CN112488359B - Multi-agent static multi-target trapping method based on RRT and OSPA distance - Google Patents
Multi-agent static multi-target trapping method based on RRT and OSPA distance Download PDFInfo
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Abstract
The invention discloses a multi-agent static multi-target trapping method based on the distance between RRT and OSPA. According to the method, firstly, an agent keeps a leader-follower formation, a path planning path is conducted on a leader, the leader moves, and after entering a trapping area, OSPA distance calculation is conducted to allocate trapping points. And finally, each intelligent agent respectively performs route planning, moves to a trapping point and forms trapping on the static target. In the aspect of path planning, path planning is carried out between an intelligent agent and a surrounding point through an RRT algorithm, the path planning time is shortened through reducing the sampling range of the intelligent agent, and finally, path optimization is carried out through a Bezier curve. The method can allocate the trapping points to the intelligent body and plan the path by itself, and can effectively shorten the trapping time under the condition of multi-target relative aggregation by adding the mode judgment.
Description
Technical Field
The invention belongs to the technical field of intelligent systems, in particular to the technical field of intelligent body trapping and path planning, and relates to a multi-intelligent body static multi-target trapping method based on RRT (Rapid-exploring Random Trees, fast explored random tree algorithm) and OSPA (Optimal Sub-patten Assignment, optimal Sub-mode allocation) distance.
Background
The path planning problem is a collision-free safety path problem for a target object to find a collision-free safety path from a starting point to an end point in a range of a designated area, and the collision-free safety path problem has wide application in the fields of airport towing, logistics storage, traffic control, robots, electronic games and the like. There are many well-established algorithms such as: the potential field method, the algorithms D and A, the double-side convex hull expansion model algorithm, the ant colony algorithm and the like, wherein the rapid search algorithm (RRT) is one of the algorithms, and is a data structure and algorithm for searching the non-convex high-dimensional space efficiently. In the distributed system, mutual collaboration among multiple agents is established, so that the distributed agent system can efficiently complete complex tasks. The trapping control problem application mainly comprises unmanned vehicle trapping, aerial target trapping, water surface/underwater target trapping and the like in the military field.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a multi-agent static multi-target trapping method based on the distance between RRT and OSPA.
The method comprises the following steps:
(1) Multi-intelligent system formation:
set S= { S of N-agent-composed enclosure bodies 1 ,s 2 ,…,s N }，s 1 S is the leader n For follower, n=2, 3, …, N;
the first order Lipschitz nonlinear dynamic equation of the leader is:
the first order Lipschitz nonlinear dynamic equation of the follower is:λ n ∈R N the position vector is the position vector of the nth agent; u (u) n ∈R N Is the control input parameter of the nth agent, R N Representing an N-dimensional vector; t is time, A, B, C is system parameter, f (lambda n T) is a continuously differentiable function and satisfies the lipschz condition.
For each follower, its control protocol is:
u n (t)＝-Z(r(t))∑a nm [λ n (t)-λ m (t-τ(t))]-Z(r(t))∑a nm [λ n (t)-λ 1 (t-τ(t))]，m＝2,3,…,N，m≠n；
wherein lambda is m (t- τ (t)) represents the nth follower s n From the mth follower s m Acquired information lambda 1 (t- τ (t)) means that the nth follower is from the leader s 1 The acquired information; τ (t) is a time-varying time-lag function and satisfiesAndindicating the upper bound of time lag%>For the time lag derivative, h is the upper bound of the time lag derivative, Z represents the control gain, r (t) is the mode at the moment of t, a nm For follower s n Sum s m And connecting the weight values.
(2) Path planning:
(2.1) within the feasible region, relative to a randomly generated point q rand Select the closest q in the tree rand Node q of (2) near Will q near Extending to q with specified step size rand Generating a new node q new Connection q near And q new Adding an extended tree, and performing iterative computation by adopting an RRT algorithm until q new Arrive at target point q goal Or a target point area, find a base path in the extended tree.
(2.2) Bessel-contouring is performed on the base path: when the K-order Bezier curve is in the K-dimensional space, the curve is composed of k+1 control points P e Composition e=0, 1, …, k; the bezier curve of the k-order is expressed as:B k (t) is bezier curve k-order output, gamma is control input parameter of path, and gamma is more than or equal to 0 and less than or equal to 1; f (F) k,e (gamma) is the k-th order mixing function of the Bernstein polynomial,/for>Is a two-term coefficient>Representing factorial, H K ∈R K×K Is an identity matrix.
(3) Determining a trapping area:
target coordinate set to be captured g= { (x) 1 ,y 1 ),(x 2 ,y 2 ),…,(x J ,y J )}，(x j ,y j ) J=1, 2, …, J being the number of targets to be captured; surrounding J targets to be captured into an irregular polygonCentroid O coordinateDistance between each object to be captured and centroid O>The radius r=max { D of the circle j -a }; the centroid O is used as the center of a circle, and the area with the radius r is the trapping area.
(4) N intelligent bodies move to the trapping area, and when the leader s 1 When reaching the boundary of the trapping area, task allocation is started:
in (1) the->Representing the real target state of the sensor w at time v,/->Sensor w, representing moment v, estimates the target state, X v,w For a true multi-target state set,to estimate a multi-objective state set; p is the norm, μ and ρ are the real target number and the estimated target number, respectively; pi (II) N Represents the set of permutations, pi (l) represents the first permutation, l=n-! The method comprises the steps of carrying out a first treatment on the surface of the c is a horizontal distance parameter representing the average circle distance error of each error potential, d is +.>And->Distance.
Taking the last moment position before each agent enters the trapping area as a starting point set eta= { eta 1 ,η 2 ,…,η N And takes the target as the final point set g= { G 1 ,G 2 ,…,G J The OSPA distance is OSPA (p, c, η, G).
(5) Composing an acquisition formation:
n intelligent agents form a static circumference formation by taking a target to be captured as a circle center, the distances between adjacent intelligent agents are equal,the intelligent body keeps the same distance with the object to be captured and has the same interval angle theta n Distributed around the object to be captured, 0 < theta n < pi, number of traps required for a single target[]Represents a rounding, and the trapping point sigma= { sigma 1,1 ,…,σ 1,β ,σ 2,1 ,…,σ 2,β ,…,σ α,β }，α＝1,2,…,J，β＝1,2,…,ε。
(6) The targets closest to the leader are captured preferentially, and then capturing is carried out sequentially from near to far according to the distance.
When the method is faced with the problem of multi-static target trapping, the method combining path planning and an OSPA algorithm can allocate the optimal trapping point to the intelligent agent and can self-route planning, and under the condition of multi-target relative aggregation, the trapping time can be effectively shortened.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a schematic diagram of a multi-agent system formation;
fig. 3 is a schematic diagram of RRT path planning;
FIG. 4 is a schematic view of a trapping region;
FIG. 5 is a diagram of a desired Capture formation.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the multi-agent static multi-target trapping method based on RRT and OSPA distance is characterized in that an agent is firstly enabled to keep leading-following formation, a path planning is carried out on a leader, the leader leading follower moves, and after entering a trapping area, OSPA distance calculation is carried out to allocate trapping points. And finally, each intelligent agent respectively performs route planning, moves to a trapping point and forms trapping on the static target. In the aspect of path planning, path planning is carried out between an intelligent agent and a surrounding point through an RRT algorithm, the path planning time is shortened through reducing the sampling range of the intelligent agent, and finally, path optimization is carried out through a Bezier curve.
The method comprises the following steps:
(1) Multi-intelligent system formation:
as shown in fig. 2, in a multi-agent system composed of sixteen agents, the set of trapping agents s= { S 1 ,s 2 ,…,s 16 (s is therein 1 S is the leader 2 ～s 16 For the follower, the follower maintains an angle and speed to track the leader.
The first order Lipschitz nonlinear dynamic equation of the leader is:
the first order Lipschitz nonlinear dynamic equation of the follower is:n＝2,3,…,16；λ n ∈R 16 the position vector is the position vector of the nth agent; u (u) n ∈R 16 The control input parameter is the control input parameter of the nth agent; t is time, A, B, C is system parameter, f (lambda n T) is a continuous and differentiable function and satisfies the lipschz condition;
for each follower, its control protocol is:
u n (t)＝-Z(r(t))∑a nm [λ n (t)-λ m (t-τ(t))]-Z(r(t))∑a nm [λ n (t)-λ 1 (t-τ(t))]，m＝2,3,…,16，m≠n；
wherein lambda is m (t- τ (t)) represents the nth follower s n From the mth follower s m Acquired information lambda 1 (t- τ (t)) means that the nth follower is from the leader s 1 The acquired information; τ (t) is a time-varying time-lag function and satisfiesAnd indicating the upper bound of time lag%>For the time lag derivative, h is the upper bound of the time lag derivative, Z represents the control gain, r (t) is the mode at the moment of t, a nm For follower s n Sum s m And connecting the weight values.
(2) Path planning:
(2.1) As shown in FIG. 3, within the feasible region, a randomly generated point q is opposed rand Select the closest q in the tree rand Node q of (2) near Will q near Extending to q with specified step size rand Generating a new node q new Connection q near And q new Adding an extended tree, and performing iterative computation by adopting an RRT algorithm until q new Arrive at target point q goal Or a target point area at a start point q init And target point q goal Finds the base path.
(2.2) since the path generated by the RRT algorithm is not smooth enough, bezier patterning is performed on the base path. The bezier curve is one of typical parametric curves for smooth path generation.
Bessel-like patterning is performed on the base path: when the K-order Bezier curve is in the K-dimensional space, the curve is composed of k+1 control points P e Composition e=0, 1, …K; the bezier curve of the k-order is expressed as:B k (t) is bezier curve k-order output, gamma is control input parameter of path, and gamma is more than or equal to 0 and less than or equal to 1; f (F) k,e (gamma) is the k-th order mixing function of the Bernstein polynomial,/for>Is a two-term coefficient>
(3) Determining a trapping area:
the target to be captured is four G 1 、G 2 、G 3 And G 4 Its coordinate set g= { (x) 1 ,y 1 ),(x 2 ,y 2 ),(x 3 ,y 3 ),(x 4 ,y 4 ) }. As shown in FIG. 4, due to uncertainty of the trapping region, a trapping circular region is formed by the centroids of the irregular polygons, four objects to be trapped are trapped into the irregular polygons, and the coordinates of the centroids of the polygons are ODistance between each object to be captured and centroid O>The radius r=max { D of the circle j -a }; the centroid O is used as the center of a circle, and the area with the radius r is the trapping area.
(4) N intelligent bodies move to the trapping area, and when the leader s 1 When the boundary of the trapping area is reached, task allocation is started.
Due to the number of agents and targets, task allocation is required to ensure that the agents can reach the optimal trapping point, and the algorithm is adopted because the distance consistency of OSPA is good. The following OSPA distance is introduced to solve the problem that the Wasserstein distance is undefined when the set is empty.
In the method, in the process of the invention,representing the real target state of the sensor w at time v,/->Sensor w, representing moment v, estimates the target state, X v,w For a true multi-objective state set,/->To estimate a multi-objective state set; p is the norm, μ and ρ are the real target number and the estimated target number, respectively; pi (II) N Represents the set of permutations, pi (l) represents the first permutation, l=n-! The method comprises the steps of carrying out a first treatment on the surface of the c is a horizontal distance parameter representing the average circle distance error of each error potential, d is +.>And->Distance.
Taking the last moment position before each agent enters the trapping area as a starting point set eta= { eta 1 ,η 2 ,…,η N And takes the target as the final point set g= { G 1 ,G 2 ,…,G J The OSPA distance is OSPA (p, c, eta, G);
(5) Composing an acquisition formation:
sixteen intelligent agents take a target to be captured as a circle center to form a static circumference formation, the distances between adjacent intelligent agents are equal,(x n ,y n ) And (5) the coordinates of the first agent. Desirably, the formation of the capture is as shown in FIG. 5, with the agent maintained at the same distance from the target to be captured and at an equal angular separation θ n Distributed around the object to be captured, 0 < theta n < pi, number of traps required for a single target +.>
The capture point σ= { σ 1,1 ,…,σ 1,β ,σ 2,1 ,…,σ 2,β ,…,σ α,β }，α＝1,2,3,4，β＝1,2,3,4。
(6) And (3) enclosing and catching: and (3) preferentially trapping the target closest to the leader, and then sequentially trapping according to the distance from the near to the far, wherein each intelligent agent plans a path according to the given starting point and the trapping point.
Claims (1)
1. The multi-agent static multi-target trapping method based on the distance between RRT and OSPA is characterized by comprising the following steps:
(1) Multi-intelligent system formation:
set S= { S of N-agent-composed enclosure bodies 1 ,s 2 ,…,s N }，s 1 S is the leader n For follower, n=2, 3, …, N;
the first order Lipschitz nonlinear dynamic equation of the leader is:
the first order Lipschitz nonlinear dynamic equation of the follower is:λ n ∈R N the position vector is the position vector of the nth agent; u (u) n ∈R N Is the control input parameter of the nth agent, R N Representing an N-dimensional vector; t is time, A, B, C is system parameter, f (lambda n T) is continuously differentiableAnd satisfies the lipschz condition;
for each follower, its control protocol is:
u n (t)＝-Z(r(t))∑a nm [λ n (t)-λ m (t-τ(t))]-Z(r(t))∑a nm [λ n (t)-λ 1 (t-τ(t))]，m＝2,3,…,N，m≠n；
wherein lambda is m (t- τ (t)) represents the nth follower s n From the mth follower s m Acquired information lambda 1 (t- τ (t)) means that the nth follower is from the leader s 1 The acquired information; τ (t) is a time-varying time-lag function and satisfiesAnd indicating the upper bound of time lag%>For the time lag derivative, h is the upper bound of the time lag derivative, Z represents the control gain, r (t) is the mode at the moment of t, a nm For follower s n Sum s m Connecting weight values;
(2) Path planning:
(2.1) within the feasible region, relative to a randomly generated point q rand Select the closest q in the tree rand Node q of (2) near Will q near Extending to q with specified step size rand Generating a new node q new Connection q near And q new Adding an extended tree, and performing iterative computation by adopting an RRT algorithm until q new Arrive at target point q goal Or a target point area, finding a basic path in the expansion tree;
(2.2) Bessel-contouring is performed on the base path: when the K-order Bezier curve is in the K-dimensional spaceThe curve is composed of k+1 control points P e Composition e=0, 1, …, k; the bezier curve of the k-order is expressed as:B k (t) is bezier curve k-order output, gamma is control input parameter of path, and gamma is more than or equal to 0 and less than or equal to 1; f (F) k,e (gamma) is the k-th order mixing function of the Bernstein polynomial,/for> Is a two-term coefficient>The following is carried out Representing factorial, H K ∈R K×K Is an identity matrix;
(3) Determining a trapping area:
target coordinate set to be captured g= { (x) 1 ,y 1 ),(x 2 ,y 2 ),…,(x J ,y J )}，(x j ,y j ) J=1, 2, …, J being the number of targets to be captured; surrounding J targets to be captured into an irregular polygon, and forming the O coordinates of the polygon centroidDistance between each object to be captured and centroid O>The radius r=max { D of the circle j -a }; taking the centroid O as the circle center, and taking the area with the radius r as the trapping area;
(4) N intelligent bodies move to the trapping area, and when the leader s 1 When reaching the boundary of the trapping area, task allocation is started:
in the method, in the process of the invention,representing the real target state of the sensor w at time v,/->Sensor w, representing moment v, estimates the target state, X v,w For a true multi-objective state set,/->To estimate a multi-objective state set; p is the norm, μ and ρ are the real target number and the estimated target number, respectively; pi (II) N Represents the set of permutations, pi (l) represents the first permutation, l=n-! The method comprises the steps of carrying out a first treatment on the surface of the c is a horizontal distance parameter representing the average circle distance error of each error potential, d is +.>And->A distance;
taking the last moment position before each agent enters the trapping area as a starting point set eta= { eta 1 ,η 2 ,…,η N And takes the target as the final point set g= { G 1 ,G 2 ,…,G J The OSPA distance is OSPA (p, c, eta, G);
(5) Composing an acquisition formation:
n intelligent agents form a static circumference formation by taking a target to be captured as a circle center, the distances between adjacent intelligent agents are equal,the intelligent body keeps the same distance with the object to be captured and has the same interval angle theta n Distributed around the object to be captured, 0 < theta n < pi, number of traps required for a single target[]Represents a rounding, and the trapping point sigma= { sigma 1,1 ,…,σ 1,β ,σ 2,1 ,…,σ 2,β ,…,σ α,β }，α＝1,2,…,J，β＝1,2,…,ε；
(6) The targets closest to the leader are captured preferentially, and then capturing is carried out sequentially from near to far according to the distance.
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| CN107943053A (en) * | 2017-12-15 | 2018-04-20 | 陕西理工大学 | A kind of paths planning method of mobile robot |
| CN110517286A (en) * | 2019-08-12 | 2019-11-29 | 杭州电子科技大学 | Single goal dynamically track based on MAS control and surround and seize method |
| CN110705803A (en) * | 2019-10-11 | 2020-01-17 | 福州大学 | Route planning method based on triangle inner center guide RRT algorithm |
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| CN107943053A (en) * | 2017-12-15 | 2018-04-20 | 陕西理工大学 | A kind of paths planning method of mobile robot |
| CN110517286A (en) * | 2019-08-12 | 2019-11-29 | 杭州电子科技大学 | Single goal dynamically track based on MAS control and surround and seize method |
| CN110705803A (en) * | 2019-10-11 | 2020-01-17 | 福州大学 | Route planning method based on triangle inner center guide RRT algorithm |
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