to handle possible initial constraint deviation, a robust controller is designed, and a robust control strategy is constituted;

[0010] Step 5, guided by constraint following, build complete constraint and non-complete constraint control design to control the underactuated two-wheel mobile robot.

[0011] As a preferred technical solution of the present application, in step 1, the underactuated two-wheel mobile robot dynamics model is established based on the Lagrange modeling method, specifically:

[0012]

[0013] Wherein, t∈R is time, q∈Rn is position vector, ∈Rn is velocity vector,

[0014] ∈Rn is acceleration vector, τ∈Rm is control input vector when m≤n, in addition, Indicates the inertia matrix, Indicates the Coriolis / centrifugal term matrix, Indicates gravity, Indicates the input matrix, functions M(·), C(·), g(·), B(·) are continuous.

[0015] As a preferred technical solution of the present application, in step 2, the underactuated two-wheel mobile robot motion control problem is described as a constraint following control problem, a constraint mathematical model is established according to the desired control performance, and is expressed in the form of servo constraint, specifically:

[0016] Define the mathematical model of first-order servo constraint:

[0017]

[0018] Wherein:

[0019] l=1,…,m, is the i-th component of , and are ;

[0020] Rewrite the first-order form of servo constraint as:

[0021]

[0022] Thus, the constraint matrix is obtained:

[0023]

[0024] Wherein, ;

[0025] Derivation is obtained Mathematical model of second-order servo constraint:

[0026]

[0027] The second-order form of the servo constraint is rewritten as:

[0028]

[0029] Thus, the constraint matrix is obtained:

[0030]

[0031] wherein, , .

[0032] As a preferred technical solution of the present application, the servo constraint in step 3 is analyzed to obtain a first-order or second-order servo constraint, and a controller not considering initial constraint deviation is designed, and the specific method is as follows:

[0033] Let , the system dynamics model can be rewritten as:

[0034]

[0035] The mathematical model of the first-order servo constraint can be rewritten as:

[0036]

[0037] wherein, ;

[0038] Let , the following is obtained:

[0039]

[0040] The servo control is:

[0041]

[0042] wherein, S∈ is an arbitrary vector, which can depend on , and .

[0043] As a preferred technical solution of the present application, in step 4, based on the controller without initial constraint deviation, an additional control action is added to handle possible initial constraint deviation, a robust controller is constructed, and an underactuated two-wheel mobile robot is controlled, and the specific method is as follows:

[0044] Based on the step 3, the initial constraint deviation controller, considering that the initial condition in practice is likely to not satisfy the constraint, an additional control action is added to deal with the initial constraint deviation, set , , The following control is proposed to deal with the possible initial condition deviation:

[0045]

[0046] where, is a constant;

[0047] The robust controller of the system is constructed as:

[0048] .

[0049] As a preferred technical solution of the present application, the step 5 is guided by constraint following, and a complete constraint and non-complete constraint control design is constructed to control the under-actuated two-wheel mobile robot, and the specific method is:

[0050] (I) Complete constraint

[0051] The complete constraint is selected as:

[0052]

[0053]

[0054] where, is a constant, which limits the constraint to move the wheels forward while keeping the pendulum approximately upright;

[0055] (II) Non-complete constraint

[0056] The non-complete constraint is selected as:

[0057]

[0058]

[0059] where, is a constant, which limits the constraint to make the moving direction of the wheels consistent with the tilting direction of the inverted pendulum, The definition domain of , for any , .

[0060] As a preferred technical scheme of the present application, the underactuated two-wheel mobile robot is provided with a computer device, which comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor performs the computer program to perform the underactuated two-wheel mobile robot control based on constraint following.

[0061] As a preferred technical scheme of the present application, the computer device comprises a computer readable storage medium, which stores a computer program, and the computer program is executed by the processor to perform the underactuated two-wheel mobile robot control based on constraint following.

[0062] The present application has the following beneficial effects:

[0063] The underactuated two-wheel mobile robot control method based on constraint following adds constraints in the underactuated two-wheel mobile robot control problem, so that the designed controller is more in line with the actual robot requirements.

[0064] The underactuated two-wheel mobile robot control method based on constraint following uses the constraint following method to control the motion of the underactuated two-wheel mobile robot, converts the expected motion characteristics into servo constraints, although the system is constrained, the control design does not need auxiliary variables (such as Lagrange multipliers) or pseudo variables (such as generalized velocities), and the complete constraint and incomplete constraint conditions are designed to control the motion of the underactuated two-wheel mobile robot, without the need to redesign the controller, having strong flexibility and high efficiency, and high practical value. BRIEF DESCRIPTION OF DRAWINGS

[0065] The accompanying drawings are included to provide a further understanding of the present application, and constitute a part of the specification, which together with the embodiments of the present application, serve to explain the present application, and do not constitute a limitation of the present application. In the drawings:

[0066] Figure 1 is a flowchart of the underactuated two-wheel mobile robot control method based on constraint following of the present application;

[0067] Figure 2 is a system performance effect comparison chart of the underactuated two-wheel mobile robot control method based on constraint following of the present application with or without complete constraints;

[0068] Figure 3 is a system angle effect comparison chart of the underactuated two-wheel mobile robot control method based on constraint following of the present application with or without complete constraints;

[0069] Figure 4 is a system performance effect comparison chart of the underactuated two-wheel mobile robot control method based on constraint following of the present application with three groups of constraint parameters in incomplete constraints;

[0070] Figure 5 is a system angle effect comparison chart of three constraint parameters of the invention based on constraint following underactuated two-wheel mobile robot control method at nonholonomic constraint. DETAILED DESCRIPTION

[0071] The preferred embodiments of the present application are described below in conjunction with the accompanying drawings, it should be understood that the preferred embodiments described herein are only used to illustrate and explain the present application, and are not used to limit the present application.

[0072] Embodiment: as shown in the figure, the invention based on constraint following underactuated two-wheel mobile robot control method, including for verifying the effectiveness of the invention scheme, the following two-wheel mobile robot underactuated problem is robust constraint control, control object and target are respectively: Figures 1-5 The control object is an underactuated two-wheel mobile robot, and the mechanical system is:

[0073]

[0074] Wherein, t∈R is time, q∈Rn is position vector, ∈Rn is velocity vector, ∈Rn is acceleration vector, τ∈Rm is control input vector when m≤n.

[0075] The system is written as the Lagrange dynamics model established in step 1:

[0076]

[0077]

[0078]

[0079]

[0080] Control target: make the number of constraints required by the underactuated two-wheel mobile robot equal to the number of control inputs.

[0081] The invention proposes an underactuated two-wheel mobile robot control method based on constraint following, including the following steps:

[0082] Step 1: based on Lagrange modeling method, establish the dynamics model of underactuated two-wheel mobile robot.

[0083] Step 2: express the motion control problem of underactuated two-wheel mobile robot as a constraint following control problem, establish a constraint mathematical model according to the expected control performance, and express it in the form of servo constraint;

[0084] ​Based on the dynamics model of under-actuated two-wheeled mobile robot, the expected motion characteristics of the system are analyzed, which provides the standard form for the following calculation steps, and the characteristics are mathematically abstracted, and the first-order servo constraint that the system needs to follow is assumed as:

[0085]

[0086] Wherein: l=1,…,m, is the i-th component of , and are the i-th component of ;

[0087] The first-order form of the servo constraint is rewritten as:

[0088]

[0089] Thus, the constraint matrix is obtained:

[0090]

[0091] Wherein, ;

[0092] The derivative is obtained, and the mathematical model of the second-order servo constraint is:

[0093]

[0094] The second-order form of the servo constraint is rewritten as:

[0095]

[0096] Thus, the constraint matrix is obtained:

[0097]

[0098] Wherein, , .

[0099] Step 3: Analyze the servo constraint to obtain the first-order or second-order servo constraint, and design a controller that does not consider the initial constraint deviation:

[0100] Let , then the dynamics model of the system can be rewritten as:

[0101]

[0102] The mathematical model of the first-order servo constraint can be rewritten as:

[0103]

[0104] Wherein, ;

[0105] Let ,

[0106]

[0107] Then the servo control is:

[0108]

[0109] where S∈ is an arbitrary vector, possibly dependent on , and .

[0110] Step 4: Based on the initial constraint bias-free controller, an additional control action is added to handle the possible initial constraint bias, and a robust controller is constructed to control the underactuated two-wheel mobile robot:

[0111] Based on the initial constraint bias-free controller in Step 3, considering that the initial condition may not satisfy the constraint in practice, an additional control action is added to handle the initial constraint bias. Let , , ;

[0112] The following control is proposed to handle the possible initial condition bias:

[0113]

[0114] where is a constant;

[0115] The robust controller of the system is constructed as:

[0116]

[0117] Step 5: Guided by constraint following, construct complete constraint and non-complete constraint control design to control the underactuated two-wheel mobile robot:

[0118] (I) Complete constraint

[0119] The complete constraint is chosen as:

[0120]

[0121]

[0122] where is a constant, limiting this constraint to move the wheels forward while keeping the pendulum approximately upright;

[0123] (2) Non-holonomic constraints

[0124] Select the nonholonomic constraints as:

[0125]

[0126]

[0127] in, is a constant, and this constraint is applied so that the direction of movement of the wheel will be consistent with the tilt direction of the inverted pendulum. The domain of , for any , .

[0128] Step 6: Use Matlab to simulate and compare the control effect with that without adding constraints and standard LQR (linear quadratic regulator). The simulation results are as follows: Figure 2 , 3, 4, and 5.

[0129] Figure 2 (a) (b) and Figure 3 (a) (b) show the system performance and system angle effects of the standard LQR control, unconstrained control and complete constrained control methods, respectively. It can be seen that after adding the complete constraint, As time increases, it gradually converges to zero, and the wheels of the underactuated two-wheeled mobile robot move forward while keeping the pendulum approximately upright. Figure 4 and Figure 5 It shows the system performance effect and system angle effect of applying nonholonomic constraint control under three sets of constraint parameters. It can be seen that after adding nonholonomic constraints, As time goes by, the value gradually converges to zero, and the direction of motion of the wheels of the underactuated two-wheeled mobile robot aligns with the tilt direction of the pendulum. The robust control method for an underactuated two-wheeled mobile robot proposed in this invention enables the underactuated two-wheeled mobile robot to exhibit desired motion characteristics in a very short time. The system exhibits stable performance and high control accuracy. Therefore, this invention can quickly and effectively solve the underactuated control problem of two-wheeled mobile robots.

[0130] Finally, it should be noted that in the description of the present invention, it should be noted that the terms "vertical", "up", "down", "horizontal", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, they cannot be understood as limiting the present invention.

[0131] In the description of the application, it also needs to be explained that, unless otherwise explicitly specified and limited, the terms "set", "install", "connect", "connect" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, or it can be connected inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0132] The above is only the preferred embodiment of the present application, and is not used to limit the present application, although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A control method for an underactuated two-wheeled mobile robot based on constraint following, characterized in that: The following steps are involved: Step 1: Based on the Lagrangian modeling method, a dynamic model of the underactuated two-wheeled mobile robot is established; Step 2: Formulate the motion control problem of the underactuated two-wheeled mobile robot in step 1 as a constrained following control problem, establish a constraint mathematical model based on the expected control performance, and express it in the form of servo constraints; Step 3: Analyze the servo constraints in step 2, obtain the first / second order servo constraints, and design a controller that does not consider the initial constraint deviation; Step 4: Based on the controller without initial constraint deviation, an additional control action is added to handle possible initial constraint deviations, and a robust controller is designed to form a robust control strategy. Step 5: Guided by constraint following, construct a complete constraint and non-complete constraint control design to control the underactuated two-wheeled mobile robot; In step 3, the servo constraints are analyzed to obtain the first / second order servo constraints, and a controller that does not consider the initial constraint deviation is designed. The specific method is as follows: set up , then the system dynamics model can be rewritten as: ； The mathematical model of the first-order servo constraint can be rewritten as: ； in, ; set up , we get the following: ； Servo control for: ； Among them, S∈ is an arbitrary vector that may depend on 、 and ,in represents the inertia matrix, represents the Coriolis / centrifugal term matrix, represents gravity, Represents the input matrix, and the functions M(·), C(·), g(·), and B(·) are continuous.

2. The control method of an underactuated two-wheeled mobile robot based on constraint following according to claim 1, characterized in that: In step 1, a dynamic model of an underactuated two-wheeled mobile robot is established based on the Lagrangian modeling method, specifically: ； Among them, t∈R is the time, q∈Rn is the position vector, ∈Rn is the velocity vector, ∈Rn is the acceleration vector, τ∈Rm is the control input vector when m≤n, and represents the inertia matrix, represents the Coriolis / centrifugal term matrix, represents gravity, Represents the input matrix, and the functions M(·), C(·), g(·), and B(·) are continuous.

3. The control method of an underactuated two-wheeled mobile robot based on constrained following according to claim 1, characterized in that: In step 2, the motion control problem of the underactuated two-wheeled mobile robot is formulated as a constrained following control problem. A constraint mathematical model is established based on the desired control performance and expressed in the form of servo constraints, specifically: Define the mathematical model of the first-order servo constraint: ； in: l=1,…,m , yes The i-th component of and All ; The first-order form of the servo constraint can be rewritten as: ； Thus we get the constraint matrix: ； in, ; Taking the derivative, we get the mathematical model of the second-order servo constraint: ； The second-order form of the servo constraint is rewritten as: ； Thus we get the constraint matrix: ； in, , .

4. The control method of an underactuated two-wheeled mobile robot based on constraint following according to claim 1, characterized in that: In step 4, based on the controller without initial constraint deviation, an additional control action is added to handle possible initial constraint deviations, and a robust controller is constructed to control the underactuated two-wheeled mobile robot. The specific method is as follows: Based on the controller without initial constraint deviation in step 3, considering that the initial conditions may not satisfy the constraints in practice, an additional control action is added to deal with the initial constraint deviation. , , ; The following controls are proposed to handle possible deviations from initial conditions: ； in, is a constant; The robust controller of the system is constructed as: 。 5. The control method of an underactuated two-wheeled mobile robot based on constrained following according to claim 1, characterized in that: In step 5, guided by constraint following, a complete constraint and non-complete constraint control design is constructed to control the underactuated two-wheeled mobile robot. The specific method is as follows: (1) Complete constraints Select the complete constraint as: ； ； in, is a constant that constrains this constraint to move the wheel forward while keeping the pendulum approximately upright; (2) Non-holonomic constraints Select the nonholonomic constraints as: ； ； in, is a constant, and this constraint is applied so that the direction of movement of the wheel will be consistent with the tilt direction of the inverted pendulum. The domain of , for any .

6. A computer device for an underactuated two-wheeled mobile robot based on constrained following, characterized in that: The underactuated two-wheeled mobile robot is provided with a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method described in any one of claims 1 to 5 is implemented to control the underactuated two-wheeled mobile robot based on constraint following.

7. A computer device for an underactuated two-wheeled mobile robot based on constrained following, characterized in that: The computer device includes a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the method according to any one of claims 1 to 5 is implemented to control an underactuated two-wheeled mobile robot based on constrained following.

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