Fixed time formation control method for incomplete constraint robot formation
Through the fixed-time formation control method of non-holonomic constrained robot formation, the follower perception module and observer are used to calculate the leader's speed, which solves the formation breakdown problem caused by communication interruption and leader speed uncertainty, and improves the control accuracy and energy utilization.
Patent Information
- Application Number
- CN202510859638.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-25
- Publication Date
- 2025-09-26
AI Technical Summary
Existing non-holonomic constrained robot formation control methods are prone to problems such as formation breakdown, low control accuracy, poor real-time performance and high energy consumption when communication is interrupted and the leader's speed information is unknown.
Initial information is obtained through the perception modules of each follower, the leader's speed is calculated using an observer, and the linear and angular velocities are calculated under the constraints of the hyperbolic tangent function to achieve formation control within a fixed time. Energy optimization is performed by combining the adaptive law estimate and the barrier function.
The accuracy and real-time performance of robot formation control are improved, energy consumption is reduced, and formation stability is ensured in the event of communication interruption and uncertainty of the leader's speed.
Smart Images
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Abstract
Description
Technical Field
[0001] The present application relates to the field of robot formation control, and in particular to a fixed-time formation control method for a non-holonomically constrained robot formation. Background Art
[0002] Non-holonomic robots have achieved significant development worldwide due to their outstanding performance in numerous application scenarios. They demonstrate unique advantages, particularly when performing high-risk missions in extreme environments. They are playing an increasingly critical role in intelligence gathering, resource exploration, and military operations, where human access is dangerous or difficult. However, despite these advances, non-holonomic robots still have significant shortcomings. For example, they can be easily affected by communication disruptions caused by adverse weather conditions or enemy information warfare activities. Impaired communications can make it difficult for non-holonomic robots to obtain and utilize the precise position and orientation data of their surrounding companions, potentially leading to a breakdown in formation.
[0003] In some cases, a variety of control technologies have been applied to the formation control of non-holonomic constrained mobile robots, but the following problems still exist: First, most control methods do not fully consider the formation control problem under communication denial conditions. For example, communication interruption caused by severe weather conditions or enemy information warfare will lead to the paralysis of the entire formation system, and then cause the failure of the mission; Second, most control methods only use the upper bound information of the navigator's speed for estimation when the navigator's speed information is unknown. Obviously, such methods are very conservative and have poor real-time performance; Third, large logarithmic control methods often only focus on the speed of the formation and ignore the energy consumption problem. However, for robots, the energy carried by the robots themselves is very limited. Summary of the Invention
[0004] The purpose of this application is to provide a fixed-time formation control method for a non-holonomic constrained robot formation, which can improve the control accuracy, real-time performance and energy utilization of the robots.
[0005] To achieve the above objectives, this application provides the following solutions:
[0006] This application provides a fixed-time formation control method for a non-holonomic constrained robot formation, comprising:
[0007] Determine range error constraints, azimuth error constraints, range boundaries, and azimuth boundaries;
[0008] Using the perception modules of each follower, the initial information of each follower at the current moment is obtained; the initial information includes: position, heading angle, relative distance from the navigator, and relative azimuth angle from the navigator; the follower and the navigator are both robots;
[0009] According to the range error constraint, azimuth error constraint, range boundary, azimuth boundary and the relative distance between each follower and the leader at the current moment, a preset performance conversion and normalization process is used to obtain the update rate of the error variable at the current moment, the barrier function at the current moment and the adaptive law estimate at the current moment;
[0010] Based on the initial information, an observer is used to calculate the speed of the leader corresponding to each follower at the current moment;
[0011] According to the error variable at the current moment, the obstacle function at the current moment, the update rate of the adaptive law estimate at the current moment, and the speed of the leader corresponding to each follower at the current moment, the linear velocity and angular velocity of the follower at the next moment are calculated under the constraint of the hyperbolic tangent function, and the followers are controlled to complete the formation control within a fixed time.
[0012] According to the specific embodiments provided in this application, this application has the following technical effects:
[0013] The present application provides a fixed-time formation control method for a non-holonomic constrained robot formation, which obtains the initial information of each follower at the current moment through the follower's respective perception module, effectively avoiding the problem of being unable to complete formation control under communication denial conditions, and each follower performs subsequent calculations based on the information obtained by its respective perception module, thereby improving the accuracy of the acquired data and thus improving the control accuracy of the robot; based on the initial information, an observer is used to calculate the speed information of each follower corresponding to the leader, and real-time estimation is performed so that each follower can calculate the speed information of its corresponding leader, thereby improving the real-time performance of the robot in estimating the leader's speed information; through the hyperbolic tangent function for constraint, the linear velocity and angular velocity of the follower at the next moment are calculated based on the current moment distance tracking error variable, the current moment azimuth tracking error variable, the current moment obstacle function, the current moment speed of the leader corresponding to each follower and the estimated value of the adaptive law, while ensuring the robot speed, energy use is constrained, saving energy consumption and improving the energy utilization rate of the robot. BRIEF DESCRIPTION OF THE DRAWINGS
[0014] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.
[0015] Figure 1 A flowchart of a fixed-time formation control method for a non-holonomic constrained robot formation provided in one embodiment of the present application.
[0016] Figure 2 A schematic structural diagram of a fixed-time formation control system for a non-holonomic constrained robot formation provided in one embodiment of the present application. DETAILED DESCRIPTION
[0017] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.
[0018] In complex formation control, the primary considerations are the safety of the robots themselves and the range limitations of their sensor devices. This is crucial to ensure that the robots can interact with each other and avoid collisions within their effective range. Secondly, the robots themselves have very limited energy resources; insufficient power can lead to failures in the formation system. Therefore, designing a controller that can both conserve energy and improve robot control accuracy is of great research interest.
[0019] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.
[0020] In an exemplary embodiment, Figure 1 As shown, a fixed-time formation control method for a non-holonomic constrained robot formation is provided. The method is executed by a computer device, specifically a computer device such as a terminal or a server, or a terminal and a server. In the embodiment of the present application, the method is applied to a server as an example for description, and includes the following steps S1 to S5. Among them:
[0021] Step S1: Determine the range error constraint, azimuth error constraint, range boundary, and azimuth boundary.
[0022] Furthermore, step S1 specifically includes: setting formation control constraints; the formation control constraints include: distance constraints, azimuth constraints, expected values of the relative distance between the two robots, and expected values of the relative azimuth between the two robots; based on the formation control constraints, determining distance error constraints, azimuth error constraints, distance boundaries, and azimuth boundaries.
[0023] Specifically, the calculation formula for defining the distance error is:
[0024]
[0025] The calculation formula for the azimuth error is defined as:
[0026]
[0027] Among them, e df is the distance error; d f is the relative distance between the two robots; is the expected value of the relative distance between the two robots; is the azimuth error; is the relative orientation angle between the two robots; is the expected value of the relative orientation angle between the two robots.
[0028] Specifically, the distance constraint is: 0<d min,f <d f <d max,f , where d min,f The minimum distance for the follower to avoid collision; d f is the relative distance between the two robots; d max,f The maximum distance for followers to maintain communication connectivity.
[0029] The angle constraints are: in, is the maximum azimuth angle between the leader and the follower; is the relative orientation angle between the two robots.
[0030] Furthermore, from the calculation formula of distance constraint and distance error, the distance error constraint can be obtained as: The azimuth error constraint is:
[0031] Step S2: Using the perception modules of each follower, obtain the initial information of each follower at the current moment; the initial information includes: position, heading angle, relative distance from the navigator, and relative azimuth angle from the navigator; both the follower and the navigator are robots.
[0032] Specifically, the calculation formula for the robot's position and heading angle is:
[0033]
[0034] in, represents the linear velocity of the i-th robot in the X-axis direction, where i = 1, 2, ..., N; v i represents the linear velocity of the i-th robot; ψ i represents the heading angle of the i-th robot; represents the linear velocity of the i-th robot in the Y-axis direction; w i represents the angular velocity of the i-th robot.
[0035] Specifically, the calculation formula for determining the robot formation model is:
[0036]
[0037] Among them, d f is the relative distance between the follower and the leader; x f The position of the follower in the X-axis direction; x l is the position of the navigator in the X-axis direction; y f The position of the follower in the Y-axis direction; l is the position of the navigator in the Y-axis direction; is the azimuth of the follower; ψ f is the heading angle of the follower.
[0038] Step S3: Based on the distance error constraint, azimuth error constraint, distance boundary, azimuth boundary and the relative distance between each follower and the leader at the current moment, a preset performance conversion and normalization process is used to obtain the update rate of the error variable at the current moment, the barrier function at the current moment and the adaptive law estimate at the current moment.
[0039] Furthermore, the error variable at the current moment includes: the distance error variable at the current moment and the azimuth error variable at the current moment; the obstacle function at the current moment includes: the distance obstacle function at the current moment and the azimuth obstacle function at the current moment. Step S3 specifically includes the following steps:
[0040] Step S31: According to the range error constraint and the azimuth error constraint, a preset performance conversion is adopted to obtain the range error after conversion at the current moment and the azimuth error after conversion at the current moment.
[0041] Specifically, based on the control method of the preset performance function, the distance error constraint and the azimuth error constraint are transformed into asymmetric constraints with preset performance, and the distance error constraint after transformation at the current moment and the azimuth error constraint after transformation at the current moment are obtained. The distance error constraint after transformation at the current moment is: -χ df β df <e df <β df , The azimuth error constraint after conversion at the current moment: Among them, χ df represents the distance boundary function, is the azimuth boundary function.
[0042] Step S32: normalizing the converted distance error and the converted azimuth error at the current moment to obtain a current distance error variable and a current azimuth error variable.
[0043] Furthermore, the calculation formula of the distance error variable at the current moment is:
[0044]
[0045] β df =(β df,0 -β df,∞ )exp(-ν df t)+β df,∞ .
[0046]
[0047] The calculation formula of the azimuth error variable at the current moment is:
[0048]
[0049] Among them, df (t) is the follower distance error variable at time t; e df is the distance error of the follower at time t; β df is the follower distance performance function at time t; β df,0 is the difference between the maximum distance and the expected distance; β df,∞ is the steady-state boundary of the distance performance function; ν df is the attenuation factor of the distance performance function; time t is the current time; d max,f The maximum distance for followers to maintain communication connectivity; is the expected value of the relative distance between the two robots; is the follower azimuth error variable at time t; is the azimuth error of the follower at time t; is the follower azimuth performance function at time t; is the difference between the maximum azimuth and the expected azimuth; is the steady-state boundary of the azimuth performance function; is the attenuation factor of the azimuth performance function; is the maximum azimuth angle between the leader and the follower; is the expected value of the relative orientation angle between the two robots.
[0050] Specifically, according to the distance error constraint and the azimuth error constraint after the current moment transformation, a normalized transformation is performed to obtain the distance error variable constraint and the azimuth error variable constraint at the current moment. df <ζ df (t)<1, the azimuth error variable constraint at the current moment:
[0051] Step S33: Determine the range of the current time range error variable and the range of the current time azimuth error variable according to the distance boundary and the azimuth boundary.
[0052] Step S34: Determine the current moment distance barrier function and the current moment azimuth barrier function according to the range of the current moment distance error variable and the range of the current moment azimuth error variable.
[0053] Furthermore, the expression of the distance barrier function at the current moment is:
[0054]
[0055] The expression of the azimuth barrier function at the current moment is:
[0056]
[0057] Among them, B df is the distance barrier function of the follower at the current moment; is the upper boundary of the follower distance; ζ df is the lower boundary of the follower distance; df is the distance error variable of the follower at the current moment; is the follower's azimuth obstacle function at the current moment; is the upper boundary of the follower’s azimuth; is the lower boundary of the follower’s azimuth; is the azimuth error variable of the follower at the current moment.
[0058] Step S35: Calculate the update rate of the adaptive law estimation value at the current moment based on the current distance error variable, the current azimuth error variable, the distance boundary, the azimuth boundary, and the relative distance between each follower and the leader at the current moment.
[0059] Furthermore, the calculation formula of the estimated value of the adaptive law at the current moment is:
[0060]
[0061] in, is the update rate of the estimated value of the adaptive law at the current moment; γ and κ i are all design parameters, κ i is the design parameter of the i-th robot; df is the correlation function of the distance error variable; β df is the follower distance performance function at the current moment; is the correlation function of the azimuth error variable; is the follower azimuth performance function at the current moment; df is the relative distance between a follower and the leader at the current moment; is the estimated value of the adaptive law at the current moment; is the upper boundary of the follower distance; ζ df is the lower boundary of the follower distance; df is the distance error variable of the follower at the current moment; is the upper boundary of the follower’s azimuth; is the lower boundary of the follower’s azimuth; is the azimuth error variable of the follower at the current moment.
[0062] Step S4: Based on the initial information, an observer is used to calculate the speed of the leader corresponding to each follower at the current moment.
[0063] Furthermore, step S4 includes: calculating the position of the navigator corresponding to each follower at the current moment according to the initial information; and calculating the speed of the navigator corresponding to each follower at the current moment using an observer according to the position of the navigator corresponding to each follower at the current moment.
[0064] Furthermore, the calculation formula for the position of the leader corresponding to each follower at the current moment is:
[0065]
[0066] The calculation formula for the speed of the leader corresponding to each follower at the current moment is:
[0067]
[0068] Among them, x l is the X-axis position of the leader corresponding to a follower at the current moment; f is the X-axis position of a follower at the current moment; d f is the relative distance between a follower and the leader at the current moment; ψ f is the heading angle of a follower at the current moment; is the relative azimuth between a follower and the leader at the current moment; l The Y-axis position of the leader corresponding to a follower at the current moment; f The Y-axis position of a follower at the current moment; is the second state and parameter ε of the observer corresponding to a follower at the current moment f The ratio of is used to realize the observation value of the corresponding navigator's speed; η 2f is the second state of the observer at the current moment corresponding to a follower; ε f is the adjustment parameter; is the derivative of the leader’s position; is the error of the observer of a follower.
[0069] Specifically, f =η 2f +μ f η 1f , Υ f is the sum of the first and second states of the observer of a follower. From the calculation formula of the speed of the leader corresponding to each follower at the current moment, we can know that is the second state and parameter ε of the observer corresponding to a follower at the current moment f The ratio of is used to realize the observation value of the corresponding leader's speed, and the estimation error is and is a parameter.
[0070] Specifically, the observer is a high-gain observer. The relevant expression of the observer is:
[0071]
[0072] Among them, ε f Parameters designed for designers, is the derivative of the first state of the observer of a follower; η 2f is the second state of the observer of a follower; is the derivative of the second state of the observer of a follower; μ f is a parameter, μ f is chosen so that s 2 +μ f s+1 is Hurwitz's; η 1f is the first state of the observer of a follower; p l The location information of the navigator of a follower;.
[0073] Step S5: Based on the error variable at the current moment, the obstacle function at the current moment, the update rate of the adaptive law estimate at the current moment, and the speed of the leader corresponding to each follower at the current moment, the linear velocity and angular velocity of the follower at the next moment are calculated under the constraint of the hyperbolic tangent function, and the followers are controlled to complete the formation control within a fixed time.
[0074] Furthermore, the formula for calculating the linear velocity of the follower at the next moment is:
[0075]
[0076] The formula for calculating the angular velocity of the follower at the next moment is:
[0077]
[0078] Among them, v f is the linear velocity of the follower at the next moment; α vf The virtual control line speed of the follower; is the relative azimuth between a follower and the leader at the current moment; g df and are all controller parameters; B df is the distance barrier function of the follower at the current moment; is the second state and parameter ε of the observer corresponding to a follower at the current moment f The ratio of is used to realize the observation value of the corresponding navigator’s speed; Γ 1f for Representative symbol of; is the derivative of the follower distance performance function at the current moment; e df is the distance error; σ f is the adjustment parameter of the tanh function; ψ f is the heading angle of a follower at the current moment; is the relative azimuth between a follower and the leader at the current moment; w f is the angular velocity of the follower at the next moment; α wf The virtual control angular velocity of the follower; is the follower's azimuth obstacle function at the current moment; is the derivative of the follower's azimuth performance function at the current moment; is the azimuth error; Γ 2f for 's representative symbol.
[0079] In a specific embodiment, the present application is further described using a multi-robot formation consisting of three followers and one navigator as an example. In this embodiment, the multi-robot formation includes three follower nodes (robot i (i = 1, 2, 3, 4) and one navigator node (robot 0). The followers measure their own position, heading angle, and velocity information through their own sensing modules. At the same time, the observer calculates the position of the navigator corresponding to each follower, enabling each follower to reconstruct the position of the navigator, while being unable to measure the velocity information of the leader.
[0080] The specific steps are as follows: the robot formation model is determined by the calculation formula of the robot formation model, and then the constrained formation error is determined through step S3, and then converted into a situation with performance constraints through steps S31-S34. Then, based on the initial information, the position of the navigator corresponding to each follower at the current moment is calculated, and the speed of the navigator is observed in real time through the observer. Finally, the fixed-time formation device is designed based on the information obtained.
[0081] The relevant parameters are as follows: l =60*sin(0.02t),y l =-60*cos(0.01t)+60, select the maximum communication distance as d max,f =5m, the minimum collision avoidance distance is d min,f =3m, the expected distance is The expected angle information is The performance function is:
[0082]
[0083] parameter (f=1,2,3),ε1=ε2=ε3=0.5,μ1=μ2=μ3=20, the initial value of the system q0=[0,0,0] T ,q1=[-4.2,0,π / 4] T ,q2=[-2.5,-3,0] T ,q3=[-4,-1,-π / 9] T , where q0 is the position and heading information of the leader; q1 is the position and heading information of the first follower; q2 is the position and heading information of the second follower; q3 is the position and heading information of the third follower; η 1f =[0,0] T ,η 2f =[0,0] T .
[0084] The beneficial effects of the fixed-time formation control method for a non-holonomic constrained robot formation proposed in this application are mainly manifested in:
[0085] The present application provides a fixed-time formation control method for a non-holonomic constrained robot formation, which obtains the initial information of each follower at the current moment through the follower's respective perception module, effectively avoiding the problem of being unable to complete formation control under communication denial conditions, and each follower performs subsequent calculations based on the information obtained by its respective perception module, thereby improving the accuracy of the acquired data and thus improving the control accuracy of the robot; based on the initial information, an observer is used to calculate the speed information of each follower corresponding to the leader, and real-time estimation is performed so that each follower can calculate the speed information of its corresponding leader, thereby improving the real-time performance of the robot in estimating the leader's speed information; through the hyperbolic tangent function for constraint, the linear velocity and angular velocity of the follower at the next moment are calculated based on the current moment distance tracking error variable, the current moment azimuth tracking error variable, the current moment obstacle function, the current moment speed of the leader corresponding to each follower and the estimated value of the adaptive law, while ensuring the robot speed, energy use is constrained, saving energy consumption and improving the energy utilization rate of the robot.
[0086] Based on the same inventive concept, embodiments of the present application also provide a fixed-time formation control system for a nonholonomic constrained robot formation. The solution to the problem provided by this system is similar to the solution described in the aforementioned method. Therefore, the specific limitations of the embodiments of the fixed-time formation control system for one or more nonholonomic constrained robot formations provided below can be found in the limitations of the fixed-time formation control method for a nonholonomic constrained robot formation described above and will not be repeated here.
[0087] In an exemplary embodiment, a fixed-time formation control system for a nonholonomic constrained robot formation is provided, comprising: a nonholonomic constrained robot system module, a formation distance and angle system module, a leader position reconstruction module, a high-gain observer module, a controller module, and an adaptive law module.
[0088] The distance and angle system module of the formation is used to set the formation control constraints and determine the distance error constraint, azimuth error constraint, distance boundary and azimuth boundary based on the formation control constraints; the formation control constraints include: distance constraint, azimuth constraint, the expected value of the relative distance between the two robots and the expected value of the relative azimuth between the two robots.
[0089] The perception module is used to obtain the initial information of each follower at the current moment; the initial information includes: position, heading angle, relative distance from the navigator, and relative azimuth to the navigator; the followers and the navigator are both robots.
[0090] The navigator position reconstruction module is used to calculate the position of the navigator corresponding to each follower at the current moment based on the initial information.
[0091] The high-gain observer module is used to calculate the speed of the navigator corresponding to each follower at the current moment using an observer according to the position of the navigator corresponding to each follower at the current moment.
[0092] The adaptive law module is used to obtain the update rate of the current error variable, the current obstacle function and the estimated value of the adaptive law at the current moment by using preset performance conversion and normalization processing based on the range error constraint, azimuth error constraint, range boundary, azimuth boundary and the relative distance between each follower and the leader at the current moment.
[0093] The controller module is used to calculate the linear velocity and angular velocity of the follower at the next moment under the constraint of the hyperbolic tangent function based on the error variable at the current moment, the obstacle function at the current moment, the estimated value of the adaptive law at the current moment and the speed of the leader corresponding to each follower at the current moment.
[0094] The non-holonomic constraint robot system module is used to receive the linear velocity and angular velocity of the follower at the next moment calculated by the controller module, and control the follower to complete formation control within a fixed time.
[0095] The input end of the non-holonomic constraint robot system module is connected to the output end of the controller module. The output end of the non-holonomic constraint robot is respectively connected to the input ends of the formation distance and angle constraint module, the navigator position reconstruction module, and the high-gain observer module. The output end of the perception module is connected to the input end of the navigator module. The input end of the controller module is respectively connected to the output ends of the formation distance and angle constraint module and the adaptive law module. The output end of the formation distance and angle constraint module is connected to the input end of the adaptive law module.
[0096] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0097] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.
Claims
1. A fixed-time formation control method for a nonholonomically constrained robot formation, characterized in that: The fixed-time formation control method of the non-holonomic constrained robot formation comprises: Determine range error constraints, azimuth error constraints, range boundaries, and azimuth boundaries; Obtaining initial information of each follower at the current moment; the initial information includes: position, heading angle, relative distance from the navigator, and relative azimuth to the navigator; the follower and the navigator are both robots; the initial information is obtained by the followers using their respective perception modules; According to the range error constraint, azimuth error constraint, range boundary, azimuth boundary and the relative distance between each follower and the leader at the current moment, a preset performance conversion and normalization process is used to obtain the update rate of the error variable at the current moment, the barrier function at the current moment and the adaptive law estimate at the current moment; Based on the initial information, an observer is used to calculate the speed of the leader corresponding to each follower at the current moment; According to the error variable at the current moment, the obstacle function at the current moment, the update rate of the adaptive law estimate at the current moment, and the speed of the leader corresponding to each follower at the current moment, the linear velocity and angular velocity of the follower at the next moment are calculated under the constraint of the hyperbolic tangent function, and the followers are controlled to complete the formation control within a fixed time.
2. The fixed-time formation control method for a nonholonomic constrained robot formation according to claim 1, characterized in that: Determine the range error constraint, azimuth error constraint, range boundary, and azimuth boundary, including: Setting formation control constraints; the formation control constraints include: distance constraint, azimuth constraint, expected value of relative distance between two robots, and expected value of relative azimuth between two robots; According to the formation control constraints, a range error constraint, an azimuth error constraint, a range boundary, and an azimuth boundary are determined.
3. The fixed-time formation control method for a nonholonomic constrained robot formation according to claim 2, characterized in that: The distance error constraint is: The azimuth error constraint is: Among them, d min,f The minimum distance for the follower to avoid collision; is the expected value of the relative distance between the two robots; e df is the distance error; d max,f The maximum distance for followers to maintain communication connectivity; is the maximum azimuth angle between the leader and the follower; is the expected value of the relative orientation angle between the two robots; is the azimuth error.
4. The fixed-time formation control method for a nonholonomic constrained robot formation according to claim 1, characterized in that: The error variables at the current moment include: the distance error variable at the current moment and the azimuth error variable at the current moment; the obstacle function at the current moment includes: the distance obstacle function at the current moment and the azimuth obstacle function at the current moment; According to the distance error constraint, azimuth error constraint, distance boundary, azimuth boundary and the relative distance between each follower and the leader at the current moment, the preset performance conversion and normalization processing are used to obtain the update rate of the error variable at the current moment, the barrier function at the current moment and the adaptive law estimate at the current moment, specifically including: According to the range error constraint and the azimuth error constraint, a preset performance conversion is used to obtain a range error after conversion at the current moment and an azimuth error after conversion at the current moment; According to the distance error converted at the current moment and the azimuth error converted at the current moment, normalization processing is performed to obtain the distance error variable at the current moment and the azimuth error variable at the current moment; Determining a range of a current time range error variable and a range of a current time azimuth error variable according to the distance boundary and the azimuth boundary; Determine the current moment distance barrier function and the current moment azimuth barrier function according to the range of the current moment distance error variable and the range of the current moment azimuth error variable; The update rate of the adaptive law estimation value at the current moment is calculated according to the current moment distance error variable, the current moment azimuth error variable, the distance boundary, the azimuth boundary and the relative distance between each follower and the leader at the current moment.
5. The fixed-time formation control method for a nonholonomic constrained robot formation according to claim 4, characterized in that: The calculation formula of the distance error variable at the current moment is: b df =(β df,0 -b df,∞ )exp(-n df t)+b df,∞ ; The calculation formula of the azimuth error variable at the current moment is: Among them, df (t) is the follower distance error variable at time t; e df is the distance error of the follower at time t; β df is the follower distance performance function at time t; β df,0 is the difference between the maximum distance and the expected distance; β df,∞ is the steady-state boundary of the distance performance function; ν df is the attenuation factor of the distance performance function; time t is the current time; d max,f The maximum distance for followers to maintain communication connectivity; is the expected value of the relative distance between the two robots; is the follower azimuth error variable at time t; is the azimuth error of the follower at time t; is the follower azimuth performance function at time t; is the difference between the maximum azimuth and the expected relative azimuth; is the steady-state boundary of the azimuth performance function; is the attenuation factor of the azimuth performance function; is the maximum azimuth angle between the leader and the follower; is the expected value of the relative orientation angle between the two robots.
6. The fixed-time formation control method for a nonholonomic constrained robot formation according to claim 4, characterized in that: The expression of the distance barrier function at the current moment is: The expression of the azimuth barrier function at the current moment is: Among them, B df is the distance barrier function of the follower at the current moment; is the upper boundary of the follower distance; ζ df is the lower boundary of the follower distance; df is the distance error variable of the follower at the current moment; is the follower's azimuth obstacle function at the current moment; is the upper boundary of the follower’s azimuth; is the lower boundary of the follower’s azimuth; is the azimuth error variable of the follower at the current moment.
7. The fixed-time formation control method for a nonholonomically constrained robot formation according to claim 4, characterized in that: The calculation formula for the update rate of the adaptive law estimate at the current moment is: in, is the update rate of the estimated value of the adaptive law at the current moment; γ and κ i are all design parameters, κ i is the design parameter of the i-th robot; df is the correlation function of the distance error variable; β df is the follower distance performance function at the current moment; is the correlation function of the azimuth error variable; is the follower azimuth performance function at the current moment; d f is the relative distance between a follower and the leader at the current moment; is the estimated value of the adaptive law at the current moment; is the upper boundary of the follower distance; ζ df is the lower boundary of the follower distance; df is the distance error variable of the follower at the current moment; is the upper boundary of the follower’s azimuth; is the lower boundary of the follower’s azimuth; is the azimuth error variable of the follower at the current moment.
8. The fixed-time formation control method for a nonholonomic constrained robot formation according to claim 1, characterized in that: Based on the initial information, an observer is used to calculate the speed of the leader corresponding to each follower at the current moment, specifically including: Calculate the current position of the leader corresponding to each follower based on the initial information; According to the position of the navigator corresponding to each follower at the current moment, the observer is used to calculate the speed of the navigator corresponding to each follower at the current moment.
9. The fixed-time formation control method for a nonholonomic constrained robot formation according to claim 8, characterized in that: The calculation formula for the current position of each follower corresponding to the leader is: The calculation formula for the speed of the leader corresponding to each follower at the current moment is: Among them, x l is the X-axis position of the leader corresponding to a follower at the current moment; f is the X-axis position of a follower at the current moment; d f is the relative distance between a follower and the leader at the current moment; ψ f is the heading angle of a follower at the current moment; is the relative azimuth between a follower and the leader at the current moment; l The Y-axis position of the leader corresponding to a follower at the current moment; f The Y-axis position of a follower at the current moment; is the second state and parameter ε of the observer corresponding to a follower at the current moment f The ratio of is used to realize the observation value of the corresponding navigator's speed; η 2f is the second state of the observer at the current moment corresponding to a follower; ε f To adjust the parameters; is the derivative of the leader’s position; is the error of the observer of a follower.
10. The fixed-time formation control method for a nonholonomic constrained robot formation according to claim 9, characterized in that: The formula for calculating the linear velocity of the follower at the next moment is: The formula for calculating the angular velocity of the follower at the next moment is: Among them, v f is the linear velocity of the follower at the next moment; α vf The virtual control line speed of the follower; is the relative azimuth between a follower and the leader at the current moment; g df and are all controller parameters; B df is the distance barrier function of the follower at the current moment; is the second state and parameter ε of the observer corresponding to a follower at the current moment f The ratio of is used to realize the observation value of the corresponding navigator’s speed; Γ 1f for Representative symbol of; is the derivative of the follower distance performance function at the current moment; e df is the distance error; σ f is the adjustment parameter of the tanh function; ψ f is the heading angle of a follower at the current moment; is the relative azimuth between a follower and the leader at the current moment; w f is the angular velocity of the follower at the next moment; α wf The virtual control angular velocity of the follower; is the follower's azimuth obstacle function at the current moment; is the derivative of the follower's azimuth performance function at the current moment; is the azimuth error; Γ 2f for 's representative symbol.