A robot relative positioning method independent of continuous excitation
By constructing a relative position observer and utilizing the relative distance and velocity information between robots, the problem of continuous excitation required for robot relative positioning was solved, achieving fast and accurate relative positioning and reducing hardware costs and constraints on motion patterns.
Patent Information
- Application Number
- CN202410384391.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-01
- Publication Date
- 2025-10-24
- Estimated Expiration
- 2044-04-01
AI Technical Summary
In existing technologies, robot relative positioning methods require continuously stimulated motion, which increases the robot's load and the constraints on its motion patterns. Furthermore, it is difficult to achieve relative positioning without external base stations in complex environments.
By constructing a relative position observer and utilizing the relative distance and velocity information between robots to establish a linear regression relationship, and combining dynamic extension and hybrid techniques, a finite-time adaptive relative position observer is designed to achieve relative positioning that does not depend on continuous excitation.
Achieving rapid and accurate relative positioning within a limited time reduces hardware costs, improves the adaptability of multi-robot systems in complex environments, and relaxes the requirements for robot movement.
Smart Images
Figure CN118501805B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of robot positioning technology, and in particular to a robot relative positioning method independent of continuous excitation. BACKGROUND
[0002] In recent years, with the rapid development of multi-robot systems, unmanned swarm cooperation to perform complex tasks has attracted great attention in the academic field, and is widely used in industrial, agricultural, military and other fields, such as cooperative handling, regional reconnaissance, disaster rescue, agricultural irrigation, power inspection and other scenes. Relative positioning is the basis for robots to perform tasks autonomously. In actual tasks, various signal interferences, obstacles, and difficult deployment of positioning base stations often occur in the environment, and the traditional robot positioning method based on anchor points will be greatly limited. Therefore, it is very important to design a relative positioning method without relying on external base stations and only using on-board lightweight sensors.
[0003] The widely used relative positioning method requires the robot to perform continuous excitation motion, that is, the robots have continuous relative motion, which greatly restricts the motion form of the robots. If the robot is in a static state or parallel motion state, in order to realize the requirement of continuous excitation in relative positioning, the existing method generally uses hardware design, such as installing multiple UWB tags on each robot, to ensure that the relative position between robots is observable, but this greatly increases the load of the robot. From the algorithm level, a relative positioning method for robots independent of continuous excitation has not been found. SUMMARY
[0004] Therefore, the present application provides a robot relative positioning method independent of continuous excitation, which does not rely on external base stations, does not require the installation of additional hardware, and relaxes the requirement of continuous excitation motion of the robot. By constructing a relative position observer, the relative position estimates between robots converge to the true relative position in a limited time without continuous excitation input, with fast positioning speed and high accuracy.
[0005] The robot relative positioning method independent of continuous excitation of the present application comprises the following steps:
[0006] Step 1: Robot i obtains the relative distance between itself and neighbor robot j, its own speed and the speed of neighbor robot j; using the essential correlation properties of relative position, orientation, distance and speed, a relationship between the relative orientation between robot i and its neighbor robot j and the distance, relative position, relative speed between robots i and j is established;
[0007] Step 2, transforming the relation described in Step 1 into a homogeneous linear time-varying system by introducing an auxiliary dynamic extended signal with the same dynamics as the relation described in Step 1 but with initial values defined by oneself; based on the properties of the base matrix of the homogeneous linear system and the superposition principle of the linear system on the initial state, solving the homogeneous linear time-varying equation and taking the initial value of the solution of the homogeneous linear time-varying equation as the constant parameter to be identified, obtaining a linear constant parameter equation about the relative position, the auxiliary dynamic extended signal, the base matrix and the parameter to be identified;
[0008] Step 3, applying a linear filter operator to the linear constant parameter equation described in Step 2 to transform it into a linear regression equation containing only measurable signals of the relative distance and the relative velocity between the robots; and using dynamic regression extension and mixing technology to realize decoupling of the regression vector and the parameter vector to be identified in the linear regression equation, obtaining a plurality of scalar linear regression equations;
[0009] Step 4, constructing a relative position observer for the plurality of scalar linear regression equations obtained in Step 3; when the regression quantity of the scalar linear regression equation obtained in Step 3 satisfies the interval excitation, i.e. the space spanned by the relative velocity filter values of the robots can cover the entire space within a given time interval, the relative position observer is used to realize the estimation of the relative position.
[0010] Preferably, the parameter estimator in the observer uses finite-time gradient estimation and finite-time least square estimation.
[0011] Preferably, in Step 1, the relation between the relative position of the robot i and its neighbor robot j and the distance and the relative velocity between the robots i and j is:
[0012]
[0013] wherein, is the first derivative of the relative position g ij ; g ij = (q i -q j ) / ||q i -q j ||, q i and q j are the positions of the robots i and j respectively; d ij is the distance between the robots i and j; r ij = q i -q j is the relative position between the robots i and j; v ij = v i -v j is the relative velocity between the robots i and j.
[0014] Preferably, in step 2, the auxiliary signal is defined as
[0015]
[0016] Then, the linear time-varying system is generated according to (1)-(2):
[0017]
[0018] where
[0019] The solution of (3) is: where, is the base matrix;
[0020] Then, e ij (0) is defined as the parameter θ i to be identified; θ i The mapping relationship between the relative position of the robot and the auxiliary signal is given by (4):
[0021]
[0022] At this time, the time-varying relative position estimation problem is converted into the identification problem of the constant parameter vector θ i .
[0023] Preferably, in step 3, the specific operation is as follows:
[0024] A linear filter operator is defined to act on the relationship In combination with the linear constant parameter equation (4) described in step 2, it is converted into a linear regression equation containing only measurable signals:
[0025]
[0026] where y i is a linear combination of the measurable signals of the robot, and θ i represent the known regression quantity and the parameter to be identified, respectively; y i and are defined as follows:
[0027]
[0028]
[0029] where κ ij , φ ij are the filtered values of the relative distance and the relative velocity between the robots, ξ ij , is the auxiliary signal, and G2[·] is a linear filter operator;
[0030] After dynamic expansion regression and mixing, a plurality of scalar linear regression equations are obtained:
[0031]
[0032] Preferably, in step 4, the constructed finite-time gradient relative position observer is:
[0033]
[0034] wherein is a pre-defined auxiliary signal, γ i > 0 is an observer gain; is a finite-time parameter estimator, μ i ∈ (0, 1) is a pre-defined parameter, satisfies
[0035]
[0036] The relative position observer can converge to the true relative position value within a finite time t c under the following interval excitation condition (9):
[0037]
[0038] Advantages:
[0039] The present application first establishes a linear regression relationship between distance, speed and relative position, then converts the time-varying parameter estimation problem into a constant parameter identification problem, and establishes a mapping between the to-be-identified parameters and the relative position, then combines dynamic expansion and mixing technology and linear filtering technology to obtain a finite-time adaptive relative position observer. Under the action of the relative position observer which does not depend on continuous excitation, only the distance and relative speed measurement values that can be observed between robots are used, and only the filtered values of the relative speed need to satisfy the interval excitation condition, so that the relative position estimation values between robots can be made consistent and converge to the true relative position value within a finite time. The present application does not need to deploy external base stations, improves the adaptability of the multi-robot system in complex environments, does not need to install a large number of additional sensors to obtain information, significantly reduces the hardware cost, and at the same time relaxes the continuous excitation motion requirement, realizes fast relative positioning under the condition that the motion of the robot satisfies the interval excitation, and greatly relaxes the special requirements of the traditional relative positioning algorithm on the motion trajectory of the robot. BRIEF DESCRIPTION OF DRAWINGS
[0040] Figure 1The overall framework of the relative positioning method of the application not dependent on continuous excitation.
[0041] Figure 2 The robot motion trajectory of the first set of two-dimensional simulation experiments.
[0042] Figure 3 The relative positioning results of the first set of two-dimensional simulation experiments; wherein (a) is the relative positioning result of the No. 1 robot and the No. 2 robot; (b) is the relative positioning result of the No. 1 robot and the No. 3 robot.
[0043] Figure 4 The robot motion trajectory of the second set of three-dimensional simulation experiments.
[0044] Figure 5 The relative positioning results of the second set of three-dimensional simulation experiments; wherein (a) is the relative positioning result of the No. 1 robot and the No. 2 robot; (b) is the relative positioning result of the No. 1 robot and the No. 3 robot.
[0045] Figure 6 The flight trajectory of the third set of real experiments of unmanned aerial vehicles from the top view.
[0046] Figure 7 The relative positioning results of the third set of real experiments. DETAILED DESCRIPTION
[0047] The application will be described in detail below with reference to the accompanying drawings and examples.
[0048] The application provides a robot relative positioning method not dependent on continuous excitation.
[0049] Since each robot can only perceive the distance information of the neighbor robot and the speed information of itself, the relative position of the neighbor robot cannot be directly obtained, and the direct relative position relationship of the robot is time-varying, the time-varying parameter estimation problem involves difficult problems such as nonlinear estimation, and usually requires the relative motion between the robots to maintain continuous excitation, therefore, it is extremely challenging to estimate the relative position of the robot from the algorithm aspect. The application relaxes the continuous excitation condition, and the core idea is to cleverly convert the time-varying relative position estimation into a constant parameter estimation, and then combine the dynamic expansion and regression technology and the adaptive estimation theory to design a limited time adaptive relative position observer under interval excitation, so as to realize the rapid and effective estimation in a limited time while relaxing the continuous excitation condition. The design block diagram of the application is shown in Figure 1 The specific steps include the following steps:
[0050] Step 1: Construct a constant parameter vector to convert the time-varying signal estimation problem into a parameter identification problem
[0051] The present application considers N robots to perform a relative positioning task, and the dynamic model of robot i is described as:
[0052]
[0053] wherein is the position of robot i, is the velocity input of robot i.
[0054] The sensing topological relationship between robots is represented by a directed graph , wherein the point set is the set of robots, and the edge set is the set of edges. If (i,j)∈ε, it means that robot i can sense robot j and measure the relative distance with robot j. The set of all neighbors of robot i is denoted by . Meanwhile, the undirected graph is defined as the communication topological relationship between robots, if means that robots i and j can exchange their respective information. The information available to each robot includes: the relative distance d ij ||q i -q j || with neighbor robots, the velocity v i of itself, and the velocity v j of neighbors.
[0055] According to the distance and velocity information available to each robot, the relative position relationship is analyzed, and a linear regression equation can be generated, as follows:
[0056] First, the essential correlation attributes of the relative position g ij =(q i -q j ) / ||q i -q j ||, the distance d ij , the relative position r ij =q i -q j , and the relative velocity v ij =v i -v j between robots are analyzed, and the following relationship is established:
[0057]
[0058] Then, in order to avoid directly estimating the time-varying nonlinear relative position signal, an auxiliary dynamic extension signal with the same dynamics as relationship (1) but with a self-defined initial value is introduced, and relationship (1) is converted into a homogeneous linear time-varying system; in this embodiment, the auxiliary signal is defined as:
[0059]
[0060] Then, the homogeneous linear time-varying system
[0061]
[0062] where
[0063] Then, based on the basis matrix property of the homogeneous linear system and the superposition principle of linear system on initial state, the homogeneous linear time-varying equation (3) is solved, and the initial value of the solution of the homogeneous linear time-varying equation (3) is taken as the constant parameter to be identified, so that the linear constant parameter equation about the relative position, the auxiliary dynamic extended signal, the basis matrix and the parameter to be identified is obtained. In the embodiment, the solution of equation (3) can be represented by the basis matrix , that is, The e ij (0) is defined as the parameter θ i to be identified. i The mapping relationship between the robot relative position is transformed into the linear constant parameter equation, as shown in equation (4).
[0064]
[0065] At this time, the time-varying relative position estimation problem is transformed into the identification problem of the constant parameter vector θ i .
[0066] Step two: generating the linear regression relationship between the parameter to be identified and the distance and speed
[0067] According to the parameter θ i to be identified obtained in step one, the relative position is represented as In addition, the relative position, the distance and the speed satisfy the equation The linear filter operator is applied to both sides, so that the linear regression relationship containing only the measurable signals of the relative distance and the relative speed between the robots is obtained:
[0068]
[0069] where y i and are the linear combination of the measurable signals of the robots and the known regression quantity, respectively, and are defined as follows:
[0070]
[0071]
[0072] where κ ij , φ ijξ is the filtered value of relative distance and relative velocity between robots ij , G2[·] is a linear filter operator.
[0073] Extending the number of robots to N, the linear regression equation (5) becomes
[0074] y R = φ R θ R
[0075] where y R = col(y1,y2,…,y N ), φ R = diag{φ 1j ,φ 2j ,…,φ Nj}, θ R = [I d ,…,I d ] T θ i .
[0076] Step three: design a relative position observer independent of persistent excitation to generate the estimate of relative position
[0077] According to the linear regression relationship obtained in step two, if we want to get accurate parameter estimates Traditional parameter estimation methods, such as gradient descent estimator, least squares estimator, etc., require persistent excitation of the regression quantity to get exponential convergence results of parameter estimates. In the field of relative positioning of robots, this regression quantity is usually the speed or displacement of robot motion, which greatly restricts the motion mode of the robot. In this invention, in order to relax the strict assumption of persistent excitation, the dynamic regression extension and mixing technology is used to decouple the regression vector and the parameter vector to be identified in the linear regression equation (5) to obtain multiple scalar linear regression equations. Specifically, the filtered processing of equation (5) is to obtain the following linear regression equation:
[0078]
[0079] After d-1 filter operators are processed, the linear regression equation is extended to
[0080] Y i = Φ ij θ i (6)
[0081] where Y i = col(y i ,H1[y i ],…,Hd-1 [y i ]), Then multiply the left side of equation (6) by the adjoint matrix adj(Φ ij ) of Φ ij , and get the regression equation as follows:
[0082]
[0083] where Since Δ ij is a scalar, the present application decouples the linear regression equation (6) into d scalar linear regression equations:
[0084]
[0085] Then based on equation (7), a relative position observer is designed, which is used to estimate the relative position when the regressor of equation (7) satisfies the interval excitation, i.e. the space spanned by the relative velocity filtered values of robots can cover the whole space in a given time interval. The parameter estimator in the relative position observer can use finite time gradient estimation, finite time least square estimation, etc. The relative position observer designed in the present embodiment does not depend on continuous excitation as follows:
[0086]
[0087]
[0088]
[0089]
[0090]
[0091] where and η i are pre-given auxiliary signals, γ i > 0 is the observer gain, is a finite time parameter estimator, μ i ∈ (0, 1) is a pre-given parameter, satisfies
[0092]
[0093] The relative position observer no longer requires the regressor Δ ij (t) to be continuously excited, but only needs to satisfy the following interval excitation condition (9) to converge to the true value of the relative position within a finite time t c
[0094]
[0095] Based on the proposed method, three groups of experiments were conducted: the first group of simulation experiments was used to verify the relative positioning capability of the proposed method in a two-dimensional plane, the second group of simulation experiments was used to verify the relative positioning capability of the proposed method in three-dimensional space, and the third group of physical experiments was used to verify the relative positioning capability of the proposed method running on an actual UAV.
[0096] Figure 2 The non-continuous excitation motion trajectories of the robots in the first set of simulation experiments are shown. Robot 3 is always stationary, while robots 1 and 2 stop moving after 5 seconds and remain stationary. Figure 3 The relative positioning results of the three robots in the two-dimensional plane are shown. Taking robot 1 as the reference robot, it can be seen that the relative position estimates between the three robots quickly converge to the true value.
[0097] Figure 4 The non-continuous excitation motion trajectories of the robots in the second set of simulation experiments are shown. Robot 3 is always stationary, while robots 1 and 2 stop moving and remain stationary after 10 seconds of movement. Figure 5 The relative positioning results of the three robots in three-dimensional space are shown. Taking robot 1 as the reference robot, it can be seen that the relative position estimates between the three robots quickly converge to the true value.
[0098] Figure 6 and Figure 7 The non-continuous excitation motion trajectories and relative positioning results of each robot in the third set of physical experiments are shown respectively. Similarly, the three robots stop moving and remain stationary after 40 seconds of movement. It can be seen that the proposed method can achieve relative positioning within the allowable error range when running on an actual drone.
[0099] Through simulation and physical verification, it can be shown that the use of this relative positioning method that does not rely on continuous excitation can achieve fast and accurate relative positioning when the robot cannot meet the requirements of continuous excitation movement.
[0100] Compared with the traditional anchor-based navigation positioning method, the application can realize reliable relative positioning accuracy without deploying external base stations, so that the multi-robot system has stronger adaptability in complex environment. Moreover, the application does not need to install a large number of sensors on the robot to obtain information in practical application, which significantly reduces the hardware cost, and only uses low-cost and lightweight on-board sensors such as UWB, IMU, etc., thereby expanding the applicable range of the robot in extreme conditions. Meanwhile, the application can relax the continuous excitation motion requirement without increasing the hardware load, realize fast relative positioning under the condition that the motion of the robot meets the interval excitation, and greatly relax the special requirements of the traditional relative positioning algorithm on the motion trajectory of the robot.
[0101] To sum up, the above is only a preferred embodiment of the application, and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the protection scope of the application.
Claims
1. A method of robot relative positioning independent of persistent excitation, characterized by, The method comprises the following steps: Step 1, a robot i obtains its relative distance with a neighbor robot j, its own speed and the speed of the neighbor robot j; By using the essential correlation properties of relative position, orientation, distance and speed, a relationship between the relative orientation between the robot i and the neighbor robot j and the distance, the relative position and the relative speed between the robot i and the robot j is established; Step 2, the relationship in step 1 is converted into a homogeneous linear time-varying equation by introducing an auxiliary dynamic expansion signal which has the same dynamics as the relationship in step 1 but has a self-defined initial value; based on the basic matrix properties of the homogeneous linear system and the superposition principle of the linear system on the initial state, the homogeneous linear time-varying equation is solved, and the initial value of the solution of the homogeneous linear time-varying equation is taken as a constant parameter to be identified, so that a linear constant parameter equation about the relative orientation, the auxiliary dynamic expansion signal, the basic matrix and the parameter to be identified is obtained; Step 3, a linear filtering operator is applied to the linear constant parameter equation in step 2 to convert it into a linear regression equation containing only measurable signals of the relative distance and the relative speed between the robots; and a dynamic regression expansion and mixing technology is used to realize decoupling of the regression vector and the parameter vector to be identified in the linear regression equation, so that a plurality of scalar linear regression equations are obtained; Step 4, a relative position observer is constructed for the plurality of scalar linear regression equations obtained in step 3; when the regression amount of the scalar linear regression equation obtained in step 3 satisfies the interval excitation, i.e. the space formed by the rotation of the filtered values of the relative speed between the robots can cover the entire space within a given time interval, the relative position observer is used to realize estimation of the relative position.
2. The method of claim 1, wherein, The parameter estimator in the observer uses finite-time gradient estimation and finite-time least square estimation.
3. The method of claim 1, wherein, In step 1, the relationship between the relative orientation between the robot i and the neighbor robot j and the distance, the relative speed between the robot i and the robot j is: （1） wherein is a first derivative of the relative position between the robots gij ; , qi , qj are positions of the robots i , j ; are distances between the robots i , j ; are relative positions between the robots i , j ; are relative velocities between the robots i , j .
4. The method of claim 3, wherein, In step 2, the auxiliary signal is defined : （2） Then, the linear time-varying equation is generated according to (1)-(2): （3） wherein ; The solution of equation (3) is: wherein, is the base matrix; Then is defined as the parameter to be identified ; The mapping relationship between the robot relative position and the robot absolute position is given by equation (4): （4） At this point, the time-varying relative position estimation problem is transformed into a constant parameter vector identification problem.
5. The method of claim 4, wherein, Step 3 is specifically: Defining a linear filter operator , acting on the relation , in combination with the linear constant parameter equation (4) described in step 2, into a linear regression equation containing only measurable signals: （5） After dynamic expansion regression and mixing, a plurality of scalar linear regression equations are obtained: 。 6. The method of claim 5, wherein, In step 4, the constructed finite-time gradient relative position observer is: （8） wherein is a predetermined auxiliary signal, is an observer gain; is a finite-time parameter estimator, ; ; is a predetermined parameter, satisfies The relative position observer can be operated in a finite time if the following interval excitation condition (9) is satisfied. Inner convergence to the true value of the relative position: （9）。