Low-complexity preset time optimal formation control method for incomplete robots

Abstract

The invention discloses a low-complexity preset time optimal formation control method for incomplete robots, and relates to the technical field of intelligent robot control and multi-agent cooperative control. Comprising the steps that collision avoidance and communication distance constraints between adjacent robots are uniformly converted into formation error constraints by using a funnel technology, collision between the adjacent robots is avoided, and the complexity of a controller is reduced; a preset time nonlinear command filtering technology with self-adaptive parameters is integrated to avoid the problem of calculation complexity, and the convergence performance of the system in preset time is realized; on-line approximation is carried out on system uncertainty by combining a generalized fuzzy neural network, a control strategy is optimized in real time by using a reinforcement learning mechanism, and dual minimization of formation errors and control energy is realized; and low-complexity preset time optimal safety collision avoidance formation control of multiple robots is realized. The method not only can effectively reduce the control complexity, but also has the advantages of high convergence speed, low energy consumption and the like.

Description

Technical Field

[0001] This invention belongs to the field of intelligent robot control and multi-agent cooperative control technology, specifically relating to a low-complexity preset time optimal formation control method for non-holonomic robots. Background Technology

[0002] In recent years, with the rapid development of intelligent robots and multi-agent systems, non-holonomic mobile robots have been widely used in various complex collaborative tasks, such as area surveillance, trajectory tracking, post-disaster search and rescue, environmental monitoring and military patrol, due to their simple structure, high mobility and adaptability.

[0003] In practical formation control, nonholonomic mobile robots suffer from nonholonomic constraints, meaning their degrees of freedom are limited. Therefore, their dynamic characteristics must be carefully considered when designing the controller. Furthermore, the relative motion and spatial position between robots are closely related, making collision avoidance a crucial issue in formation control. Only by avoiding collisions can safe formation and stable operation of multi-robot systems be achieved.

[0004] To address the aforementioned issues, various safe formation control strategies have been proposed. A typical approach is to introduce control barrier Lyapunov functions, incorporating safety constraints into the control law design process to effectively avoid collisions between adjacent robots while maintaining system stability. While these methods theoretically offer robust safety mechanisms, they face numerous challenges in practical applications. Specifically, to ensure system stability, complex control barrier functions appear in the controller, significantly increasing its computational complexity and implementation burden. Furthermore, although existing formation control algorithms based on linear filtering and backstepping techniques mitigate the computational complexity issue to some extent, they cannot predefine the system's convergence time during the control design phase and cannot simultaneously minimize formation error and control input. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a low-complexity preset time optimal formation control method for nonholonomic robots. This method aims to reduce the complexity of the control scheme, achieve the pre-setting of the system's convergence time during the control design stage, and simultaneously minimize formation error and control input, thereby realizing efficient and safe formation control of nonholonomic mobile robot systems with uncertainties.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A low-complexity, preset-time optimal formation control method for nonholonomic robots includes the following steps:

[0008] Step 101: Use funnel technology to unify the collision avoidance and communication distance constraints between adjacent robots into formation error constraints;

[0009] Step 102: Integrate predefined time nonlinear command filtering techniques with adaptive parameters;

[0010] Step 103: Combine generalized fuzzy neural networks to approximate the system uncertainty online, and use reinforcement learning mechanisms to optimize the control strategy in real time;

[0011] Step 104: Implement low-complexity preset time optimal safe collision avoidance formation control for multiple robots.

[0012] Furthermore, in step 101, a first nonlinearity is established. ( The dynamic model of a following nonholonomic mobile robot is as follows:

[0013] (1)

[0014] in, For robots Location coordinates, For robots The heading angle, For robots linear velocity, For robots angular velocity, For robots Control torque, robot The relevant dynamic matrix is ​​represented as follows:

[0015] ; ;

[0016] ; ; ,

[0017] in, For robots The radius of the wheel, For robots The width of the car body is half. For robots The damping coefficient, For robots The parameters, and For robots The parameters, For robots The body weight, For robots The mass of a wheel, and For robots The parameters, and For robots Moment of inertia between components;

[0018] The dynamic model of the leading mobile robot is as follows:

[0019] (2)

[0020] To achieve the control objective, the following lemma is given, laying the theoretical foundation for subsequent controller design and stability analysis.

[0021] Lemma 1: Consider a given... The system described, in which and .make It is a continuous Lyapunov function, if ,in , , If the constant value indicates that the controlled system is stable at the preset time and the region of convergence is... The convergence time is .

[0022] Lemma 2: For any variable and defined in Continuous functions on And satisfy ( If ), then the inequality holds. Sum of equations Established.

[0023] Lemma 3: For any variable and integers There exists a constant , making the inequality Established.

[0024] Lemma 4: For any variable Sum of odd integers There are positive numbers and , making the inequality Established.

[0025] Lemma 5: For any variable and parameters This makes the following inequalities true:

[0026] .

[0027] Lemma 6: If the variable satisfy ( If (where is a constant), then there exists a constant. , and This makes the following inequalities true:

[0028] ,

[0029] in, .

[0030] Furthermore, in step 101, the low-complexity preset-time optimal formation control method for nonholonomic robots with collision avoidance constraints and communication distance constraints is as follows:

[0031] Define the relative distance between two adjacent non-holonomic mobile robots. and relative heading angle They are respectively and , where variables and To prevent collisions between robots and maintain communication links between them, the relative distance... Apply the following constraints:

[0032] (3)

[0033] in, This represents the minimum safe distance required to avoid collisions between two adjacent robots. This represents the maximum permissible distance between two adjacent robots to ensure continuous communication and network connectivity. Furthermore, to avoid singularity issues, the following constraints are imposed on the relative heading angle:

[0034] (4)

[0035] in, It is the upper limit of the allowable relative heading angle deviation.

[0036] Assume the desired relative distance between two adjacent robots The relative heading angle is And they satisfy and Therefore, the relative distance and relative heading angle errors can be expressed as: and To avoid the problems of high controller complexity and poor implementability caused by the introduction of complex control barrier functions in existing formation control schemes, this invention introduces funnel control technology and defines the following constraints:

[0037] (5)

[0038] in, ( ) is the boundary function of the funnel, and the function First-order differentiable and .

[0039] Therefore, the initial value of the funnel boundary function is chosen as follows: and This ensures that the funnel constraint (5) always covers the relative distance constraint (3) and the relative heading angle constraint (4), thereby achieving integrated control of formation error constraint, collision avoidance safety constraint and communication constraint.

[0040] Furthermore, in step 102, the process is as follows:

[0041] Define coordinate transformation as , , , , , ,in ( () is the optimal virtual control signal The output uses the following nonlinear preset time command filter:

[0042] (6)

[0043] Among them, design parameters , and It is a constant. It is the ratio of even integers to odd integers, parameter yes The estimate and the estimation error is , It is a monotonically decreasing function and a constant. ,parameter The update rate , It is a positive number.

[0044] The selected performance index function is

[0045] (7)

[0046] in, and Represents the ideal optimal virtual control signal and and The ideal and optimal actual control signal is given. Furthermore, based on the Bellman optimization principle, the Hamilton-Jacobi-Bellman (HJB) equation is introduced to characterize the analytical solution structure of the optimal control problem.

[0047] (8)

[0048] when At that time, As the ideal optimal virtual controller .when At that time, As the ideal optimal virtual controller Since the optimal value function corresponding to the left side of HJB equation (8) exists and is unique, the ideal optimal virtual control signal and the ideal actual control signal can be obtained by solving... Once obtained, one can know.

[0049] , , ,

[0050] , , ;

[0051] However, due to the nonlinear term Since it is unknown, it cannot be directly used in controller design. Therefore, in order to ensure that the designed controller can achieve the preset time stability and optimality of the controlled system, the nonlinear term is... and Decomposed into:

[0052] ; ;

[0053] in, , ,

[0054] ,

[0055] ,

[0056] ,

[0057] Unknown nonlinear function and They are respectively:

[0058] ;

[0059] .

[0060] Furthermore, in step 103, a generalized fuzzy neural network can be used. Approximating the aforementioned unknown nonlinear function, we can obtain... Approximation error satisfy , For positive numbers, use and right An estimation is performed, and the estimation error is... , .

[0061] The update rate of a generalized fuzzy neural network is evaluated as follows:

[0062] (9)

[0063] Among them, matrix Design parameters It is a constant. yes A 3D identity matrix and design parameters satisfy .

[0064] The update rate design for implementing the generalized fuzzy neural network is as follows:

[0065] (10)

[0066] The optimal virtual control signal design is as follows:

[0067] (11)

[0068] Using generalized fuzzy neural networks and To identify the unknown nonlinear functions present in the system. and ,Right now , Approximation error and satisfy and , and It is a positive constant. (Definition) ,use right An estimation is performed, and the estimation error is... .

[0069] parameter The update rate is designed as follows:

[0070] (12)

[0071] in, The design parameters are positive.

[0072] The optimal actual control signal design is as follows:

[0073] (13)

[0074] in, , .

[0075] Furthermore, in step 103, the preset time stability of the closed-loop system is proved by selecting an appropriate Lyapunov function based on the designed virtual control signal and actual control signal, the evaluation-execution update rate and the adaptive parameter update rate.

[0076] Step 1: Based on the defined error transformation Taking its derivative yields

[0077] (14)

[0078] (15)

[0079] The Lyapunov function is selected as follows:

[0080] (16)

[0081] based on and the designed virtual control signals Evaluation - Execution Update Rate and , The derivative with respect to time is

[0082] (17)

[0083] According to (17) and Lemma 3, we can obtain (18)-(20).

[0084] (18)

[0085] (19)

[0086] (20)

[0087] Furthermore, according to (17), we can further obtain:

[0088] (twenty one)

[0089] (twenty two)

[0090] Furthermore, by rearranging (17)-(22), we can obtain:

[0091] (twenty three)

[0092] in, .

[0093] Step 2: Based on the defined error transformation Taking its derivative, we get:

[0094] (twenty four)

[0095] (25)

[0096] By Lemma 2 and approximation as well as We can obtain:

[0097] (26)

[0098] (27)

[0099] The Lyapunov function is selected as follows:

[0100] (28)

[0101] Based on (24)-(27), and similar to (18)-(22), and the designed actual control signals Evaluation - Execution Update Rate and and parameter update rate , The derivative with respect to time can be summarized as follows:

[0102] (29)

[0103] According to (29) and Lemma 4, we can obtain (30) and (31):

[0104] (30)

[0105] (31)

[0106] According to (29) and Lemma 5, we can obtain (32) and (33):

[0107] (32)

[0108] (33)

[0109] Furthermore, according to (29) and Lemma 6, we can further obtain:

[0110] (34)

[0111] Where, constant , It is a matrix The smallest eigenvalue.

[0112] definition , as well as Furthermore, by rearranging (29)-(34), we can obtain:

[0113] (35)

[0114] in,

[0115] .

[0116] Based on Lemma 1 and (35), it can be seen that the controlled system is stable at the actual preset time, and ,in

[0117] ,

[0118] .

[0119] Furthermore, based on coordinate transformation and It can be known

[0120] (36)

[0121] As can be seen from (36), the proposed control method can guarantee the relative distance error. and relative heading angle error This does not violate the constraints imposed by the performance funnel, therefore the relative distance can be further explained. and relative heading angle It does not violate any constraints.

[0122] Furthermore, in step 104, simulation verification is performed using Matlab software, considering a system consisting of four followers and one leader, where the relevant parameters of the nonholonomic mobile robot model are as follows;

[0123] , , ,

[0124] , , , ;

[0125] The leader's trajectory is set as follows:

[0126] ;

[0127] The relevant design parameters are selected as follows: , , , , , ,, , , , ;

[0128] The funnel boundary function is set as ;

[0129] The relevant initial conditions are selected as follows , , , , .

[0130] Compared with the prior art, the present invention has the following beneficial effects:

[0131] 1. The present invention provides a nonholonomic robot safe formation control method based on funnel control technology. By utilizing performance funnel technology, the collision avoidance problem between adjacent robots is transformed into an error constraint problem. There is no need to construct complex control obstacle functions, which can effectively reduce the design complexity of the controller and ensure that the safety distance requirements are met in any initial state, thereby achieving stable and safe formation between nonholonomic robots.

[0132] 2. The present invention provides a nonholonomic robot safety formation control method based on nonlinear preset time command filtering technology. By designing a command filter with convergence performance within a preset time, the stability of the controlled system within the preset time is achieved. Moreover, the convergence time can be set offline during the controller design stage, without depending on the initial state and design parameters of the system, thereby improving the predictability of system operation and the controllability of task scheduling.

[0133] 3. The present invention provides a nonholonomic robot formation control method based on reinforcement learning technology. By constructing a policy update mechanism, the system can learn and optimize the control policy online in an unknown dynamic environment, achieving adaptive balance of multi-objective performance indicators. This ensures system stability and safety while minimizing formation error and control input, thereby improving the efficiency and intelligence level of overall collaborative control.

[0134] The above content is merely a summary description of the technical solution of the present invention, intended to provide a preliminary understanding of the overall concept of the present invention. To more comprehensively understand the technical means employed in the present invention and to implement it accordingly, and to make the objectives, features, and advantages of the present invention clearer, the present invention will now be described in detail with reference to specific embodiments. Attached Figure Description

[0135] To more intuitively illustrate the technical solutions adopted in the embodiments of the present invention, the relevant drawings are briefly described below. It should be understood that these drawings are only used to illustrate some specific embodiments of the present invention and do not constitute a limitation on the scope of the present invention. Those skilled in the art can also obtain other forms of drawings or improved solutions based on these drawings without any creative effort.

[0136] Figure 1 This is a flowchart of the present invention;

[0137] Figure 2 This is a schematic diagram of the control principle of the present invention;

[0138] Figure 3 This is a schematic diagram of the movement trajectories of the follower robot and the leader robot in this invention;

[0139] Figure 4 This is a schematic diagram showing the relative distance between adjacent robots in this invention;

[0140] Figure 5 This is a schematic diagram illustrating the relative distance error between adjacent robots in this invention;

[0141] Figure 6 This is a schematic diagram of the relative heading angle between adjacent robots in this invention;

[0142] Figure 7 This is a schematic diagram of the optimal control input signal in this invention. Detailed Implementation

[0143] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. It should be understood that the described embodiments are only some examples of the present invention, and not all of them. Those skilled in the art can conceive of various different structures or design schemes based on these drawings and descriptions without creative effort, and these should all fall within the protection scope of the present invention. The components in the embodiments shown in the drawings can be arranged and designed in various ways. Therefore, the detailed description below does not constitute a limitation on the protection scope of the present invention, but rather a description of some preferred embodiments of the present invention.

[0144] It should be noted that in the following figures, the same or similar reference numerals and letters are used to indicate parts that are similar in function or structure. Therefore, once an element has been defined or described in one figure, it usually does not need to be described again in subsequent figures.

[0145] This invention presents a pre-time optimal safe formation control scheme based on performance funneling and nonlinear command filtering. The funneling technique effectively avoids the highly nonlinear modeling and complex differentiation calculations encountered by traditional control obstacle functions when handling safety constraints, significantly simplifying the controller structure and enhancing the system's engineering feasibility. Simultaneously, a nonlinear pre-time command filter is designed to further improve the control system's rapid response capability and time consistency performance. Furthermore, based on a reinforcement learning-based optimization strategy, formation error and control energy consumption are minimized simultaneously while satisfying collision avoidance and communication constraints, thereby improving the overall system's tracking accuracy and control efficiency.

[0146] like Figure 1-2 As shown, a low-complexity preset-time optimal formation control method for a nonholonomic robot includes the following steps:

[0147] Step 101: Use funnel technology to unify the collision avoidance and communication distance constraints between adjacent robots into formation error constraints;

[0148] Step 102: Integrate preset time nonlinear command filtering techniques with adaptive parameters;

[0149] Step 103: Combine generalized fuzzy neural networks to approximate the system uncertainty online, and use reinforcement learning mechanisms to optimize the control strategy in real time;

[0150] Step 104: Implement low-complexity preset time optimal safe collision avoidance formation control for multiple robots.

[0151] Specifically, in step 101, the first unknown nonlinearity is established. ( The dynamic model of a following nonholonomic mobile robot is as follows:

[0152] (1)

[0153] in, For robots Location coordinates, For robots The heading angle, For robots linear velocity, For robots angular velocity, For robots Control torque, robot The relevant dynamic matrix is ​​represented as follows:

[0154] ; ;

[0155] ; ; ,

[0156] in, For robots The radius of the wheel, For robots The width of the car body is half. For robots The damping coefficient, For robots The parameters, and For robots The parameters, For robots The body weight, For robots The mass of a wheel, and For robots The parameters, and For robots Moment of inertia between components;

[0157] The dynamic model of the leading mobile robot is as follows:

[0158] (2)

[0159] To achieve the control objective, the following lemma is given, laying the theoretical foundation for subsequent controller design and stability analysis.

[0160] Lemma 1: Consider a given... The system described, in which and .make It is a continuous Lyapunov function, if ,in , , If the constant value indicates that the controlled system is stable at the preset time and the region of convergence is... The convergence time is .

[0161] Lemma 2: For any variable and defined in Continuous functions on And satisfy ( If ), then the inequality holds. Sum of equations Established.

[0162] Lemma 3: For any variable and integers There exists a constant , making the inequality Established.

[0163] Lemma 4: For any variable Sum of odd integers There are positive numbers and , making the inequality Established.

[0164] Lemma 5: For any variable and parameters This makes the following inequalities true.

[0165] .

[0166] Lemma 6: If the variable satisfy ( If (where is a constant), then there exists a constant. , and This makes the following inequalities true.

[0167] ,

[0168] in, .

[0169] Specifically, step 101 also includes the following methods:

[0170] Define the relative distance between two adjacent non-holonomic mobile robots. and relative heading angle They are respectively and , where variables and To prevent collisions between robots and maintain communication links between them, the relative distance... Apply the following constraints:

[0171] (3)

[0172] in, This represents the minimum safe distance required to avoid collisions between two adjacent robots. This represents the maximum permissible distance between two adjacent robots to ensure continuous communication and network connectivity. Furthermore, to avoid singularity issues, the following constraints are imposed on the relative heading angle:

[0173] (4)

[0174] in, It is the upper limit of the allowable relative heading angle deviation.

[0175] Assume the desired relative distance between two adjacent robots The relative heading angle is And they satisfy and Therefore, the relative distance and relative heading angle errors can be expressed as: and To avoid the problems of high controller complexity and poor implementability caused by the introduction of complex control barrier functions in existing formation control schemes, this invention introduces funnel control technology and defines the following constraints:

[0176] (5)

[0177] in, ( ) is the boundary function of the funnel, and the function First-order differentiable and .

[0178] Therefore, the initial value of the funnel boundary function is chosen as follows: and This ensures that the funnel constraint (5) always covers the relative distance constraint (3) and the relative heading angle constraint (4), thereby achieving integrated control of formation error constraint, collision avoidance safety constraint and communication constraint.

[0179] Specifically, in step 102, the process is as follows:

[0180] Define coordinate transformation as , , , , , ,in ( () is the optimal virtual control signal The output uses the following nonlinear preset time command filter:

[0181] (6)

[0182] Among them, design parameters , and It is a constant. It is the ratio of even integers to odd integers, parameter yes The estimate and the estimation error is , It is a monotonically decreasing function and a constant. ,parameter The update rate , It is a positive number.

[0183] The selected performance index function is:

[0184] (7)

[0185] in, and Represents the ideal optimal virtual control signal and and The ideal and optimal actual control signal is given. Furthermore, based on the Bellman optimization principle, the Hamilton-Jacobi-Bellman (HJB) equation is introduced to characterize the analytical solution structure of the optimal control problem.

[0186] (8)

[0187] when At that time, As the ideal optimal virtual controller .when At that time, As the ideal optimal virtual controller Since the optimal value function corresponding to the left side of HJB equation (8) exists and is unique, the ideal optimal virtual control signal and the ideal actual control signal can be obtained by solving... Once obtained, it can be known that:

[0188] , , ,

[0189] , , ;

[0190] However, due to the nonlinear term Since it is unknown, it cannot be directly used in controller design. Therefore, in order to ensure that the designed controller can achieve the preset time stability and optimality of the controlled system, the nonlinear term is... and Decomposed into:

[0191] ;

[0192] ;

[0193] in, , ,

[0194] ,

[0195] ,

[0196] ,

[0197] Unknown nonlinear function and They are respectively:

[0198] ;

[0199] .

[0200] In step 103, a generalized fuzzy neural network is used. Approximating the aforementioned unknown nonlinear function, we can obtain... Approximation error satisfy , For positive numbers, use and right An estimation is performed, and the estimation error is... , .

[0201] The update rate of a generalized fuzzy neural network is evaluated as follows:

[0202] (9)

[0203] Among them, matrix Design parameters It is a constant. yes A 3D identity matrix and design parameters satisfy .

[0204] The update rate design for implementing the generalized fuzzy neural network is as follows:

[0205] (10)

[0206] The optimal virtual control signal design is as follows:

[0207] (11)

[0208] Using generalized fuzzy neural networks and To identify the unknown nonlinear functions present in the system. and ,Right now , Approximation error and satisfy and , and It is a positive constant. (Definition) ,use right An estimation is performed, and the estimation error is... .

[0209] parameter The update rate is designed as follows:

[0210] (12)

[0211] in, The design parameters are positive.

[0212] The optimal actual control signal design is as follows:

[0213] (13)

[0214] in, , .

[0215] Specifically, in step 103, based on the designed virtual control signal and actual control signal, the evaluation-execution update rate and the adaptive parameter update rate, the preset time stability of the closed-loop system is proved by selecting an appropriate Lyapunov function;

[0216] Step 1: Based on the defined error transformation Taking its derivative yields

[0217] (14)

[0218] (15)

[0219] The Lyapunov function is selected as follows:

[0220] (16)

[0221] based on and the designed virtual control signals Evaluation - Execution Update Rate and , The derivative with respect to time is

[0222] (17)

[0223] According to (17) and Lemma 3, we can obtain (18)-(20).

[0224] (18)

[0225] (19)

[0226] (20)

[0227] Furthermore, according to (17), we can further obtain:

[0228] (twenty one)

[0229] (twenty two)

[0230] Furthermore, by rearranging (17)-(22), we can obtain:

[0231] (twenty three)

[0232] in, .

[0233] Step 2: Based on the defined error transformation Taking its derivative, we get:

[0234] (twenty four)

[0235] (25)

[0236] By Lemma 2 and approximation as well as We can obtain:

[0237] (26)

[0238] (27)

[0239] The Lyapunov function is selected as follows:

[0240] (28)

[0241] Based on (24)-(27), and similar to (18)-(22), and the designed actual control signals Evaluation - Execution Update Rate and and parameter update rate , The derivative with respect to time can be summarized as follows:

[0242] (29)

[0243] According to (29) and Lemma 4, we can obtain (30) and (31):

[0244] (30)

[0245] (31)

[0246] According to (29) and Lemma 5, we can obtain (32) and (33):

[0247] (32)

[0248] (33)

[0249] Furthermore, according to (29) and Lemma 6, we can further obtain:

[0250] (34)

[0251] Where, constant , It is a matrix The smallest eigenvalue.

[0252] definition , as well as Furthermore, by rearranging (29)-(34), we can obtain:

[0253] (35)

[0254] in,

[0255] .

[0256] Based on Lemma 1 and (35), it can be seen that the controlled system is stable at the actual preset time, and ,in

[0257] ,

[0258] .

[0259] Furthermore, based on coordinate transformation and It can be known

[0260] (36)

[0261] As can be seen from (36), the proposed control method can guarantee the relative distance error. and relative heading angle error This does not violate the constraints imposed by the performance funnel, therefore the relative distance can be further explained. and relative heading angle It does not violate any constraints.

[0262] Specifically, in step 104, simulation verification is performed using Matlab software, considering a system consisting of four followers and one leader, where the relevant parameters of the nonholonomic mobile robot model are as follows;

[0263] , , ,

[0264] , , , ;

[0265] The leader's trajectory is set as follows:

[0266] ;

[0267] The relevant design parameters are selected as follows: , , , , , , , , , ;

[0268] The funnel boundary function is set as ;

[0269] The relevant initial conditions are selected as follows , , , , .

[0270] Simulation results are as follows Figure 3-7 As shown, the movement trajectories of the leader and follower robots are as follows: Figure 3 As shown, Figure 4 It shows the changes in relative distance and relative distance error. Figure 5 A trajectory diagram relative to the heading angle was plotted. Figure 6The control input trajectory diagram of the robot is shown. The comprehensive simulation results demonstrate that the method proposed in this invention can effectively ensure that the following robot completes the tracking task of the leader robot within a preset time, and that the relative position error and relative heading angle error remain within the preset range. This further verifies the comprehensive performance of the designed control strategy in ensuring system convergence speed, formation accuracy, and control stability.

[0271] Compared to traditional linear command filtering techniques, this invention, by designing a nonlinear preset-time command filter, not only avoids the problem of repeatedly differentiating the virtual control function but also significantly reduces the dependence on filter parameter adjustment, thereby improving the system's robustness to parameter uncertainties. Simultaneously, this filter possesses preset-time convergence characteristics, ensuring that the controlled system achieves state stability within a pre-set time, thus enhancing the predictability of control performance and the speed of time response.

[0272] Unlike existing safe formation control strategies based on control obstacle functions, this invention introduces funnel technology to transform the safety constraint problem, which originally involved the relative distance and relative heading angle between adjacent robots, into a unified constraint problem of relative distance error and relative heading angle error. This transformation not only avoids the complex construction of control obstacle functions and the difficulties in adjusting related parameters, but also effectively reduces the mathematical complexity and implementation difficulty of controller design. Furthermore, funnel technology possesses excellent convergent control characteristics, ensuring that errors always evolve within the desired range, thereby achieving safe cooperative operation of robot swarms in dynamic environments.

[0273] To further enhance the intelligence and optimality of the control strategy, this invention introduces an adaptive reinforcement learning mechanism to achieve continuous optimization of system performance. In the constructed reinforcement learning framework, a performance function is designed with formation error and control input as the main indicators. Through continuous interaction with the environment, the system learns the optimal control strategy in real time to minimize this performance function. This allows the system to maintain good learning ability and control performance in scenarios with unknown system dynamics or frequently changing environments.

[0274] The above description is merely a preferred embodiment of the present invention, intended to illustrate the principles and features of the invention, and not to limit the invention. For those skilled in the art, various modifications, substitutions, or equivalent improvements can be made without departing from the spirit and essence of the invention, and all such modifications should be considered to fall within the protection scope of the invention. Furthermore, it should be noted that the same or similar reference numerals and letters used in the drawings are used to denote corresponding or similar components; if a component has already been defined in a drawing, it will not be repeated in subsequent drawings.

[0275] The above description is merely a specific embodiment of the present invention, intended to aid in understanding the principles and technical solutions of the present invention, and is not intended to limit the scope of protection of the present invention. For those skilled in the art, any easily implemented modifications, substitutions, or equivalent variations made under the technical guidance disclosed in this invention should be considered to fall within the scope of protection of this invention.

Claims

1. A low-complexity, preset-time optimal formation control method for nonholonomic robots, characterized in that: Includes the following steps: Step 101: Use funnel technology to unify the collision avoidance and communication distance constraints between adjacent robots into formation error constraints; Step 102: Integrate preset time nonlinear command filtering techniques with adaptive parameters; Step 103: Combine generalized fuzzy neural networks to approximate the system uncertainty online, and use reinforcement learning mechanisms to optimize the control strategy in real time; Step 104: Implement low-complexity preset time optimal safe collision avoidance formation control for multiple robots.

2. The low-complexity preset-time optimal formation control method for a nonholonomic robot according to claim 1, characterized in that: Step 101 includes the following methods: Establish the first with unknown nonlinearity ( The dynamic model of a following nonholonomic mobile robot is as follows: (1) in, For robots Location coordinates, For robots The heading angle, For robots linear velocity, For robots angular velocity, For robots Control torque, robot The relevant dynamic matrix is ​​represented as follows: ； ； ； ； ， in, For robots The radius of the wheel, For robots The width of the car body is half. For robots The damping coefficient, For robots The parameters, and For robots The parameters, For robots The body weight, For robots The mass of a wheel, and For robots The parameters, and For robots Moment of inertia between components; The dynamic model of the leading mobile robot is as follows: (2) The following lemma is given to lay the theoretical foundation for subsequent controller design and stability analysis; Lemma 1: Consider a given... The system described, in which and ,make It is a continuous Lyapunov function, if ,in , , If the constant value indicates that the controlled system is stable at the preset time and the region of convergence is... The convergence time is ; Lemma 2: For any variable and defined in Continuous functions on And satisfy ( If ), then the inequality holds. Sum of equations Established; Lemma 3: For any variable and integers There exists a constant , making the inequality Established; Lemma 4: For any variable Sum of odd integers There are positive numbers and , making the inequality Established; Lemma 5: For any variable and parameters This makes the following inequalities true: Lemma 6: If the variable satisfy , If is a constant, then there exists a constant. , and This makes the following inequalities true: ， in, .

3. The low-complexity preset-time optimal formation control method for a nonholonomic robot according to claim 1, characterized in that: Step 101 also includes the following method: Define the relative distance between two adjacent non-holonomic mobile robots. and relative heading angle They are respectively and , where variables and ; To prevent collisions between robots and maintain communication links between them, the relative distance... Apply the following constraints: (3) in, This represents the minimum safe distance required to avoid collisions between two adjacent robots. This represents the maximum permissible distance between two adjacent robots to ensure continuous communication and network connectivity; furthermore, to avoid singularity issues, the following constraints are imposed on the relative heading angle: (4) in, It is the upper limit of the allowable relative heading angle deviation; Assume the desired relative distance between two adjacent robots The relative heading angle is And they satisfy and Therefore, the relative distance and relative heading angle errors can be expressed as: and To avoid the problems of high controller complexity and poor implementability caused by the introduction of complex control barrier functions in existing formation control schemes, funnel control technology is introduced and the following constraints are defined: (5) in, ( ) is the boundary function of the funnel, and the function First-order differentiable and ; Therefore, the initial value of the funnel boundary function is chosen as follows: and This ensures that the funnel constraint (5) always covers the relative distance constraint (3) and the relative heading angle constraint (4), thereby achieving integrated control of formation error constraint, collision avoidance safety constraint and communication constraint.

4. The low-complexity preset-time optimal formation control method for a nonholonomic robot according to claim 1, characterized in that: Step 102 includes the following methods: Define coordinate transformation as , , , , , ,in , , is the optimal virtual control signal The output uses the following nonlinear preset time command filter: (6) Among them, the filter parameters , and It is a constant. It is the ratio of even integers to odd integers, parameter yes The estimate and the estimation error is , It is a monotonically decreasing function and a constant. ,parameter The update rate , It is a positive number; The selected performance index function is: (7) in, and Represents the optimal virtual control signal and and The optimal actual control signal is given; therefore, based on the Bellman optimization principle, the following HJB equation is introduced to characterize the analytical solution structure of the optimal control problem: (8) when At that time, As the optimal virtual controller ,when At that time, As the optimal virtual controller Since the optimal value function corresponding to the left side of HJB equation (8) exists and is unique, the optimal virtual control signal and the actual control signal can be obtained by solving... Once obtained, it can be known that: ， ， ， ， ， ; However, due to the nonlinear term Since it is unknown, it cannot be directly used in controller design; therefore, to ensure that the designed controller can achieve the preset time stability and optimality of the controlled system, the nonlinear term is... and Decomposed into: ； ； in, , , ， ， ， Unknown nonlinear function and They are respectively: ； 。 5. The low-complexity preset-time optimal formation control method for a nonholonomic robot according to claim 4, characterized in that: In step 103, a generalized fuzzy neural network is used. Approximating the aforementioned unknown nonlinear function, we can obtain... Approximation error satisfy , For positive numbers, use and right An estimation is performed, and the estimation error is... , ; The update rate of a generalized fuzzy neural network is evaluated as follows: (9) Among them, matrix Design parameters It is a constant. yes A 3D identity matrix and design parameters satisfy ; The update rate design for implementing the generalized fuzzy neural network is as follows: (10) The optimal virtual control signal design is as follows: (11) Using generalized fuzzy neural networks and To identify the unknown nonlinear functions present in the system. and ,Right now , Approximation error and satisfy and , and For positive integers, define ,use right An estimation is performed, and the estimation error is... ; parameter The update rate is designed as follows: (12) in, Positive design parameters; The optimal actual control signal design is as follows: (13) in, , .

6. The low-complexity preset-time optimal formation control method for a nonholonomic robot according to claim 5, characterized in that: In step 103, based on the designed virtual control signal and actual control signal, the evaluation-execution update rate and the adaptive parameter update rate, the preset time stability of the closed-loop system is proved by selecting the Lyapunov function; Step 1: Based on the defined error transformation Taking its derivative yields (14) (15) The Lyapunov function is selected as follows: (16) based on and the designed virtual control signals Evaluation - Execution Update Rate and , The derivative with respect to time is: (17) According to (17) and Lemma 3, we can obtain (18)-(20). (18) (19) (20) Furthermore, according to (17), we can further obtain: (21) (22) Furthermore, by rearranging (17)-(22), we can obtain: (23) in, ; Step 2: Based on the defined error transformation Taking its derivative, we get: (24) (25) By Lemma 2 and approximation as well as We can obtain: (26) (27) The Lyapunov function is selected as follows: (28) Based on (24)-(27), and similar to (18)-(22), and the designed actual control signals Evaluation - Execution Update Rate and and parameter update rate , The derivative with respect to time can be summarized as follows: (29) According to (29) and Lemma 4, we can obtain (30) and (31): (30) (31) According to (29) and Lemma 5, we can obtain (32) and (33): (32) (33) Furthermore, according to (29) and Lemma 6, we can further obtain: (34) Where, constant , It is a matrix The smallest eigenvalue; definition , as well as Furthermore, by rearranging (29)-(34), we can obtain: (35) in, Based on Lemma 1 and (35), it can be seen that the controlled system is stable at the actual preset time, and ,in ， 。 Furthermore, based on coordinate transformation and It can be known (36) As can be seen from (36), the proposed control method can guarantee the relative distance error. and relative heading angle error This does not violate the constraints imposed by the performance funnel, therefore the relative distance needs further explanation. and relative heading angle It does not violate any constraints.

7. The low-complexity preset-time optimal formation control method for a nonholonomic robot according to claim 1, characterized in that: In step 104, simulation verification is performed using Matlab software. Consider a system consisting of four followers and one leader. The parameters of the nonholonomic mobile robot model are as follows. ， ， ， ， ， ， ； The leader's trajectory is set as follows: The design parameters are selected as follows: , , , , , , , , , ; The funnel boundary function is set as ; The initial conditions are selected as follows , , , , .

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