CN114200833B - Control method for dynamic area coverage of robot network based on observer - Google Patents
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Abstract
The invention discloses a control method for dynamic area coverage of a robot network based on an observer, which designs the observer which approximates an environment density function of a task area by using basis function information and sensor measurement information so as to solve the problem that the environment information is not completely known. Then, based on the approximate environment density function, a controller of the robot is designed to drive the robot network to change the position configuration in real time, so that the robot network can achieve good area coverage effect under the condition that a movable target exists in a task area. Through designing the observer and the controller of the robot network, and analyzing and proving related theory, the method realizes the optimization of the robot network to the dynamic area coverage monitoring effect, achieves good coverage effect, and can solve the coverage control problem of the robot network to the dynamic area with incompletely known area information caused by the existence of the movable target and the unknown characteristic of the movable target.
Description
Technical Field
The invention belongs to the field of robot control, and in particular relates to a control method for dynamic area coverage of a robot network based on an observer.
Background
The multi-robot collaborative region coverage technology is widely applied to application scenes such as environmental monitoring, space exploration, resource exploration, pollutant removal and the like. The application of these robot network area coverage involves optimization and robot control related theory and methods. The robot network coverage technology drives a group of mobile robots to be dispersed in a task area through cooperative cooperation among robots, and realizes effective coverage monitoring of the robot network to the whole area through real-time position control, and realizes the optimal coverage monitoring effect as much as possible.
The environment of a task area considered by the existing multi-robot collaborative area coverage method is a static environment, a moving path of each robot is obtained through an algorithm, and then the robots are driven to move according to the planned path so as to complete the coverage task. However, when an important movable target object exists in the area, the environment of the task area is a more complex dynamic environment, and the area information is not completely known due to the unknown characteristics of the movable target, so that a robot path planned in advance is difficult to ensure good coverage effect.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides a control method for covering a dynamic region of a robot network based on an observer, which solves the technical problem that the existing robot network covering method has poor covering effect when the movable target exists and the region information caused by unknown characteristics of the movable target is not completely known.
To achieve the above object, according to a first aspect of the present invention, there is provided a control method for observer-based robot network dynamic area coverage, including:
s1, obtaining the approximate importance degree of a movable target in the area based on observers of robots in a robot network
S2, according toEstablishing an approximation metric function of a robot network to an area coverage effectWherein (1)>p i The current position of the robot is N, the number of the robots is V i A Voronoi partition allocated to a robot i is allocated, and q is any point in the area;
s3, based on the approximate metric function, aiming at tracking the mass centers of the Voronoi partitions, and establishing controllers of the robots asTo control each robot;
wherein omega i 、v i 、θ ei Angular velocity, linear velocity, voronoi partition centroid, angular error, k of robot i, respectively 3 ,k 4 ∈R + For normal coefficients, ρ is the disturbance margin.
Preferably, step S1 comprises:
based on a matrix of basis functions Φ (q, t) describing the importance of a movable object to an arbitrary point q in an area, the current position p of each robot i Is of the ambient density phi α (p i And t) and communication information among the robot networks, and establishing observers of all robots.
Preferably, an undirected graph is usedDescribing a communication connection between robotic networks, whereinFor edge sets, A (t) is an adjacency matrix;
the observer of each robot is:
wherein k is 1 ,k 2 ∈R + As a coefficient of the normal quantity,l ij (t) is an undirected graph->Laplacian matrix, gamma i (t)＝Φ(p i (t),t)Φ(p i (t),t) T ，χ i (t)＝Φ(p i (t),t)Φ α (p i (t),t)，Φ(p i (t), t) is the basis function matrix describing the importance of the object at position p i Value of phi α (p i (t), t) is robot +.>Current position p i Ambient density perception value of (2).
Preferably, the method comprises the steps of,
position error of each robot
Angle error of each robotWherein,
preferably, the robot network is an incomplete wheeled robot network.
Preferably, the kinematic model of the non-complete wheeled robot is:
wherein the method comprises the steps ofp i ＝[x i ,y i ] T ∈R 2 Is that the robot is in the regionIn (a) position, θ i Is robot->Angle, omega i And v i Angular and linear speeds, d, respectively, of robot i i (t) satisfies for the input disturbance: d i (t) || < ρ, ρ being the disturbance limit.
According to a second aspect of the present invention, there is provided a control device for observer-based robot network dynamic area coverage, comprising:
a first processing module, configured to obtain an approximate importance level of a movable target in the area based on observers of robots in a robot network
A second processing module for according toEstablishing an approximation metric function of a robot network to an area coverage effectWherein (1)>p i The current position of the robot is N, the number of the robots is V i A Voronoi partition allocated to a robot i is allocated, and q is any point in the area;
the control module is used for establishing controllers of all robots as targets of tracking the mass centers of the Voronoi partitions based on the approximate metric functionTo control each robot;
wherein omega i 、v i 、θ ei Angular velocity, linear velocity, voronoi partition centroid, angular error, k of robot i, respectively 3 ,k 4 ∈R + For normal coefficients, ρ is the disturbance margin.
In general, the above technical solutions conceived by the present invention, compared with the prior art, enable the following beneficial effects to be obtained:
1. the control method for the coverage of the dynamic area of the robot network based on the observer provided by the invention designs the observer which approximates the environment density function of the task area by using the basis function information and the sensor measurement information so as to solve the problem that the environment information is not completely known. Then, based on the approximate environment density function, a controller of the robot is designed to drive the robot network to change the position configuration in real time, so that the robot network can achieve good area coverage effect under the condition that a movable target exists in a task area.
2. According to the control method for the dynamic area coverage of the robot network based on the observer, which is provided by the invention, various motion states of robots are considered to be subjected to different types of incomplete constraint in reality, and an incomplete system has good advantages in aspects of saving energy, reducing weight, improving reliability and the like, so that the robot for executing the area coverage task uses the incomplete wheel type robot, and compared with a first-order integral robot model established in the existing control method, the control method has the advantages that the close degree of the characteristics in reality of the robot is not high, the control precision is not high, the coverage effect is poor, and the control method is closer to the characteristics of the actual working of the robot, so that the control precision can be further improved, and the good area coverage effect is realized.
3. According to the control method for the coverage of the dynamic area of the robot network based on the observer, the observer is built firstly, and then the controller is built based on the observer, namely the observer and the controller of the robot are separately designed, so that the observer and the controller are not coupled, and the reliability and the adaptability of the system are improved; the designed controller does not need to plan a moving path of the robot before the robot moves, but continuously adjusts the control output of the controller in the moving process of the robot, so that the controller can adapt to dynamically-changed environments and has stronger robustness and reliability.
Drawings
FIG. 1 is a flow chart of a control method for observer-based robot network dynamic area coverage provided by the invention;
FIG. 2 is a flow chart of the operation of the main control module of the robot;
FIG. 3 is a schematic diagram of an under-actuated wheeled robot model provided by the present invention;
FIG. 4 is a schematic diagram of Voronoi division provided by the present invention;
FIG. 5 shows the 8 robot pair coefficients α provided by the present invention 1 Is a graph of estimated variation of (a);
FIG. 6 shows the 8 robot pair coefficients α provided by the present invention 2 Is a graph of estimated variation of (a);
FIG. 7 shows the 8 robot pair coefficients α provided by the present invention 3 Is a graph of estimated variation of (a);
FIG. 8 is a graph of the change of the measurement function, the angle error and the distance error with time provided by the invention;
fig. 9 is a diagram of a motion trail of the robot network dynamic region coverage provided by the invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The embodiment of the invention provides a control method for dynamic area coverage of a robot network based on an observer, which is shown in fig. 1-2 and comprises the following steps:
s1, obtaining the approximate importance degree of a movable target in the area based on observers of robots in a robot network
Specifically, based on the observers of each robot in the robot network, a coefficient matrix describing the approximate importance degree of the movable object in the area is estimated
Further, step S1 includes:
according to the basic function matrix phi (q, t) describing the importance of the movable target to any point q in the area, each robot current position p i Is of the ambient density phi α (p i And t) and communication information among the robot networks, and establishing observers of all robots.
Further, using undirected graphsDescribing a communication connection between robot networks, wherein +.>For edge sets, A (t) is an adjacency matrix;
the observer of each robot is:
wherein k is 1 ,k 2 ∈R + As a coefficient of the normal quantity,l ij (t) is an undirected graph->Laplacian matrix, gamma i (t)＝Φ(p i (t),t)Φ(p i (t),t) T ，χ i (t)＝Φ(p i (t),t)Φ α (p i (t),t)，Φ(p i (t), t) isBasis function matrix describing importance of object at position p i Value of phi α (p i (t), t) is robot +.>At the current position p i Ambient density perception value of (2).
Further, the robotic network is an incomplete wheeled robotic network.
Further, the kinematic model of the incomplete wheeled robot is:
wherein the method comprises the steps ofp i ＝[x i ,y i ] T ∈R 2 Is the position of the robot in the area, θ i Is the angle of the robot, omega i And v i The angular velocity and the linear velocity of the robot i, ||d, respectively i (t) d is the input disturbance i (t) || < ρ, ρ being the disturbance limit.
Specifically, step S1 includes:
and L1, modeling and analyzing the robot network area coverage task.
As shown in fig. 3, consider a robot network for an under-actuated wheeled robot (i.e., a non-full wheeled robot) comprising N robotsIn the task area Q epsilon R 2 The coverage task is executed, and the kinematic model of the under-actuated wheeled robot is as follows:
wherein,p i ＝[x i ,y i ] T ∈R 2 is the position of the robot in the area, θ i Is the angle of the robot, v i ,ω i The speed and angular speed control inputs are respectively provided, d i (t) || < ρ is the input perturbation, ρ is the perturbation margin, ρ > 0.
The performance of each robot-carried coverage monitoring actuator (e.g., sensor, camera, etc.) is modeled as a gaussian function:
wherein Q is E Q, beta i > 0 is a function coefficient, sigma 1 Is the width of the gaussian function f. The importance of each point q in the region is described using the ambient density function as:
where M is the number of movable objects in the region, α= [ α ] 1 ,α 2 ,…,α M ] T ∈R M Is an unknown coefficient matrix representing the actual importance of the movable object; phi (q, t) = [ phi ] 1 (q,t),φ 2 (q,t),…,φ M (q,t)] T Is a matrix of basis functions, each movable object importance spatial propagation model is:
is the position of object j, c j Is the limit of speed c j ＞0，σ 2 Is the width of the gaussian function phi. It is assumed that the basis function Φ (q, t) is known by the robot network and that each robot also carries a deviceThe current position p of the robot is measured i Is of the ambient density phi α (p i T). Describing the coverage effect of the robot network on the area by adopting a measurement function:
the larger the value of the metric function H (P, t) the better the coverage effect. We do Voronoi division of the task area with the current position of each robot:
the robot networks can calculate own Voronoi partitions through communication, as shown in fig. 4, black dots ". Cndot" represent robot positions, voronoi partitions are performed on the 100×100 area, and different color areas represent the Voronoi partitions allocated to each robot. We consider only the coverage monitoring effect of each robot within the respective Voronoi partition, ignoring outside the partition, so there are:
using undirected graphsTo describe a communication connection between robot networks, whereinA (t) is an adjacency matrix, and the neighbor set of the robot i is N i (t)＝{V i ∪V j Not equal to 0, j not equal to i, j e V, diagram +.>The laplace matrix is L (t) = [ L ij (t)]∈R N×N Wherein when->l ij (t)<0, otherwise l ij (t) =0, and +.>The characteristics of the division by Vronoi are known as undirected graph +.>Is always communicated.
And L2, designing an observer to perform environment secret function estimation.
An observer is designed for each robot based on known basis functions and environmental density measurements for the current position of each robot and using communication information between the robot networks to obtain an estimate of alpha
The parameter matrix values estimated for robot i, i.e. the unknown coefficient matrix to be estimated, k 1 ,k 2 ∈R + Is a normal quantity coefficient, ++>Variable gamma i (t)＝Φ(p i (t),t)Φ(p i (t),t) T ，χ i (t)＝Φ(p i (t),t)Φ α (p i (t),t)。
The designed observer can be proved by using the Lasal invariance principle, and the following steps can be realized:
obtaining the estimation of the coefficient matrix alpha
The above completes the estimation of the environment.
As shown in fig. 5-7, in a 100×100 area containing 3 important movable objects, the change situation of three coefficients estimated by 8 robots using observers is shown, and it can be seen that each robot can accurately estimate three coefficients.
S2, according toEstablishing an approximation metric function of a robot network to an area coverage effectWherein (1)>P is the function of the ambient density approximated by an observer i The current position of the robot is N, the number of the robots is V i A Voronoi partition allocated to a robot i is allocated, and q is any point in the area;
s3, based on the approximate metric function, aiming at tracking the mass centers of the Voronoi partitions, and establishing controllers of the robots asTo control each robot;
wherein omega i 、v i 、θ ei Angular velocity, linear velocity, voronoi partition centroid, angular error, k of robot i, respectively 3 ,k 4 ∈R + For normal coefficients, ρ is the disturbance margin.
Further, each robotPosition error of (2)
Angle error of each robotWherein,
specifically, steps S2-S3 are for designing an under-actuated wheeled robot controller.
Coefficient matrix estimated by each robot using its observerObtaining an approximate density functionBased on the density function estimated by the observer, an approximate metric function is obtained:
and (3) calculating the derivative of each robot position of the robot network:
wherein,the method comprises the following steps:
wherein,for the quality of the robot ivorooi partition,is the centroid that is the partition of the robot ivoro.
It follows that, when the position p of the robot i i Position C at its Voronoi centroid vi When the coverage effect of the robot network to the allocated Voronoi partition is optimal, and when each robot in the robot network reaches the optimal coverage effect in the respective Voronoi partition, the robot network is realizedLocally optimal coverage of the real task area Q. Therefore, to achieve optimal coverage, we design the controller to drive the robots to track the centroids of the respective Voronoi sections. Defining a position error: />Angle error::>wherein,
the controller for designing the underactuated wheeled robot is as follows:
wherein k is 3 ,k 4 ∈R + For normal coefficients, ρ is the boundary of the disturbance.
The change of the measurement function with time and the error change of the states of the 8 underactuated robots in the robot network from the expected state are shown in FIG. 8, in whichFrom->The change in time t shows that the metric function increases with time over the period of time just started, indicating that the coverage is optimized and then remains unchanged over time. From θ respectively e The angular velocity input omega in the designed controller can be seen from the curves of E and time t i The angle of the robot i can be tracked to a desired angle within a limited time, and the linear velocity v i The position of robot i can be made to converge progressively to 0 with the desired position (centroid position of Voronoi partition).
The motion trajectories of the movable target and the robot network in the whole control process are shown in fig. 9, wherein solid lines represent the motion trajectories of the movable target, each broken line represents the motion trajectory of one robot, the initial position is represented by 'x', and the final position is represented by 'O'. It can be seen that the initial position configuration of the robot network is not optimal, then the robot approaches the moving important target and moves the robot network dynamically to configure the position as the target moves.
The control device for the observer-based robot network dynamic area coverage provided by the invention is described below, and the control device for the observer-based robot network dynamic area coverage described below and the control method for the observer-based robot network dynamic area coverage described above can be referred to correspondingly.
The embodiment of the invention provides a control device for robot network dynamic area coverage based on an observer, which comprises the following components:
a first processing module, configured to obtain an approximate importance level of a movable target in the area based on observers of robots in a robot network
A second processing module for according toEstablishing an approximation metric function of a robot network to an area coverage effectWherein (1)>p i The current position of the robot is N, the number of the robots is V i A Voronoi partition allocated to a robot i is allocated, and q is any point in the area;
the control module is used for establishing controllers of all robots as targets of tracking the mass centers of the Voronoi partitions based on the approximate metric functionTo control each robot;
wherein omega i 、v i 、θ ei Angular velocity, linear velocity, voronoi partition centroid, angular error, k of robot i, respectively 3 ,k 4 ∈R + For normal coefficients, ρ is the disturbance margin.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (5)
1. A control method for observer-based robot network dynamic area coverage, comprising:
s1, obtaining the approximate importance degree of a movable target in the area based on observers of robots in a robot network
S2, according toEstablishing an approximation metric function of a robot network to an area coverage effectWherein (1)>p i The current position of the robot is N, the number of the robots is V i A Voronoi partition allocated to a robot i is allocated, and q is any point in the area;
s3, based on the approximate metric function, aiming at tracking the mass centers of the Voronoi partitions, and establishing controllers of the robots asTo control each robot;
wherein omega i 、v i 、C vi 、θ ei Angular velocity, linear velocity, voronoi partition centroid, angular error, k of robot i, respectively 3 ,k 4 ∈R + Is a normal coefficient, and ρ is a disturbance limit;
the step S1 comprises the following steps:
based on a matrix of basis functions Φ (q, t) describing the importance of a movable object to an arbitrary point q in an area, the current position p of each robot i Is of the ambient density phi α (p i T) and communication information between the robot networks, and establishing observers of all robots;
using undirected graphsDescribing a communication connection between robot networks, wherein +.>For edge sets, A (t) is an adjacency matrix;
the observer of each robot is:
wherein k is 1 ,k 2 ∈R + As a coefficient of the normal quantity,l ij (t) is an undirected graphLaplacian matrix, gamma i (t)＝Φ(p i (t),t)Φ(p i (t),t) T ，χ i (t)＝Φ(p i (t),t)Φ α (p i (t),t)，Φ(p i (t), t) is the basis function matrix describing the importance of the object at position p i Value of phi α (p i (t), t) is a robotCurrent position p i Ambient density perception value of (2).
2. The method for controlling observer-based dynamic area coverage of a robot network according to claim 1,
position error of each robot
Angle error of each robotWherein,
3. the observer-based control method for dynamic area coverage of a robot network according to claim 1, wherein the robot network is a non-complete wheeled robot network.
4. A control method for observer-based robot network dynamic area coverage according to claim 3, wherein the kinematic model of the incomplete wheeled robot is:
wherein i is E V, p i ＝[x i ,y i ] T ∈R 2 Is the position of the robot in the area, θ i Is a robotAngle, omega i And v i Angular and linear speeds, d, respectively, of robot i i (t) satisfies for the input disturbance: d i (t) || < ρ, ρ being the disturbance limit.
5. A control device for observer-based robot network dynamic area coverage, comprising:
a first processing module, configured to obtain an approximate importance level of a movable target in the area based on observers of robots in a robot network
A second processing module for according toEstablishing an approximation metric function of a robot network to an area coverage effectWherein (1)>p i The current position of the robot is N, the number of the robots is V i A Voronoi partition allocated to a robot i is allocated, and q is any point in the area;
the control module is used for establishing controllers of all robots as targets of tracking the mass centers of the Voronoi partitions based on the approximate metric functionTo control each robot;
wherein omega i 、v i 、C vi 、θ ei Angular velocity, linear velocity, voronoi partition centroid, angular error, k of robot i, respectively 3 ,k 4 ∈R + Is a normal coefficient, and ρ is a disturbance limit;
based on a matrix of basis functions Φ (q, t) describing the importance of a movable object to an arbitrary point q in an area, the current position p of each robot i Is of the ambient density phi α (p i T) and communication information between the robot networks, and establishing observers of all robots;
using undirected graphsDescribing a communication connection between robot networks, wherein +.>For edge sets, A (t) is an adjacency matrix;
the observer of each robot is:
wherein k is 1 ,k 2 ∈R + As a coefficient of the normal quantity,l ij (t) is an undirected graphLaplacian matrix, gamma i (t)＝Φ(p i (t),t)Φ(p i (t),t) T ，χ i (t)＝Φ(p i (t),t)Φ α (p i (t),t)，Φ(p i (t), t) is the basis function matrix describing the importance of the object at position p i Value of phi α (p i (t), t) is a robotCurrent position p i Ambient density perception value of (2).
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| 李晶 ; .基于高斯估算的最优覆盖控制在多无人机协同任务规划中应用研究.中国多媒体与网络教学学报(中旬刊).2020,(第08期),全文. * |
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