Multi-mobile-robot formation method based on distributed preset time state observer

A technology of mobile robots and state observers, which is applied in the direction of instruments, motor vehicles, non-electric variable control, etc., can solve the problems of not being able to complete task requirements well, and achieve the effects of improving effects, high precision, and ensuring accuracy

Active Publication Date: 2020-05-29
NANJING UNIV OF POSTS & TELECOMM
5 Cites 7 Cited by

AI-Extracted Technical Summary

Problems solved by technology

[0002] A single mobile robot has limited capabilities in information acquisition, processing, and autonomous control a...
View more

Abstract

The invention discloses a multi-mobile-robot formation method based on a distributed preset time state observer. The invention belongs to the technical field of multi-mobile-robot cooperative control.The invention discloses the multi-mobile-robot formation method based on the distributed preset time state observer, the distributed preset time observer can directly observe the real formation errorvalue of a slave mobile robot and the position, angle and angular velocity of a host, the convergence time of the observer can be set offline in advance, and the accuracy, flexibility and safety of the observation effect can be guaranteed; a mobile robot formation controller provided by the invention also uses a preset time algorithm such that the time for completing the formation of a formationcan be ensured to be preset offline; meanwhile, a GPS positioning system, a laser radar and an inertia measurement unit (including an accelerometer, a gyroscope and a magnetometer) are used for obtaining the relative position and angle between the mobile robots, high precision can be guaranteed, it is guaranteed that the observation value of the observer is closer to the actual value, and the effect of multi-mobile-robot formation is improved.

Application Domain

Position/course control in two dimensionsVehicles

Technology Topic

Inertial measurement unitMobile robot +8

Image

  • Multi-mobile-robot formation method based on distributed preset time state observer
  • Multi-mobile-robot formation method based on distributed preset time state observer
  • Multi-mobile-robot formation method based on distributed preset time state observer

Examples

  • Experimental program(1)

Example Embodiment

[0045] In order to better understand the content of the patent of the present invention, the technical solutions of the present invention are further described below with reference to the accompanying drawings and specific embodiments.
[0046] like Figure 1-6 As shown, the multi-mobile robot formation method based on distributed preset time observer includes the following steps:
[0047] Step 1: Kinematics modeling: According to the operating characteristics of the multi-mobile robot, establish the kinematic equation of the multi-mobile robot. The kinematic model of the multi-mobile robot is as follows: figure 2 shown. The mobile robot is selected as a wheeled robot under the two-dimensional plane of the global coordinate system, and its kinematic equations can be described as follows:
[0048]
[0049] where i is the number of the mobile robot; N is a normal number, indicating the number of multi-mobile robots; Δ={1,2,...,N} is the number set of multi-mobile robots; x i ,y i is the position information of the ith mobile robot; θ i represents the heading angle of the ith mobile robot; v i ,ω i For the control input, it represents the speed and rotation angular velocity of the i-th mobile robot, respectively.
[0050] Step 2: Communication topology description: establish a communication network architecture between multiple mobile robots, and build a master-slave architecture of multiple mobile robots. Establish a master-slave architecture of N+1 multi-mobile robots, set one mobile robot as the master with the number 0, and the remaining N mobile robots as the slaves with the number i, i∈Δ for collaborative formation; To have a graph to express the communication topology relationship. The expression steps of the undirected weighted graph are as follows: The topological relationship between the slaves is G N ={υ,ε}, the set of N mobile robot nodes is defined as υ={υ 1 ,υ 2 ,...,υ N}, the weighted edge between mobile robots numbered i and j, i, j∈Δ is defined as ε={(υ i ,υ j )|υ i ,υ j ∈υ}. The topological relationship of the entire multi-mobile robot system is G N+1 , the description of the direct communication connection between the i-th slave mobile robot and the host mobile robot is constant b i , the communication topology relationship matrix between the host mobile robot and the slave mobile robot can be established as B=diag{b 1 ,b 2 ,...,b N}, and combined with the Laplacian matrix L in the slave communication topology, the communication topology of the entire multi-mobile robot system can be expressed as matrix M=L+B. In this embodiment, three mobile robots are selected as slaves, and the numbers are respectively slave 1, slave 2, and slave 3; the master number is master 0. Its communication topology is described as image 3 As shown, at least one slave has direct information communication with master 0.
[0051] Step 3: State Observer Design: Design a distributed preset time state observer, so that the slave can obtain the observed value of the master state within the preset time. The state observer is designed as:
[0052]
[0053] in, are the state observations of the i-th slave mobile robot to the host mobile robot; k x ,k y ,k θ 0, c x ,c y ,c θ1/λ min (M) and λ x ,λ y ,λ θ is the parameter of the observer; ρ x ,ρ y ,ρ θ is the preset time function; a ij is the element in the adjacency matrix in the undirected weighted graph.
[0054] Wherein, the preset time function is defined as follows:
[0055]
[0056] where, t k ,T k ,k∈{x,y,θ} are the initial time and the preset time interval, respectively, and h is a positive integer parameter.
[0057] The control objectives of the formation controller are:
[0058]
[0059] where δ ki ,k∈{x,y,θ} is the error system between the master and the i-th slave mobile robot, and the specific relationship is as follows
[0060]
[0061] where x i (t),y i (t), θ i (t) represent the horizontal and vertical positions and heading angles of the i-th slave mobile robot in the global coordinate system, respectively, x 0 (t),y 0 (t), θ 0 (t) represent the horizontal and vertical positions and heading angles of the host mobile robot in the global coordinate system, respectively, The target distance that needs to be maintained between the i-th slave and the master in the horizontal and vertical directions.
[0062] Step 4: Formation controller design: Input the observations to the multi-mobile robot formation controller to realize the pre-set time cooperative formation of the multi-mobile robots. The formation control method of multiple mobile robots is as follows Figure 4 As shown, the design of the formation controller is:
[0063]
[0064] where u xi ,u yi is a virtual controller, defined as follows
[0065]
[0066] Among them, a x ,a y ,a θ0 and r x ,r y ,r θ 0 is a constant coefficient; are the first derivative of the state observation value of the i-th slave mobile robot to the host mobile robot; e xi ,e yi ,e θi is the error system between adjacent mobile robots based on the described communication topology, and the specific relationship is as follows
[0067]
[0068] in, It is the target distance that needs to be maintained between the i-th slave and the j-th slave in the horizontal and vertical directions.
[0069] In this embodiment, each mobile robot is installed with a GPS positioning system, a laser radar 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 information obtained by the GPS positioning system is not accurate enough, lidar can make up for this error.
[0070] In this embodiment, the parameters of the distributed preset time state observer are selected as h=2, k x =k y =k θ =1, c x =c y =c θ = 2. Since it is the control structure of the inner and outer loops, the preset convergence time of the inner loop attitude needs to be faster than the preset convergence time of the outer loop position, so we choose T x =T y =2s, T θ =1s. The kinematic state of the host of the entire multi-mobile robot system is
[0071]
[0072] The initial states of the master and slave are respectively x 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.
[0073] The proof process of the convergence of the distributed preset time state observer designed by the present invention is as follows:
[0074] definition First, we prove the observation error of slave i in the x direction at a preset time T x converges to zero. Will and T x Bringing it into the observer equation 2, we can get
[0075]
[0076] make The Lyapunov function is chosen as and get the derivation
[0077]
[0078] Among them, κ x for u 0x the upper bound. Since M is a positive definite matrix, there is an invertible matrix Ω such that M=Ω T Ω. Therefore we can get
[0079]
[0080] Integrate the above formula and bring in c x1/λ min (M), we can get
[0081]
[0082] in t∈[t 0 ,t 0 +T x ) stage, multiply the left and right sides of Equation 12 by ρ x 2
[0083]
[0084] It is further derived
[0085]
[0086] Solving the differential equation in Equation 14, we get
[0087]
[0088]
[0089] By presetting the properties of the scaling function, we can get in t∈[t 0 +T x ,t 0 +T x +T x ) stage, due to 2k x λ min (M)>0 and Then V(t)≤0, further 0≤V(t)≤V(t 0 +T x )=0. So in t∈[t 0 +T x ,t 0 +T x +T x ) stage, V(t)≡0. In the same way, we can get in t∈[t 0 +T x ,+∞) stage, V(t)≡0.
[0090] From the above, we can get at preset time T x converges to zero. Similar to the above proof method, we can prove that and respectively at the preset time T x with T θ converges to zero.

PUM

no PUM

Description & Claims & Application Information

We can also present the details of the Description, Claims and Application information to help users get a comprehensive understanding of the technical details of the patent, such as background art, summary of invention, brief description of drawings, description of embodiments, and other original content. On the other hand, users can also determine the specific scope of protection of the technology through the list of claims; as well as understand the changes in the life cycle of the technology with the presentation of the patent timeline. Login to view more.

Similar technology patents

Knowledge base supported spatial database design method

InactiveCN101477549AGuaranteed accuracyAchieve an optimized design
Owner:CHINESE ACAD OF SURVEYING & MAPPING

Log backup method and device and smart card

InactiveCN102567146AGuaranteed accuracy
Owner:BEIJING WATCH DATA SYST

Train tracking method based on information redundancy

ActiveCN104149822AGuaranteed accuracyKeep Tracking
Owner:NARI TECH CO LTD

Classification and recommendation of technical efficacy words

  • Guaranteed accuracy
  • High precision

Method for forecasting short-term power in wind power station

InactiveCN102102626AHigh precision
Owner:NORTH CHINA ELECTRIC POWER UNIV (BAODING) +1

Numerical control machine tool wear monitoring method

InactiveCN102091972AHigh precisionReal-time monitoring of tool wear
Owner:HUAZHONG UNIV OF SCI & TECH +1

Advertisement recommendation method and apparatus

ActiveCN104965890AHigh precisionPrecise screening
Owner:SHENZHEN TENCENT COMP SYST CO LTD
Who we serve
  • R&D Engineer
  • R&D Manager
  • IP Professional
Why Eureka
  • Industry Leading Data Capabilities
  • Powerful AI technology
  • Patent DNA Extraction
Social media
Try Eureka
PatSnap group products