CN111208829B - Multi-mobile-robot formation method based on distributed preset time state observer - Google Patents
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Abstract
The invention discloses a multi-mobile-robot formation method based on a distributed preset time state observer, which belongs to the technical field of multi-mobile-robot cooperative control, and the multi-mobile-robot formation method based on the distributed preset time state observer can be used for directly observing the real formation error value of a slave mobile robot and the position, angle and angular speed of a host, can be used for carrying out offline setting on the convergence time of the observer in advance, and can ensure the accuracy, flexibility and safety of the observation effect; the mobile robot formation controller also uses a preset time algorithm, so that the time for completing formation of the formation can be ensured to be preset offline; meanwhile, the relative position and angle between the mobile robots are obtained by using a GPS (global positioning system), a laser radar and an inertial measurement unit (comprising an accelerometer, a gyroscope and a magnetometer), so that high precision can be ensured, the observed value of an observer is ensured to be closer to an actual value, and the formation effect of multiple mobile robots is improved.
Description
Technical Field
The invention belongs to the technical field of multi-mobile-robot cooperative control, and particularly relates to a multi-mobile-robot formation method based on a distributed preset time state observer.
Background
The limited capabilities of the single mobile robot in the aspects of information acquisition, processing, autonomous control and planning and the like make the single mobile robot not capable of well meeting the task requirements in some large and complex task environments and spaces. The multi-mobile robot system is a set consisting of a plurality of mobile robots with independent and autonomous capabilities, which are integrated to form a robot formation, are coordinated with each other and can avoid conflicts.
The multi-mobile robot system has the characteristics of distributivity in the aspects of space, time, information, resources, functions and the like, and has the characteristics of complementarity and redundancy in addition to the aspects of time and space, thereby showing the obvious advantages of the multi-mobile robot system: the multi-mobile robot system can greatly enhance the working capacity, greatly improve the working efficiency, enlarge the function and working range and enhance the robustness and fault tolerance of the system.
Common cooperative control methods at present comprise a leader following method, a behavior-based method, a virtual structure method, a graph theory-based method, an artificial potential field method and the like; collaborative architectures are divided into centralized and distributed.
In the centralized architecture, the master mobile robot needs to communicate with all the slave mobile robots, so that the working capacity and the load capacity of the master mobile robot are higher; under a distributed architecture, the communication topology of the whole multi-mobile robot can be described by using a directed graph or an undirected graph, the slave mobile robot only communicates with the adjacent slave mobile robots to obtain local target information, and the local target information and the local information are depended on to make adjustment according to the local information and the local information in an intelligent and autonomous manner, so that the next behavior action of the slave mobile robot is updated, and finally a common expected task target is realized.
In the distributed formation control of a plurality of mobile robots, a mobile robot model has the characteristics of nonlinearity and underactuation, so that the design of a distributed formation controller becomes a main difficulty. The distributed state observer can help all slave mobile robots to obtain the state information of the master mobile robot, so that the complex distributed formation control problem is simplified into a single mobile robot control problem, and the design difficulty of the distributed formation controller is greatly reduced.
In the existing research, the observer and the controller are mostly designed to be gradual time, limited time and limited time convergence. Wherein the asymptotic time takes infinity to converge to the target value; the limited time needs to depend on the initial state condition of the whole system; the convergence time of the finite time cannot be set arbitrarily. The observer and the controller are designed to ensure that the system state error is converged within a preset time, so that the whole multi-mobile robot can achieve a good formation control effect.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a multi-mobile-robot formation method based on a distributed preset time state observer, which realizes the cooperative formation of the preset time of multiple mobile robots by means of the design of the distributed preset time state observer and the design of a preset time mobile robot controller.
The technical scheme is as follows: in order to achieve the purpose, the invention provides the following technical scheme:
the multi-mobile-robot formation method based on the distributed preset time state observer comprises the following steps:
step 1) kinematic modeling: establishing a kinematic equation of the multi-mobile robot according to the operational characteristics of the multi-mobile robot;
step 2) communication topology description: establishing a communication network architecture among the multiple mobile robots, and constructing a master-slave architecture of the multiple mobile robots;
step 3), designing a state observer: designing a distributed preset time state observer to realize that the slave computer obtains an observed value of the state of the host computer within preset time;
step 4), designing a formation controller: and inputting the observed values into a multi-mobile-robot formation controller so as to realize the preset time cooperative formation of the multi-mobile-robot.
Further, in step 1), the kinematic modeling is that the mobile robot selects a wheeled robot moving under a two-dimensional plane of a global coordinate system, and a kinematic equation of the wheeled robot can be described as follows:
wherein i is the number of the mobile robot; n is a normal number and represents the number of the multiple mobile robots; Δ = {1,2,.., N } is a set of multiple mobile robot numbers; x is the number of i ,y i Position information for the ith mobile robot; theta i Representing a course angle of the ith mobile robot; v. of i ,ω i For the control input, the speed and the rotation angular speed of the ith mobile robot are represented respectively.
Further, in step 2), the communication topology describes: establishing a master-slave framework of N +1 multiple mobile robots, and setting one mobile robot as a host, wherein the serial number of the mobile robot is 0; the rest N mobile robots are used as slave machines, the serial number of the slave machines is i, i belongs to delta, and the slave machines are subjected to cooperative formation; the communication topological relation between the host and the slave is expressed by an undirected authorized graph.
Further, the expression steps of the undirected weighted graph are as follows: the topological relation among the slaves is G N And (v, epsilon) and defining a set of N mobile robot nodes as v = (v) 1 ,υ 2 ,...,υ N And defining a weight edge between mobile robots with the numbers of i and j, i, j epsilon delta as epsilon = { (upsilon) i ,υ j )|υ i ,υ j E, upsilon }; the topological relation of the whole multi-mobile-robot system is G N+1 The i-th slave mobile robot and the master mobile robot have direct communication connection and are described as a constant b i The communication topological relation matrix of the master mobile robot and the slave mobile robot can be established to be B = diag { B } 1 ,b 2 ,...,b N And combining with a laplacian matrix L in the slave communication topology, the communication topology of the whole multi-mobile-robot system can be represented as a matrix M = L + B.
Further, in step 3), the state observer is designed as follows:
wherein the content of the first and second substances,
the state observation values of the ith slave mobile robot to the master mobile robot are respectively obtained; k is a radical of x ,k y ,k θ ＞0，c x ,c y ,c θ ＞1/λ min (M) and λ x ,λ y ,λ θ Is a parameter of the observer; ρ is a unit of a gradient x ,ρ y ,ρ θ Is a preset time function; a is a ij Is an element in the adjacency matrix in the undirected weighted graph.
Further, the preset time function is defined as follows:
wherein, t 0 ,T k K ∈ { x, y, θ } is the initial time and the predetermined time interval, respectively, and h is a positive integer parameter.
Further, in step 4), the control targets of the formation controller are:
wherein, delta ki K ∈ { x, y, θ } is an error system of the master and the ith slave mobile robot, and the specific relation is as follows
Wherein x is i (t),y i (t),θ i (t) respectively representing the transverse and longitudinal positions and the course angle of the ith slave mobile robot in the global coordinate system, x 0 (t),y 0 (t),θ 0 (t) respectively representing the transverse position, the longitudinal position and the course angle of the host mobile robot under the global coordinate system,
the target distance required to be kept between the ith slave computer and the host computer in the transverse direction and the longitudinal direction is obtained;
further, in step 4), the formation controller is designed to:
in the formula u xi ,u yi For the virtual controller, the following is defined
Wherein, a x ,a y ,a θ > 0 and r x ,r y ,r θ A constant coefficient is more than 0;
the first derivatives of the state observed values of the ith slave mobile robot to the master mobile robot are respectively; e.g. of the type xi ,e yi ,e θi For an error system between adjacent mobile robots based on the described communication topology, the specific relation is as follows:
wherein the content of the first and second substances,
the target distance to be kept for the ith slave and the jth slave in the transverse direction and the longitudinal direction is obtained.
Has the beneficial effects that: compared with the prior art, the distributed preset time observer based multi-mobile-robot formation method of the distributed preset time state observer can directly observe the real formation error value of the slave mobile robots and the position, angle and angular speed of the host, can preset the convergence time of the observer off-line, and can ensure the accuracy, flexibility and safety of the observation effect; the mobile robot formation controller also uses a preset time algorithm, so that the time for completing formation of the formation can be ensured to be preset offline; meanwhile, the relative position and angle between the mobile robots are obtained by using a GPS (global positioning system), a laser radar and an inertial measurement unit (comprising an accelerometer, a gyroscope and a magnetometer), so that high precision can be ensured, the observed value of an observer is ensured to be closer to an actual value, and the formation effect of multiple mobile robots is improved.
Drawings
FIG. 1 is a flow chart of a multi-mobile-robot formation method based on a distributed pre-set time state observer;
FIG. 2 is a kinematic model of a multi-mobile robot;
FIG. 3 is a schematic diagram illustrating a communication topology of multiple mobile robots in an embodiment;
FIG. 4 is a schematic diagram of a multi-mobile robot formation control method;
FIG. 5 is a diagram illustrating an observation result of a distributed predetermined time observer according to an embodiment;
FIG. 6 is a diagram of simulation results of formation of multiple mobile robots in an embodiment.
Detailed Description
For a better understanding of the contents of the present patent application, the technical solutions of the present invention will be further described below with reference to the accompanying drawings and specific examples.
As shown in fig. 1-6, the method for forming a multi-mobile robot formation based on a distributed preset time observer includes the following steps:
step 1: modeling the kinematics: and establishing a kinematic equation of the multi-mobile robot according to the operational characteristics of the multi-mobile robot, wherein a kinematic model of the multi-mobile robot is shown in FIG. 2. The mobile robot is selected as a wheeled robot under a two-dimensional plane of a global coordinate system, and the kinematic equation of the mobile robot can be described as follows:
wherein i is the number of the mobile robot; n is a normal number and represents the number of the multiple mobile robots; Δ = {1, 2.., N } is a set of multiple mobile robot numbers; x is the number of i ,y i Position information of the ith mobile robot; theta i Representing the heading angle of the ith mobile robot; v. of i ,ω i For the control input, the speed and the rotation angular speed of the ith mobile robot are represented respectively.
Step 2: communication topology description: and establishing a communication network architecture among the multiple mobile robots, and establishing a master-slave architecture of the multiple mobile robots. Establishing a master-slave framework of N +1 multiple mobile robots, setting one mobile robot as a master machine with the number of 0, setting the rest N mobile robots as slave machines with the number of i, and performing collaborative formation by i belonging to delta; the communication topological relation between the host and the slave is expressed by using an undirected authorized graph. The expression steps of the undirected weighted graph are as follows:the topological relation among the slaves is G N And (6) the N mobile robot node sets are defined as upsilon = { upsilon }, and the N mobile robot node sets are defined as upsilon = 1 ,υ 2 ,…,υ N And the weighted side between the mobile robots with the numbers of i and j, i, j epsilon delta is defined as epsilon = { (upsilon) i ,υ j )|υ i ,υ j E.v }. The topological relation of the whole multi-mobile robot system is G N+1 The i-th slave mobile robot and the master mobile robot have direct communication connection and are described as a constant b i The communication topological relation matrix of the master mobile robot and the slave mobile robot can be established as B = diag { B } 1 ,b 2 ,…,b N And combining with a laplacian matrix L in the slave communication topology, the communication topology of the whole multi-mobile-robot system can be represented as a matrix M = L + B. In the embodiment, three mobile robots are selected as slaves, and the numbers of the slaves are slave 1, slave 2 and slave 3 respectively; the host number is host 0. The communication topology is described as shown in fig. 3, and at least one slave computer has direct information communication with the master computer 0.
And step 3: designing a state observer: and designing a distributed preset time state observer to realize that the slave computer obtains an observed value of the state of the host computer within preset time. The state observer is designed as follows:
wherein the content of the first and second substances,
the state observation values of the ith slave mobile robot to the master mobile robot are respectively obtained; k is a radical of x ,k y ,k θ ＞0，c x ,c y ,c θ ＞1/λ min (M) and λ x ,λ y ,λ θ Is a parameter of the observer; rho x ,ρ y ,ρ θ Is a preset time function; a is ij Is an element in the adjacency matrix in the undirected weighted graph.
Wherein the preset time function is defined as follows:
wherein, t k ,T k K is an initial time and a preset time interval respectively, and h is a positive integer parameter.
The control targets of the formation controller are:
wherein, delta ki K ∈ { x, y, θ } is an error system of the master and the ith slave mobile robot, and the specific relation is as follows
Wherein x is i (t),y i (t),θ i (t) respectively representing the transverse and longitudinal positions and the course angle of the ith slave mobile robot in the global coordinate system, x 0 (t),y 0 (t),θ 0 (t) respectively representing the transverse and longitudinal positions and the course angle of the host mobile robot under the global coordinate system,
the target distance between the ith slave and the host in the transverse direction and the longitudinal direction needs to be kept.
And 4, step 4: designing a formation controller: and inputting the observed values into a multi-mobile-robot formation controller so as to realize the preset time cooperative formation of the multi-mobile-robot. As shown in fig. 4, a formation controller of a multi-mobile robot is designed as follows:
in the formula u xi ,u yi For the virtual controller, the following is defined
Wherein, a x ,a y ,a θ > 0 and r x ,r y ,r θ A constant coefficient is more than 0;
the first derivatives of the state observed values of the ith slave mobile robot to the master mobile robot are respectively; e.g. of a cylinder xi ,e yi ,e θi For the error system between adjacent mobile robots based on the described communication topology, the specific relation is as follows
Wherein the content of the first and second substances,
the target distance to be kept for the ith slave and the jth slave in the transverse direction and the longitudinal direction is obtained.
In this embodiment, each mobile robot is installed with a GPS positioning system, a lidar and an inertial measurement unit including an accelerometer, a gyroscope and a magnetometer to obtain the relative position and angle between the mobile robots. When the GPS positioning system does not acquire accurate enough information, the laser radar can make up for the error.
In the present embodiment, the parameters of the distributed pre-set time state observer are chosen to be h =2,k x ＝k y ＝k θ ＝1，c x ＝c y ＝c θ And (2). Because the control structure of the inner ring and the outer ring is adopted, the preset convergence time of the inner ring posture needs to be faster than the preset convergence time of the outer ring position, and T is selected x ＝T y ＝2s，T θ =1s. The kinematic state of the main machine of the whole multi-mobile robot system is
The initial states of the host and the slave are x respectively 0 (0)＝0，y 0 (0)＝1，θ 0 (0)＝arctan1；x 1 (0)＝-2，y 1 (0)＝2，θ 1 (0)＝2；x 1 (0)＝5，y 1 (0)＝1，θ 1 (0)＝0；x 1 (0)＝2，y 1 (0)＝-3，θ 1 (0)＝1。
The process for proving the convergence of the distributed preset time state observer designed by the invention is as follows:
definition of
First we demonstrate the observation error of the slave i in the x direction
Can be in a preset time T x Inner convergence to zero. Will be provided with
And T x Substituting into observer equation 2, one can get
Order to
Choosing Lyapunov function as
And derived to obtain
Wherein, κ x Is u 0x The upper bound of (c). Since M is a positive constant momentArray, therefore there is an invertible matrix Ω, so that M = Ω T Omega. Thus we can get
Integral upper type belt conveyer c x ＞1/λ min (M) we can get
At t e [ t ∈ [ [ t ] 0 ,t 0 +T x ) Step, multiply the left and right sides of equation 13 by ρ x 2
Further derive it
Solving the differential equation in equation 15 to obtain
By presetting the nature of the scaling function, we can get
At t ∈ [ t ] 0 +T x ,t 0 +T x +T x ) Stage due to 2k x λ min (M) > 0 and
then V (t) is less than or equal to 0, and further V (t) is less than or equal to 0 and less than or equal to V (t) 0 +T x ) =0. Thus at t e [ t ∈ [ [ t ] 0 +T x ,t 0 +T x +T x ) Stage, V (t) ≡ 0. By the same way, the method obtains the value in t E [ t ∈ [ [ t ] 0 +T x , + ∞) phase, V (t) ≡ 0.
In conclusion, we can conclude that
At a preset time T x Converging to zero. Similar to the above-described proving method, we can prove that
And
respectively at preset time T x And T θ Converging to zero.
Claims (6)
1. A multi-mobile-robot formation method based on a distributed preset time state observer is characterized by comprising the following steps: comprises the following steps:
step 1) kinematic modeling: establishing a kinematic equation of the multi-mobile robot according to the operational characteristics of the multi-mobile robot;
step 2) communication topology description: establishing a communication network architecture among the multiple mobile robots, and constructing a master-slave architecture of the multiple mobile robots;
step 3) designing a state observer: designing a distributed preset time state observer to realize that the slave computer obtains an observed value of the state of the host computer within preset time; the state observer is designed as follows:
wherein the content of the first and second substances,
the state observation values of the ith slave mobile robot to the master mobile robot are respectively obtained; k is a radical of formula x ,k y ,k θ ＞0，c x ,c y ,c θ ＞1/λ min (M) and λ x ,λ y ,λ θ Is a parameter of the observer;
ρ x ,ρ y ,ρ θ is a preset time function; a is ij Is the element in the adjacency matrix in the undirected weighted graph;
step 4), designing a formation controller: inputting the observed values into a multi-mobile-robot formation controller to realize the preset time collaborative formation of the multi-mobile robots; the design of the formation controller is as follows:
in the formula u xi ,u yi For the virtual controller, the following is defined
Wherein, a x ,a y ,a θ Greater than 0 and r x ,r y ,r θ A constant coefficient is more than 0;
the first derivatives of the state observed values of the ith slave mobile robot to the master mobile robot are respectively; e.g. of a cylinder xi ,e yi ,e θi For the error system between neighboring mobile robots based on the described communication topology, the relation is as follows:
wherein the content of the first and second substances,
the target distance required to be kept for the ith slave machine and the jth slave machine in the transverse direction and the longitudinal direction is obtained.
2. The method for multi-mobile-robot formation based on the distributed preset-time state observer according to claim 1, wherein: in the step 1), the kinematic modeling is that the mobile robot selects a wheeled robot moving under a two-dimensional plane of a global coordinate system, and a kinematic equation of the wheeled robot is described as follows:
wherein i is the number of the mobile robot; n is a normal number and represents the number of the multiple mobile robots; Δ = {1, 2.., N } is a set of multiple mobile robot numbers; x is the number of i ,y i Position information of the ith mobile robot; theta i Representing a course angle of the ith mobile robot; v. of i ,ω i For the control input, the speed and the rotation angular speed of the ith mobile robot are represented respectively.
3. The method for formation of multiple mobile robots based on the distributed preset time state observer according to claim 2, wherein in the step 2), the communication topology describes: establishing a master-slave framework of N +1 multiple mobile robots, and setting one mobile robot as a host, wherein the serial number of the mobile robot is 0; the rest N mobile robots are used as slave machines, the serial numbers of the slave machines are i, i belongs to delta, and cooperative formation is carried out; the communication topological relation between the host and the slave is expressed by an undirected authorized graph.
4. The distributed preset-time-state-observer-based multi-mobile-robot formation method according to claim 3, wherein: the expression steps of the undirected ownership graph are as follows: the topological relation among the slaves is G N And (v, epsilon), wherein the N mobile robot node sets are defined as v ={υ 1 ,υ 2 ,...,υ N And defining a weight edge between mobile robots with the numbers of i and j, i, j epsilon delta as epsilon = { (upsilon) i ,υ j )|υ i ,υ j E, upsilon }; the topological relation of the whole multi-mobile-robot system is G N+1 The i-th slave mobile robot and the master mobile robot have direct communication connection and are described as a constant b i The communication topological relation matrix of the master mobile robot and the slave mobile robot can be established as B = diag { B } 1 ,b 2 ,...,b N And combining with a Laplace matrix L in the slave communication topology, the communication topology of the whole multi-mobile-robot system is represented as a matrix M = L + B.
5. The method of claim 4, wherein the predetermined time function is defined as follows:
wherein, t 0 ,T k K ∈ { x, y, θ } is the initial time and the predetermined time interval, respectively, and h is a positive integer parameter.
6. The method for multi-mobile-robot formation based on the distributed preset time state observer according to claim 5, wherein in the step 4), the control targets of the formation controller are:
wherein, delta ki K is the error system of the master machine and the ith slave machine mobile robot, and the relation formula is as follows
Wherein x is i (t),y i (t),θ i (t) respectively representing the transverse and longitudinal positions and the course angle of the ith slave mobile robot in the global coordinate system, x 0 (t),y 0 (t),θ 0 (t) respectively representing the transverse and longitudinal positions and the course angle of the host mobile robot under the global coordinate system,
the target distance between the ith slave and the host in the transverse direction and the longitudinal direction needs to be kept.
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| CN112327839B (en) * | 2020-10-27 | 2022-07-15 | 中国科学技术大学 | Formation control method, device, equipment and medium for multi-robot system |
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| CN115877718B (en) * | 2023-02-23 | 2023-05-30 | 北京航空航天大学 | Data-driven heterogeneous missile formation switching communication topology cooperative control method |
| CN117913902A (en) * | 2024-03-19 | 2024-04-19 | 山东大学 | Island micro-network state estimation method and system based on preset time observer |
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