Design method and device of finite time controller for fully state-constrained unmanned vehicle

Abstract

The present invention provides a design method and device for a finite-time controller of a fully-state-constrained unmanned vehicle, including: establishing a system kinematic equation of the unmanned vehicle, establishing an initial state equation of the unmanned vehicle based on the system kinematic equation, and establishing a system state equation of the unmanned vehicle based on the initial state equation; based on the system state equation, using a Lyapunov function to design a first control input of the controller of the unmanned vehicle, wherein the first control input is the speed applied to the left wheel of the unmanned vehicle; based on the system state equation and the first control input, using a backstepping method to design a second control input of the controller of the unmanned vehicle, wherein the second control input is the speed applied to the right wheel of the unmanned vehicle. The method and device provided by the present invention can enable the unmanned vehicle system to reach a stable state more quickly, and the dual controller design can also ensure the stability and strong robustness of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of geochemical data processing, and in particular to a design method and device for a finite time controller of a full-state constrained unmanned vehicle. Background Art

[0002] With the rapid development of communication, computer, network and other fields, the related topics of mobile robots have become a major research direction in the field of automatic control. Since mobile robots can participate in the completion of work in various complex environments, the status of robotic arms in industrial production and social life has been continuously improved. Therefore, in order to better utilize mobile robots to complete various tasks, the control problem of mobile robots has received great attention. Wheeled mobile robots (WMRs) have great potential in industrial and military applications. In the past few decades, the development of intelligent control of such small vehicles has made significant progress. Mobile robots can be used for automatic cargo loading and unloading in factory workshops, field road environment surveys and data measurement, and indoor terrain modeling, etc. In order to better utilize robots to assist in completing various tasks, more and more researchers are engaged in related research.

[0003] Wheeled mobile robot systems usually consist of two independent subsystems, a low-order system and a second-order or high-order system, which are connected together by similar inputs. It has practical engineering applications in vehicles, cranes, and underactuated robots. The control methods of underactuated mobile robots include open-loop control and closed-loop control. Open-loop control is easy to control, but has poor robustness and cannot suppress interference well. Closed-loop control is less affected by changes in its own parameters and has strong robustness. Therefore, closed-loop control of non-holonomic systems has important practical application value.

[0004] In recent years, the finite-time stabilization problem of wheeled mobile robot systems has attracted more and more attention from researchers. Compared with asymptotically stable control, finite-time control has the advantages of fast speed, high path tracking accuracy and strong robustness. Therefore, in order to solve engineering problems, finite-time control is applied to improve the steady-state and dynamic performance of the system. In addition, finite-time control can comply with strict transient response requirements, allowing related industries to improve production efficiency. In addition, some scholars have studied the group finite-time stable control algorithm of multi-wheel formations.

[0005] Many researchers have studied finite-time control methods. Some scholars have proposed a fast adaptive termination sliding mode method to achieve finite-time stability. Among them, a new global flip plane is proposed to achieve the stability of complex systems in finite time. However, sliding mode control will inevitably produce system chattering, affecting the stability of system control. Some scholars have proposed a power integral method to solve the finite-time stability problem of complex systems. In addition, some scholars have discussed the problem of wheeled mobile robot systems with finite-time output adjustment. In addition, for many engineering system problems, the output or state of the system is restricted due to system safety reasons and performance specifications. In various industrial applications, adding a power integrator is an important mathematical tool for handling constraints. Some scholars have proposed an adaptive control strategy for nonlinear dynamic systems with output constraints. There are also studies on how to track the output of wheeled mobile robot systems with time-varying output constraints, and there are also studies on the control problem of a class of random wheeled mobile robot systems. Some scholars have studied the fully state finite nonlinear system of finite-time stabilization problems.

[0006] Although many achievements have been made in the control of mobile robots, no relevant achievements have been made in the finite time control of mobile robots with full state constraints. On the one hand, in practical applications, control systems are subject to constraints from various aspects, such as speed constraints and angle constraints; on the other hand, due to the rapid development of industrial production, higher industrial production indicators and higher safety requirements force finite time control to become an important consideration. Although there are relevant studies involving the control of mobile robots under full state constraints, there is no relevant research designed for finite time control under full state, which makes the control performance of mobile robots have some defects. First, in terms of control constraints, most of the existing controls are partial constraints or output constraints, which cannot guarantee the stable performance of mobile robots; secondly, in terms of time, the existing control methods have a relatively long control time for mobile robots, which cannot meet the higher control requirements; finally, the existing controller structures are relatively complex, which also brings inconvenience to design and use.

[0007] It can be seen that the research on finite-time control of full-state constrained mobile robot systems still faces many challenges, mainly the following three problems: First, for the constraints of the system, how to design an obstacle Lyapunov function that meets the constraints; second, how to design a finite-time controller under full-state constraints; third, how to design a suitable controller based on a complex controller structure.

[0008] Therefore, how to solve the problem that current technology does not have the design of a finite-time controller under full-state constraints, and how to avoid the problem that unmanned vehicles take too long to reach a stable state, are still urgent problems to be solved by technical personnel in this field. Summary of the invention

[0009] The present invention provides a design method and device for a finite time controller of a full-state constrained unmanned vehicle, which is used to solve the problem that the current technology has no design of a finite time controller under full-state constraints and the unmanned vehicle takes too long to reach a stable state.

[0010] The present invention provides a design method for a finite time controller of a full-state constrained unmanned vehicle, comprising:

[0011] Establishing a system kinematics equation of the unmanned vehicle, establishing an initial state equation of the unmanned vehicle based on the system kinematics equation, and establishing a system state equation of the unmanned vehicle based on the initial state equation;

[0012] Based on the system state equation, the first control input of the controller of the unmanned vehicle is designed using the Lyapunov function. , wherein the first control input is the speed applied to the left wheel of the unmanned vehicle;

[0013] Based on the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , the second control input is the speed applied to the right wheel of the unmanned vehicle.

[0014] According to a design method of a finite-time controller of a full-state constrained unmanned vehicle provided by the present invention, the control input of the controller of the unmanned vehicle is designed by using the backstepping method. , including:

[0015] First, use the Lyapunov function to impose finite time constraints on the system state;

[0016] Based on the above finite time constraint results, the backstepping method is used to design the second control input of the controller of the unmanned vehicle. .

[0017] According to a design method of a finite-time controller of a full-state constrained unmanned vehicle provided by the present invention, the system kinematic equation of the unmanned vehicle is established, the initial state equation of the unmanned vehicle is established based on the system kinematic equation, and the system state equation of the unmanned vehicle is established based on the initial state equation, specifically including:

[0018] Establish the system kinematic equations of the unmanned vehicle:

[0019]

[0020] in, are the lateral and longitudinal positions of the unmanned vehicle, is the motion deflection angle of the unmanned vehicle, is the speed of an unmanned vehicle. is the angular velocity of the autonomous vehicle;

[0021] Based on the system kinematic equation, the initial state equation of the unmanned vehicle is constructed:

[0022]

[0023] in, Indicates the lateral position of the unmanned vehicle. Indicates the longitudinal position state of the unmanned vehicle, Indicates the deflection angle state of the unmanned vehicle. represents the lateral force on the left wheel of the unmanned vehicle, Represents the lateral force on the right wheel of the unmanned vehicle;

[0024] Based on the initial state equation, the system state equation of the unmanned vehicle is constructed:

[0025]

[0026] in, express The derivative of .

[0027] According to a design method of a finite-time controller of a full-state constrained unmanned vehicle provided by the present invention, the first control input of the controller of the unmanned vehicle is designed by using a Lyapunov function based on the system state equation. , specifically including:

[0028] Based on the barrier power integration technique and the system state equation, a Lyapunov function that satisfies the constraints is selected. ;

[0029] For the Lyapunov function Taking the first-order derivative we get expression;

[0030] based on Expression, for the system state Apply finite time constraints to obtain the first control input .

[0031] According to a design method of a finite-time controller for a full-state constrained unmanned vehicle provided by the present invention, the Lyapunov function The mathematical expression is as follows:

[0032]

[0033] in, Indicates the lateral position status of the unmanned vehicle; It is the upper bound of the system state and does not change over time;

[0034] The mathematical formula of the expression is as follows:

[0035]

[0036] Compute the first control input that satisfies finite-time stability It is expressed as follows:

[0037]

[0038] in, , and they are all constants.

[0039] According to a design method of a finite time controller of a full-state constrained unmanned vehicle provided by the present invention, the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , including:

[0040] Based on the barrier power integration technique, the system state equation and the first control input , select the Lyapunov function that satisfies the constraints ;

[0041] For the Lyapunov function Taking the first-order derivative we get expression;

[0042] based on Expression, for the system state Apply finite time constraints, and we get expression;

[0043] To constrain the system state As the target, based on the power integrator power integration technology, select the Lyapunov function that meets the constraints ;

[0044] For the Lyapunov function Taking the first-order derivative we get expression;

[0045] based on Expression, for the system state Apply finite time constraints to obtain the second control input .

[0046] According to a design method of a finite-time controller for a full-state constrained unmanned vehicle provided by the present invention, the Lyapunov function The mathematical expression is as follows:

[0047]

[0048] The expression is expressed by the following mathematical formula:

[0049]

[0050] in, is the virtual control law, ;

[0051] Lyapunov function The mathematical expression is as follows:

[0052]

[0053] in, , is a constant, is the upper or lower bound of the system state, is a constraint upper or lower bound on the state of the system;

[0054] Second control input The mathematical expression is as follows:

[0055]

[0056] in, is a normal number, are all known functions of , , .

[0057] A design device for a finite-time controller of a full-state constrained unmanned vehicle provided by the present invention comprises:

[0058] A state equation unit, used to establish a system kinematic equation of the unmanned vehicle, establish an initial state equation of the unmanned vehicle based on the system kinematic equation, and establish a system state equation of the unmanned vehicle based on the initial state equation;

[0059] A first control unit is used to design a first control input of a controller of the unmanned vehicle using a Lyapunov function based on the system state equation. , wherein the first control input is the speed applied to the left wheel of the unmanned vehicle;

[0060] a second control unit for controlling the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , the second control input is the speed applied to the right wheel of the unmanned vehicle.

[0061] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the method for designing a finite-time controller for a fully-state-constrained unmanned vehicle as described in any one of the above are implemented.

[0062] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a method for designing a finite-time controller for a full-state constrained unmanned vehicle as described in any one of the above.

[0063] The design method and device of the finite time controller of the full-state constrained unmanned vehicle provided by the present invention establish the system kinematic equation of the unmanned vehicle, establish the initial state equation of the unmanned vehicle based on the system kinematic equation, and establish the system state equation of the unmanned vehicle based on the initial state equation; based on the system state equation, the first control input of the controller of the unmanned vehicle is designed using the Lyapunov function Based on the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle ; Wherein, the first control input The second control input is the speed applied to the left wheel of the unmanned vehicle. The method and device provided by the present invention can enable the unmanned vehicle system to reach a stable state more quickly, and the dual controller design can also ensure the stability and strong robustness of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0065] Figure 1 A schematic flow chart of a design method for a finite-time controller of a full-state constrained unmanned vehicle provided by the present invention;

[0066] Figure 2 A motion model diagram of the unmanned vehicle provided by the present invention;

[0067] Figure 3 A flow chart of a finite time control method for a full-state constrained unmanned vehicle system provided by the present invention;

[0068] Figure 4 A full-state constraint simulation diagram of the unmanned vehicle system provided by the present invention;

[0069] Figure 5 The finite time stability simulation diagram of the unmanned vehicle system provided by the present invention;

[0070] Figure 6 A schematic diagram of the structure of a design device for a finite time controller of a full-state constrained unmanned vehicle provided by the present invention;

[0071] Figure 7 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0072] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0073] Since there is no design of finite time controller under full state constraints in current technology and the problem that it takes too long for unmanned vehicles to reach a stable state is common, Figure 1 The design method of the finite-time controller of the full-state constrained unmanned vehicle of the present invention is described. Figure 1 A flow chart of a design method for a finite-time controller of a fully state-constrained unmanned vehicle provided by the present invention is shown in FIG. Figure 1 As shown, the method includes:

[0074] Step 110, establish a system kinematic equation of the unmanned vehicle, establish an initial state equation of the unmanned vehicle based on the system kinematic equation, and establish a system state equation of the unmanned vehicle based on the initial state equation.

[0075] Specifically, the system kinematic equation of the unmanned vehicle, the initial state equation of the unmanned vehicle and the system state equation are established in sequence, and the above system state equations serve as the theoretical basis for subsequently calculating the first control input and the second control input.

[0076] Step 120, based on the system state equation, using the Lyapunov function to design the first control input of the controller of the unmanned vehicle , wherein the first control input is the speed applied to the left wheel of the unmanned vehicle.

[0077] Specifically, according to the full-state constraints of the system, a suitable barrier Lyapunov function can be designed through the barrier Lyapunov power integration technique. The theorem can ensure that the full-state finite-time controller of the system will not violate the constraints during the whole process.

[0078] Step 130: based on the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , wherein the second control input is the speed applied to the right wheel of the unmanned vehicle.

[0079] Specifically, from the kinematic model of the unmanned vehicle, we know that what is studied here is a third-order non-holonomic system, so the backstepping method can be used to design a finite-time controller. This method can be used for both high-order non-holonomic systems and second-order systems. That is, in each backstepping design, the obstacle Lyapunov function designed based on the obstacle plus power integral technology is used to derivate and scale the constructed function and design a virtual control law. , and then perform the reverse recursion to obtain the second control input of the controller in the last step , thus achieving stability for a limited time.

[0080] The method provided by the embodiment of the present invention establishes a system kinematic equation of the unmanned vehicle, establishes an initial state equation of the unmanned vehicle based on the system kinematic equation, and establishes a system state equation of the unmanned vehicle based on the initial state equation; based on the system state equation, uses the Lyapunov function to design a first control input of a controller of the unmanned vehicle Based on the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle ; Wherein, the first control input The second control input is the speed applied to the left wheel of the unmanned vehicle. The method provided by the present invention can make the unmanned vehicle system reach a stable state quickly, and the dual controller design can also ensure the stability and strong robustness of the system.

[0081] Based on any of the above embodiments, in the method, the control input of the controller of the unmanned vehicle is designed by using the backstepping method. , including:

[0082] First, use the Lyapunov function to impose finite time constraints on the system state;

[0083] Based on the above finite time constraint results, the backstepping method is used to design the second control input of the controller of the unmanned vehicle. .

[0084] Specifically, the Lyapunov function is first used to constrain the system state for a finite time, and the virtual control input of the second input, that is, the control law, is obtained. , through derivation simplification and modern control methods, ,in Then, based on the virtual control input of the second input, the backstepping method is used to perform backstepping design to obtain the virtual control law so that the system state Finite-time stability without violating constraints.

[0085] Based on any of the above embodiments, in the method, establishing a system kinematic equation of the unmanned vehicle, establishing an initial state equation of the unmanned vehicle based on the system kinematic equation, and establishing a system state equation of the unmanned vehicle based on the initial state equation specifically includes:

[0086] Establish the system kinematic equations of the unmanned vehicle:

[0087]

[0088] in, are the lateral and longitudinal positions of the unmanned vehicle, is the motion angle of the unmanned vehicle, is the speed of an unmanned vehicle. is the angular velocity of the autonomous vehicle;

[0089] Based on the system kinematic equation, the initial state equation of the unmanned vehicle is constructed:

[0090]

[0091] in, Indicates the lateral position of the unmanned vehicle. Indicates the longitudinal position state of the unmanned vehicle, Indicates the deflection angle state of the unmanned vehicle. represents the lateral force on the left wheel of the unmanned vehicle, Represents the lateral force on the right wheel of the unmanned vehicle;

[0092] Based on the initial state equation, the system state equation of the unmanned vehicle is constructed:

[0093]

[0094] in, express The derivative of .

[0095] Specifically, Figure 2 The motion model diagram of the unmanned vehicle provided by the present invention is as follows: Figure 2 As shown, the kinematic model equation of the unmanned vehicle is as follows:

[0096]

[0097] in are the lateral and longitudinal positions of the unmanned vehicle, is the motion angle of the unmanned vehicle, is the unmanned vehicle linear speed, is the angular velocity of the unmanned vehicle. By introducing coordinate transformation, we know , so the above formula can be transformed into the following:

[0098] .

[0099] Based on the above embodiment, in the method, the first control input of the controller of the unmanned vehicle is designed based on the system state equation using the Lyapunov function. , including:

[0100] Based on the barrier power integration technique and the system state equation, a Lyapunov function that satisfies the constraints is selected. ;

[0101] For the Lyapunov function Taking the first-order derivative we get expression;

[0102] based on Expression, for the system state Apply finite time constraints to obtain the first control input .

[0103] Specifically, based on the barrier power integration technique, a Lyapunov function that satisfies the constraints of the unmanned vehicle system is selected. , then find the first-order derivative of the selected function, scale and simplify it, and select the appropriate virtual control quantity , you can let ,in , that is, the designed virtual control law It can constrain the state of the unmanned vehicle and achieve finite time stability. In this design process, in order to simplify the calculation and simplify the form of the virtual control law, some inequalities are used to scale the selected Lyapunov function, thereby designing a virtual control law.

[0104] Based on the above embodiment, in this method, the Lyapunov function The mathematical expression is as follows:

[0105]

[0106] in, Indicates the lateral position status of the unmanned vehicle; It is the upper bound of the system state and does not change over time;

[0107] The mathematical formula of the expression is as follows:

[0108]

[0109] Compute the first control input that satisfies finite-time stability It is expressed as follows:

[0110]

[0111] in, , and they are all constants.

[0112] Specifically, the unmanned vehicle controller is designed based on the Lyapunov function. The specific steps are:

[0113] Step 1: Based on the barrier power integration technique, select the Lyapunov function that satisfies the constraints. :

[0114]

[0115] in, is the state of the robot, i.e., the lateral position, It is the upper bound of the system state and does not change over time;

[0116] Step 2: Lyapunov function Finding the first-order derivative shows

[0117]

[0118] Step 3, let , we can get the first control input to make the first state of the unmanned vehicle Satisfies finite time stability. Scaling the above formula through the relevant mathematical lemma yields:

[0119]

[0120] in, , thus completing the design of the first control input. The first-order input of this method can achieve good constrained stabilization for subsequent inputs.

[0121] Based on the above embodiment, in the method, the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , including:

[0122] Based on the barrier power integration technique, the system state equation and the first control input , select the Lyapunov function that satisfies the constraints ;

[0123] For the Lyapunov function Taking the first-order derivative we get expression;

[0124] based on Expression, for the system state Apply finite time constraints, and we get expression;

[0125] To constrain the system state As the target, based on the power integrator power integration technology, select the Lyapunov function that meets the constraints ;

[0126] For the Lyapunov function Taking the first-order derivative we get expression;

[0127] based on Expression, for the system state Apply finite time constraints to obtain the second control input .

[0128] Specifically, the virtual control input quantity of the second input appears in this step , which is the control law. The first step of the backstepping design is to select an appropriate Lyapunov function as in the above-mentioned first control input. , through derivation simplification and modern control methods, ,in Then the backstepping method is used to perform backstepping design to obtain the virtual control law so that the system state Finite-time stability without violating constraints.

[0129] Now we enter the second step of the backstepping design, and we can find the second control input , which is different from the above design method, this step uses the constrained barrier Lyapunov function, which can ensure that the system state is constrained and reaches finite time stability. Similarly, select the appropriate Lyapunov function as in the previous step , by taking the derivative, we can simplify ,in , and then use the backstepping method to get the second control input , making the system state Reach finite-time stability without violating constraints.

[0130] The dual controller of the unmanned vehicle system above shows that the designed controller can make the system stable for a finite time. It also shows that the output of the system can achieve finite time stability very well. The controller solves the finite time control problem of the system under the full state constraint conditions very well.

[0131] Based on the above embodiment, in this method, the Lyapunov function The mathematical expression is as follows:

[0132]

[0133] The expression is expressed by the following mathematical formula:

[0134]

[0135] in, is the virtual control law, ;

[0136] Lyapunov function The mathematical expression is as follows:

[0137]

[0138] in, , is a constant, is the upper or lower bound of the system state, is a constraint upper or lower bound on the state of the system;

[0139] Second control input The mathematical expression is as follows:

[0140]

[0141] in, is a normal number, are all known functions of ,

[0142] ,

[0143] .

[0144] Specifically, the unmanned vehicle controller is designed based on the backstepping method. The specific steps are:

[0145] Step 1, the remaining robot system can be represented as the following subsystems:

[0146]

[0147] In order to better constrain the robot system , based on the barrier power integration technique, select the Lyapunov function that satisfies the constraints :

[0148]

[0149] Similarly, taking the first-order derivative of this function, we can find that:

[0150]

[0151] Therefore, the design of virtual control system state To impose a limited time constraint:

[0152]

[0153] The relevant numerical parameters are , by designing the virtual control law The unmanned vehicle status After the virtual control law is stabilized within a limited time, the backstepping method is used to adjust the virtual control law. Make a design.

[0154] Step 2: To better constrain the system status , based on the power integrator power integration technique, select the Lyapunov function that meets the constraints .

[0155]

[0156] Taking the first derivative of this function and scaling and simplifying using the definition of a definite integral yields:

[0157]

[0158] At the same time, the designed virtual control law is:

[0159]

[0160] in, is a normal number, is a positive known function, .

[0161] Step 3: Use the above design process to design the control input :

[0162]

[0163] in , ,;

[0164] Therefore, the control input of the unmanned vehicle system The design is completed, and the dual control input designed by this control method can achieve finite time stability without violating the constraint limit.

[0165] Based on the above embodiments, the present invention provides a finite time control method for a full-state constrained unmanned vehicle system. Figure 3 The flowchart of the finite time control method of the full-state constraint unmanned vehicle system provided by the present invention is as follows: Figure 3 As shown, the method includes:

[0166] In actual unmanned vehicle motion control, motion constraint problems are often encountered. Consider the simple robot system in the figure below, whose kinematic model equation is as follows:

[0167]

[0168] in, are the lateral and longitudinal positions of the unmanned vehicle, is the motion deflection angle of the unmanned vehicle, is the unmanned vehicle linear speed, is the angular velocity of the unmanned vehicle. By introducing coordinate transformation, we know , so the above formula can be transformed into the following:

[0169]

[0170] Firstly, according to the full-state constraints of the system, a suitable barrier Lyapunov function can be designed through the barrier Lyapunov power integration technique. The theorem can ensure that the full-state finite-time controller of the system will not violate the constraints during the whole process.

[0171] Secondly, from the kinematic model of the unmanned vehicle, we know that what is studied here is a third-order nonholonomic system, so the backstepping method can be used to design a finite-time controller. This method can be used for both high-order nonholonomic systems and second-order systems. That is, in each backstepping design, the obstacle Lyapunov function designed based on the obstacle plus power integral technology is used to derive and scale the constructed function and design a virtual control law. , and then perform the reverse recursion to find the controller in the last step , thus achieving a finite time stability

[0172] Finally, through the above analysis, we can start to design virtual control laws and controllers.

[0173] Step 1: Based on the barrier power integration technique, select the Lyapunov function that satisfies the constraints of the unmanned vehicle system , then find the first-order derivative of the selected function, scale and simplify it, and select the appropriate virtual control quantity , you can let ,in , that is, the designed virtual control law It can constrain the state of the unmanned vehicle and achieve finite time stability. In this design process, in order to simplify the calculation and simplify the form of the virtual control law, we used some inequalities to scale the selected Lyapunov function to design a virtual control law.

[0174] Step 2: This step shows the second input virtual control input , which is the control law. Similarly, as in the first step, select an appropriate Lyapunov function , through derivation simplification and modern control methods, ,in Then the backstepping method is used to perform backstepping design to obtain the virtual control law so that the system state Finite-time stability without violating constraints.

[0175] Step 3: This step is the second step of the backstepping design, and the second control input can be obtained , which is different from the above design method, this step uses the constrained barrier Lyapunov function, which can ensure that the system state is constrained and reaches finite time stability. Similarly, select the appropriate Lyapunov function as in the previous step , by taking the derivative, we can simplify ,in , and then use the backstepping method to get the second control input , making the system state The dual controller of the unmanned vehicle system above shows that the designed controller can make the system stable for a limited time. It also shows that the output of the system can achieve finite time stability. The controller solves the finite time control problem of the system under the full state constraint conditions.

[0176] The present invention also provides an unmanned vehicle motion system, which includes a controller designed using the above-mentioned design method, and the controller can achieve limited-time control of the calming control of the mobile robot.

[0177] In order to verify that the finite time controller designed in the present invention makes the system satisfy the full state constraint conditions, the signal changes of each state, the following parameters are selected in MATLAB software: robot mass Wheel diameter , robot width Robot length , the initial state of the robot: , , Conduct system simulation. Use the above controller design method to design the controller , ,in By designing this controller, the system state of the unmanned vehicle can be well controlled for a limited time without breaking the constraints.

[0178] The simulation diagram below can effectively demonstrate the effectiveness of our controller design.

[0179] Figure 4 The full state constraint simulation diagram of the unmanned vehicle system provided by the present invention is as follows: Figure 4 As shown, They represent the three states of the unmanned vehicle, namely the lateral position, longitudinal position and deflection angle of the unmanned vehicle. Represent the upper or lower bound of the constraint state respectively. It can be seen that the entire state of the system can be constrained in a stable interval and maintain a good effect. Figure 5 The finite time stability simulation diagram of the unmanned vehicle system provided by the present invention is as follows: Figure 5 As shown in the figure, the designed dual controller can effectively stabilize the state of the unmanned vehicle system within a limited time, and the convergence speed is fast, which can achieve the effect in engineering.

[0180] The following describes a design device for a finite-time controller for a full-state constrained unmanned vehicle provided by the present invention. The design device for a finite-time controller for a full-state constrained unmanned vehicle described below and the design method for a finite-time controller for a full-state constrained unmanned vehicle described above can be referenced to each other.

[0181] Figure 6 The schematic diagram of the structure of the design device of the finite time controller of the full-state constrained unmanned vehicle provided by the present invention is as follows: Figure 6 As shown, the device includes a state equation unit 610, a first control unit 620 and a second control unit 630, wherein:

[0182] The state equation unit 610 is used to establish a system kinematic equation of the unmanned vehicle, establish an initial state equation of the unmanned vehicle based on the system kinematic equation, and establish a system state equation of the unmanned vehicle based on the initial state equation;

[0183] The first control unit 620 is used to design a first control input of the controller of the unmanned vehicle based on the system state equation using the Lyapunov function. , wherein the first control input is the speed applied to the left wheel of the unmanned vehicle;

[0184] The second control unit 630 is used to control the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , the second control input is the speed applied to the right wheel of the unmanned vehicle.

[0185] The design device of the finite time controller of the full-state constrained unmanned vehicle provided by the present invention establishes the system kinematic equation of the unmanned vehicle, establishes the initial state equation of the unmanned vehicle based on the system kinematic equation, and establishes the system state equation of the unmanned vehicle based on the initial state equation; based on the system state equation, the first control input of the controller of the unmanned vehicle is designed by using the Lyapunov function Based on the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle ; Wherein, the first control input The second control input is the speed applied to the left wheel of the unmanned vehicle. The device provided by the present invention can make the unmanned vehicle system reach a stable state more quickly, and the dual controller design can also ensure the stability and strong robustness of the system.

[0186] Based on the above embodiment, in the device, the control input of the controller of the unmanned vehicle is designed by backstepping method. , including:

[0187] First, use the Lyapunov function to impose finite time constraints on the system state;

[0188] Based on the above finite time constraint results, the backstepping method is used to design the second control input of the controller of the unmanned vehicle. .

[0189] On the basis of the above embodiment, in the device, the system kinematic equation of the unmanned vehicle is established, the initial state equation of the unmanned vehicle is established based on the system kinematic equation, and the system state equation of the unmanned vehicle is established based on the initial state equation, specifically including:

[0190] Establish the system kinematic equations of the unmanned vehicle:

[0191]

[0192] in, are the lateral and longitudinal positions of the unmanned vehicle, is the motion angle of the unmanned vehicle, is the speed of an unmanned vehicle. is the angular velocity of the autonomous vehicle;

[0193] Based on the system kinematic equation, the initial state equation of the unmanned vehicle is constructed:

[0194]

[0195] in, Indicates the lateral position of the unmanned vehicle. Indicates the longitudinal position state of the unmanned vehicle, Indicates the deflection angle state of the unmanned vehicle. represents the lateral force on the left wheel of the unmanned vehicle, Represents the lateral force on the right wheel of the unmanned vehicle;

[0196] Based on the initial state equation, the system state equation of the unmanned vehicle is constructed:

[0197]

[0198] in, express The derivative of .

[0199] Based on the above embodiment, in the device, the first control unit is specifically used for:

[0200] Based on the barrier power integration technique and the system state equation, a Lyapunov function that satisfies the constraints is selected. ;

[0201] For the Lyapunov function Taking the first-order derivative we get expression;

[0202] based on Expression, for the system state Apply finite time constraints to obtain the first control input .

[0203] Based on the above embodiment, in the device, the Lyapunov function The mathematical expression is as follows:

[0204]

[0205] in, Indicates the lateral position status of the unmanned vehicle; It is the upper bound of the system state and does not change over time;

[0206] The mathematical formula of the expression is as follows:

[0207]

[0208] Compute the first control input that satisfies finite-time stability It is expressed as follows:

[0209]

[0210] in, , and they are all constants.

[0211] Based on the above embodiment, in the device, the second control unit is specifically used for:

[0212] Based on the barrier power integration technique, the system state equation and the first control input , select the Lyapunov function that satisfies the constraints ;

[0213] For the Lyapunov function Taking the first-order derivative we get expression;

[0214] based on Expression, for the system state Apply finite time constraints, and we get expression;

[0215] To constrain the system state As the target, based on the power integrator power integration technology, select the Lyapunov function that meets the constraints ;

[0216] For the Lyapunov function Taking the first-order derivative we get expression;

[0217] based on Expression, for the system state Apply finite time constraints to obtain the second control input .

[0218] Based on the above embodiment, in the device, the Lyapunov function The mathematical expression is as follows:

[0219]

[0220] The expression is expressed by the following mathematical formula:

[0221]

[0222] in, is the virtual control law, ;

[0223] Lyapunov function The mathematical expression is as follows:

[0224]

[0225] in, , is a constant, is the upper or lower bound of the system state, is a constraint upper or lower bound on the state of the system;

[0226] Second control input The mathematical expression is as follows:

[0227]

[0228] in, is a normal number, are all known functions of , , .

[0229] Figure 7 An example of a physical structure diagram of an electronic device is shown in FIG. Figure 7As shown, the electronic device may include: a processor 710, a communication interface 720, a memory 730 and a communication bus 740, wherein the processor 710, the communication interface 720 and the memory 730 communicate with each other through the communication bus 740. The processor 710 may call the logic instructions in the memory 730 to execute a design method for a finite time controller of a fully state constrained unmanned vehicle, the method comprising: establishing a system kinematic equation of the unmanned vehicle, establishing an initial state equation of the unmanned vehicle based on the system kinematic equation, establishing a system state equation of the unmanned vehicle based on the initial state equation; based on the system state equation, designing a first control input of the controller of the unmanned vehicle using a Lyapunov function , wherein the first control input is the speed applied to the left wheel of the unmanned vehicle; based on the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , wherein the second control input is the speed applied to the right wheel of the unmanned vehicle.

[0230] In addition, the logic instructions in the above-mentioned memory 730 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on this understanding, the technical solution of the present invention can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.

[0231] On the other hand, the present invention also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium, and the computer program includes program instructions. When the program instructions are executed by a computer, the computer can execute the design method of a finite-time controller of a full-state constrained unmanned vehicle provided by the above methods, the method comprising: establishing a system kinematic equation of the unmanned vehicle, establishing an initial state equation of the unmanned vehicle based on the system kinematic equation, and establishing a system state equation of the unmanned vehicle based on the initial state equation; based on the system state equation, using a Lyapunov function to design a first control input of the controller of the unmanned vehicle , wherein the first control input is the speed applied to the left wheel of the unmanned vehicle; based on the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , wherein the second control input is the speed applied to the right wheel of the unmanned vehicle.

[0232] In another aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, which is implemented when the computer program is executed by a processor to execute the above-mentioned method for designing a finite-time controller of a fully-state-constrained unmanned vehicle, the method comprising: establishing a system kinematic equation of the unmanned vehicle, establishing an initial state equation of the unmanned vehicle based on the system kinematic equation, and establishing a system state equation of the unmanned vehicle based on the initial state equation; based on the system state equation, designing a first control input of the controller of the unmanned vehicle using a Lyapunov function , wherein the first control input is the speed applied to the left wheel of the unmanned vehicle; based on the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , wherein the second control input is the speed applied to the right wheel of the unmanned vehicle.

[0233] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0234] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0235] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for a finite-time controller of a fully state-constrained unmanned vehicle, characterized in that: include: Establishing a system kinematics equation of the unmanned vehicle, establishing an initial state equation of the unmanned vehicle based on the system kinematics equation, and establishing a system state equation of the unmanned vehicle based on the initial state equation; Based on the system state equation, the first control input of the controller of the unmanned vehicle is designed using the Lyapunov function. , wherein the first control input is the speed applied to the left wheel of the unmanned vehicle; calculate the first control input that satisfies finite time stability It is expressed as follows: in, , and they are all constants; Indicates the lateral position status of the unmanned vehicle; Based on the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , the second control input is the speed applied to the right wheel of the unmanned vehicle; Second control input The mathematical expression is as follows: in, is a normal number, are all known functions of , , ; in, Indicates the lateral position of the unmanned vehicle. Indicates the longitudinal position state of the unmanned vehicle, Indicates the deflection angle state of the unmanned vehicle. represents the lateral force on the left wheel of the unmanned vehicle, represents the lateral force on the right wheel of the unmanned vehicle, is a constrained upper or lower bound on the state of the system.

2. The design method of the finite time controller of the full-state constrained unmanned vehicle according to claim 1 is characterized in that: The control input of the controller of the unmanned vehicle is designed using the backstepping method , including: First, use the Lyapunov function to impose finite time constraints on the system state; Based on the above finite time constraint results, the backstepping method is used to design the second control input of the controller of the unmanned vehicle. .

3. The design method of the finite time controller of the full-state constrained unmanned vehicle according to claim 1 is characterized in that: The step of establishing a system kinematic equation of the unmanned vehicle, establishing an initial state equation of the unmanned vehicle based on the system kinematic equation, and establishing a system state equation of the unmanned vehicle based on the initial state equation specifically includes: Establish the system kinematic equations of the unmanned vehicle: in, are the lateral and longitudinal positions of the unmanned vehicle, is the motion deflection angle of the unmanned vehicle, is the speed of an unmanned vehicle. is the angular velocity of the autonomous vehicle; Based on the system kinematic equation, the initial state equation of the unmanned vehicle is constructed: Based on the initial state equation, the system state equation of the unmanned vehicle is constructed: in, express The derivative of .

4. The design method of the finite time controller of the full-state constrained unmanned vehicle according to claim 3 is characterized in that: Based on the system state equation, the first control input of the controller of the unmanned vehicle is designed using the Lyapunov function , including: Based on the barrier power integration technique and the system state equation, a Lyapunov function that satisfies the constraints is selected. ; For the Lyapunov function Taking the first-order derivative we get expression; based on Expression, for the system state Apply finite time constraints to obtain the first control input .

5. The design method of the finite time controller of the full-state constrained unmanned vehicle according to claim 4 is characterized in that: Lyapunov function The mathematical expression is as follows: in, Indicates the lateral position status of the unmanned vehicle; It is the upper bound of the system state and does not change over time; The mathematical formula of the expression is as follows: 。 6. The design method of the finite time controller of the full-state constrained unmanned vehicle according to claim 5 is characterized in that: The system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , including: Based on the barrier power integration technique, the system state equation and the first control input , select the Lyapunov function that satisfies the constraints ; For the Lyapunov function Taking the first-order derivative we get expression; based on Expression, for the system state Apply finite time constraints, and we get expression; To constrain the system state As the target, based on the power integrator power integration technology, select the Lyapunov function that meets the constraints ; For the Lyapunov function Taking the first-order derivative we get expression; based on Expression, for the system state Apply finite time constraints to obtain the second control input .

7. The design method of the finite time controller of the full-state constrained unmanned vehicle according to claim 6 is characterized in that: Lyapunov function The mathematical expression is as follows: The expression is expressed by the following mathematical formula: in, is the virtual control law, ; Lyapunov function The mathematical expression is as follows: in, , is a constant, is a constrained upper or lower bound on the state of the system.

8. A design device for a finite-time controller of a fully state-constrained unmanned vehicle, characterized in that: include: A state equation unit, used to establish a system kinematic equation of the unmanned vehicle, establish an initial state equation of the unmanned vehicle based on the system kinematic equation, and establish a system state equation of the unmanned vehicle based on the initial state equation; A first control unit is used to design a first control input of a controller of the unmanned vehicle using a Lyapunov function based on the system state equation. , wherein the first control input is the speed applied to the left wheel of the unmanned vehicle; calculate the first control input that satisfies finite time stability It is expressed as follows: in, , and they are all constants; Indicates the lateral position status of the unmanned vehicle; a second control unit for controlling the system state equation and the first control input , using the backstepping method to design the second control input of the controller of the unmanned vehicle , the second control input is the speed applied to the right wheel of the unmanned vehicle; the second control input The mathematical expression is as follows: in, is a normal number, are all known functions of , , ; in, Indicates the lateral position of the unmanned vehicle. Indicates the longitudinal position state of the unmanned vehicle, Indicates the deflection angle state of the unmanned vehicle. represents the lateral force on the left wheel of the unmanned vehicle, represents the lateral force on the right wheel of the unmanned vehicle, is a constrained upper or lower bound on the state of the system.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method for designing a finite-time controller for a fully-state-constrained unmanned vehicle as described in any one of claims 1 to 7 are implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for designing a finite-time controller for a full-state constrained unmanned vehicle as described in any one of claims 1 to 7 are implemented.

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