CN111766784B - Iterative optimization method for multi-robot pattern composition in obstacle environment - Google Patents

Iterative optimization method for multi-robot pattern composition in obstacle environment Download PDF

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CN111766784B
CN111766784B CN202010660083.2A CN202010660083A CN111766784B CN 111766784 B CN111766784 B CN 111766784B CN 202010660083 A CN202010660083 A CN 202010660083A CN 111766784 B CN111766784 B CN 111766784B
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robot
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CN111766784A (en
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张方方
王婷婷
李琦岩
彭金柱
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Zhengzhou University
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention discloses an iterative optimization method for multi-robot pattern formation in an obstacle environment, which aims to dynamically solve optimal target pattern parameters by taking the shortest total path of a plurality of robots to reach an allocated target point, ensures that all robots reach respective target points without collision, and realizes the optimization of pattern formation in the obstacle environment. The invention has the advantages that the shortest total path of a plurality of robots to reach the distributed target points is taken as a target, the optimal target pattern parameters are dynamically solved, the targets are dynamically grouped and matched to accelerate algorithm convergence, and the target patterns are formed by controlling the robots to reach the target points without collision in a dynamic barrier environment.

Description

Iterative optimization method for multi-robot pattern formation in obstacle environment
Technical Field
The invention relates to the field of robot application, in particular to an iterative optimization method for multi-robot pattern composition in an obstacle environment.
Background
In recent years, with the development of robot technology and the drive of actual demand, the application field of the robot is continuously expanded, the robot is more intelligent in function, the robustness, the stability and the efficiency are greatly improved, and the requirements of various scenes can be well met, including a family service type robot, an automatic driving automobile, a military reconnaissance robot, an unmanned aerial vehicle and the like. Robots are divided into single robots and multiple robots in number, and the single robot cannot cope with a complicated environment. Therefore, the concept of multi-agent system (MAS) was proposed in the 70's of the 20 th century, and the research of multi-agent system has been a focus in the research field of robots, and the manufacturing cost of robots has been lower and lower with the progress made in wireless communication technology, sensor technology, embedded computing, etc., which has pushed the research of multi-robot systems to some extent.
The multi-robot system is not only a system in which a single robot is superposed in number, but also a system in which a plurality of simple robots complete complex tasks through certain organization rules and information interaction. The cost of manufacturing a plurality of simple robots is lower than manufacturing a single robot with complex functions. Meanwhile, the multiple robots have better robustness and adaptability and can be better applied to complex changing environments. The research of multi-robot systems faces many problems, such as pattern formation problems, aggregation problems, cooperative movement problems, self-scheduling problems, etc. Wherein the pattern formation is to change the position of each robot in the group according to some predefined rules to form a specific shape. The pattern composition has important application value for path search, area coverage, target search and the like in various fields or scenes such as aerospace, military, disaster relief and the like.
Currently, multi-robot patterning algorithms use predetermined target positions to study the path planning from swarm robots to the predetermined target positions. In practice, however, the target positions are usually not predetermined and the swarm robots need to form different formations according to different tasks. In addition, most researches on the multi-robot pattern structure are based on an obstacle-free environment, and static and dynamic obstacles exist in an actual environment, so that the optimized target pattern generation is performed according to the initial state and task requirements of the robot in the obstacle environment, and the method has wide practical application value.
Disclosure of Invention
The invention aims to provide an iterative optimization method for the pattern composition of multiple robots in the obstacle environment, which realizes the optimization of the pattern composition of multiple robots in the obstacle environment and ensures that each robot reaches a target position without collision.
In order to achieve the purpose, the invention adopts the following technical scheme:
the iterative optimization method for the multi-robot pattern formation in the obstacle environment dynamically solves the optimal target pattern parameters by taking the shortest total path of a plurality of robots to reach the distribution target point as the aim, ensures that all the robots reach the respective target points without collision, and realizes the optimization of the pattern formation in the obstacle environment; the method comprises the following steps:
step 1, solving an optimal target pattern
Figure GDA0003864719350000021
At the kth iteration time, judging the last target pattern
Figure GDA0003864719350000022
Whether there is a target point q that the robot has reached * (k-1) is located within the safe range of the dynamic barrier and, if present, the optimal target pattern is re-solved
Figure GDA0003864719350000023
And each robot and the optimal target pattern
Figure GDA0003864719350000024
Is of the matching matrix sigma * (k) Regrouping multiple robots, otherwise optimal target pattern
Figure GDA0003864719350000025
The grouping is not changed; as the robot is to avoid collisions with obstacles and other robots, it may be far from the previously assigned target point and need to reassign the target point; after all the robots are grouped, global distribution is not performed, and target point distribution is performed by adopting the robots in the group; k is a natural number not less than 1;
step 2, planning a collision-free path;
first, each robot calculates a preferred velocity v directed to an assigned target point without considering other robots and obstacles pref (ii) a Then defining a neighborhood of robots, each robot respectively calculating a speed obstacle set (namely a speed set RVO capable of colliding), only considering other robots in the neighborhood of the robot without considering all other robots when calculating the speed obstacle set, and then selecting the speed obstacle set which is closest to the preferred speed v pref As the optimal collision avoidance velocity v opt (ii) a Each robot is based on the respective optimal collision avoidance velocity v opt Updating the position, and finally repeating the solving of the optimal target pattern in iterative control
Figure GDA0003864719350000026
A collision-free path planning part until all the robots reach the target point;
the optimal collision avoidance velocity v opt The calculation process of (2) includes:
defining neighborhood NR of robot i i Is a radical of p i (k-1) a circular area with a center and a radius of 3R; robot i calculates velocity barrier set RVO i When only the neighborhood NR need be considered i Other robots and obstacles within;
Figure GDA0003864719350000031
namely: RVO i Consider neighborhood NR for robot i i Speed obstacle area obtained by other robots
Figure GDA0003864719350000032
And a speed obstacle region obtained in consideration of the obstacle
Figure GDA0003864719350000033
A union of (1); wherein v is o Indicating the speed of the obstacle, v for static obstacles o =0, for dynamic obstacles v o ＝v do (ii) a O belongs to a range of O, and is a position set P of a plurality of static obstacles at an initial moment so (ii) a O = [ P ] when the optimal target pattern is re-solved in the iterative control so ；P do ]In which P is do A set of locations representing a plurality of dynamic obstacles;
robot i-selection RVO i Outer closest to
Figure GDA0003864719350000034
Speed of as an optimum collision avoidance speed
Figure GDA0003864719350000035
Figure GDA0003864719350000036
Wherein: AV (Audio video) i The speed of the robot i does not exceed V p The velocity set of (a); v p Is the maximum velocity of the robot.
The pattern formed by the multiple robots is a rectangular, circular or letter pattern.
The invention has the advantages that the shortest total path of a plurality of robots to reach the distributed target points is taken as a target, the optimal target pattern parameters are dynamically solved, the targets are dynamically grouped and matched to accelerate algorithm convergence, and the target patterns are formed by controlling the robots to reach the target points without collision in a dynamic barrier environment.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a simulation experiment diagram of 27 robots constituting a COL trajectory in the example.
Fig. 3 is a simulation experiment diagram of a COL pattern composed of 27 robots in the example.
Fig. 4 is a position error convergence diagram of 27 robots in the embodiment.
Fig. 5 is a schematic diagram of an embodiment in which the robot has arrived at the target point within the safety area DO of the dynamic barrier.
Detailed Description
The following describes embodiments of the present invention in detail with reference to the accompanying drawings, which are implemented on the premise of the technical solution of the present invention, and give detailed implementation manners and specific operation procedures, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 1-4, in the iterative optimization method for multi-robot pattern formation in an obstacle environment of the present invention, taking three letter patterns COL as an example, a grouping strategy is to allocate robots forming the same letter to a group, and with the shortest total path of 27 disc robots with radius R to reach an allocated target point as a target, dynamically solving an optimal target pattern parameter, ensuring that the robots reach the target without collision, thereby realizing optimization of pattern formation in the obstacle environment; the method comprises the following specific steps:
step 1, solving an optimal target pattern
Figure GDA0003864719350000041
This section mainly addresses the solution of optimal target patterns at the initial time
Figure GDA0003864719350000042
And the need to re-solve the optimal target pattern in iterative control
Figure GDA0003864719350000043
The process of (2).
At an initial time (k = 0), a position P based on a static obstacle so And initial position P of each robot n×2 (0) Solving for the optimal target pattern
Figure GDA0003864719350000044
And each robot and
Figure GDA0003864719350000045
of the matching matrix sigma * (k) And then assigned to each robot group. In an iteration control part (k is a natural number more than or equal to 1), firstly, judgment is made
Figure GDA0003864719350000046
Whether there is a target point q that the robot has reached * (k-1) is located within the safety range of the dynamic barrier, as shown in FIG. 5, the inner circle indicates the time k and the radius R do Position coordinate is p do (k) With radius R do The outer circle area of + R represents the safety area DO of the dynamic barrier, the solid dots represent target points that the robot has arrived at, and the hollow dots represent target points that the robot has not arrived at; fig. 5 shows that the robot has arrived at the target point already in the safety area DO of the dynamic obstacle, and therefore needs to be re-solved on the basis of the environment at this point
Figure GDA0003864719350000047
And regroups the robots; otherwise, if no robot reaches the target point in the safety area DO of the dynamic obstacle,
Figure GDA0003864719350000048
the packets are not changed, nor are the packets changed.
Next, we set up optimization models and constraints with the goal of minimizing the sum of the squares of the distances between the robot and the target point locations, so as to obtain the optimal target pattern at the initial time and in each iteration
Figure GDA0003864719350000051
Step 1.1, establishing an optimized target pattern model
Figure GDA0003864719350000052
Figure GDA0003864719350000053
Wherein:
Figure GDA0003864719350000054
Figure GDA0003864719350000055
the objective function C represents the sum of squares of the distances of the respective robots from the respective target points; c. C ij Represents the square of the distance between the robot i and the target point j; p is a radical of i The position coordinates of the robot i are represented,
Figure GDA0003864719350000056
representing the position coordinates, σ, of the target point j * ＝(x ij ) n×n Is an allocation matrix representing the allocation between the target point and the robot;
step 1.2, establishing optimized target pattern constraint;
step 1.2.1, the generated target pattern is positioned in an application area;
Figure GDA0003864719350000057
wherein:
Figure GDA0003864719350000058
is composed of
Figure GDA0003864719350000059
The abscissa of (a);
Figure GDA00038647193500000510
as target j plane position coordinates
Figure GDA00038647193500000511
The ordinate of (a); x min 、X max Respectively, the boundaries of the regions on the X axis; y is min 、Y max The boundaries of the regions on the Y-axis, respectively;
step 1.2.2, the generated target pattern cannot be located in an obstacle,
Figure GDA00038647193500000512
wherein:
Figure GDA0003864719350000061
a position coordinate representing a target point j; o. o i Position coordinates representing obstacles o i ∈O；R o Represents the size of the obstacle;
initial time, O = P so ，R o ＝R so (ii) a O = [ P ] when the iterative control portion needs to solve the target pattern again so ；P do ]，R o ＝[R so ,R do ]；
Wherein: p so A set of positions representing a plurality of static obstacles at an initial time; p do A set of locations representing a plurality of dynamic obstacles; r so Representing the size of the static obstacle; r do Representing the size of the dynamic obstacle;
step 1.2.3, the distance between the generated target points is at least kept at the distance of 2R;
Figure GDA0003864719350000062
wherein:
Figure GDA0003864719350000063
a position coordinate representing a target point j;
Figure GDA0003864719350000064
representing the position coordinates of the target point i; r represents the size of the robot;
solving the optimal target pattern by convex quadratic programming based on the model and the constraint
Figure GDA0003864719350000065
Each time
Figure GDA0003864719350000066
The robots need to be regrouped after the change.
Step 2, planning a collision-free path;
step 2.1, calculate the preferred speed v pref ；
Based on the optimal target pattern and intra-group distribution targets, it is first calculated that each robot obtains a preferred velocity according to equation (8) without considering other robots and obstacles
Figure GDA0003864719350000067
Figure GDA0003864719350000068
Wherein:
Figure GDA0003864719350000069
position coordinates representing a target point assigned to the robot i at the time k; p is a radical of i (k-1) position coordinates of the robot i at the time k-1; v p Is the maximum velocity of the robot; k is a >V p τ, τ is the time step;
step 2.2, calculating the optimal collision avoidance speed v opt ；
Defining neighborhood NR of robot i i Is a radical of p i (k-1) isCenter, 3R is a circular area of radius; robot i calculates velocity obstacle set RVO i Only the neighborhood NR needs to be considered i Other robots and obstacles;
Figure GDA0003864719350000071
namely: RVO i Consider neighborhood NR for robot i i Speed obstacle area obtained by other robots
Figure GDA0003864719350000072
And a speed obstacle region obtained in consideration of the obstacle
Figure GDA0003864719350000073
A union of (1); wherein v is o Indicating the speed of the obstacle, v for static obstacles o =0, for dynamic obstacles v o ＝v do ；
Robot i selects RVO i Outer closest to
Figure GDA0003864719350000074
As the optimal collision avoidance speed
Figure GDA0003864719350000075
Figure GDA0003864719350000076
Wherein: AV (Audio video) i The speed of the robot i does not exceed V p The velocity set of (a);
step 2.3, updating the position;
robot i updates the position according to equation (11):
Figure GDA0003864719350000077
solving optimal targets in iterative controlPattern(s)
Figure GDA0003864719350000078
And a collision-free path planning part until all the robots reach the target point.

Claims (2)

1. An iterative optimization method for multi-robot pattern composition in an obstacle environment is characterized in that: aiming at the shortest total path of a plurality of robots to reach the distribution target point, the optimal target pattern parameters are dynamically solved, all the robots are ensured to reach the respective target points without collision, and the pattern composition in the environment of the obstacle is optimized; the method comprises the following steps:
step 1, solving an optimal target pattern
Figure FDA0003873757250000011
At the kth iteration time, judging the last target pattern
Figure FDA0003873757250000012
Whether there is a target point q that the robot has reached * (k-1) is located within the safe range of the dynamic obstacle, and if present, the optimal target pattern is re-solved
Figure FDA0003873757250000013
And each robot and the optimal target pattern
Figure FDA0003873757250000014
Of the matching matrix sigma * (k) Regrouping multiple robots, otherwise optimizing the target pattern
Figure FDA0003873757250000015
Unchanged, grouping unchanged; as the robot is to avoid collisions with obstacles and other robots, it may be far from the previously assigned target point and need to reassign the target point; after all the robots are grouped, global distribution is not performed, and target point distribution is performed by adopting the robots in the group; k isA natural number of not less than 1;
step 2, planning a collision-free path;
first, each robot calculates a preferred velocity to point to an assignment target point without considering other robots and obstacles; then, defining a neighborhood of the robots, respectively calculating a speed obstacle set by each robot, only considering other robots in the neighborhood of the robot without considering all other robots when calculating the speed obstacle set, and then selecting a speed which is closest to the preferred speed and is out of the speed obstacle set as an optimal collision avoidance speed; each robot updates the position according to the respective optimal collision avoidance speed, and finally, the optimal target pattern is solved in the repeated iteration control
Figure FDA0003873757250000016
A collision-free path planning part until all the robots reach the target point;
the calculation process of the optimal collision avoidance speed comprises the following steps:
defining neighborhood NR of robot i i Is the position coordinate p of the robot i at the time k-1 i (k-1) as a center, 3R as a circular area of radius, R representing the size of the robot; robot i calculates velocity obstacle set RVO i When only the neighborhood NR need be considered i Other robots and obstacles;
Figure FDA0003873757250000021
namely: RVO i Consider neighborhood NR for robot i i Speed obstacle area obtained by other robots
Figure FDA0003873757250000022
And a speed obstacle region obtained in consideration of the obstacle
Figure FDA0003873757250000023
A union of (1); wherein v is o Indicating the velocity of the obstacle forStatic obstacle v o =0, for dynamic obstacles v o ＝v do (ii) a O belongs to a range of O, and is a position set P of a plurality of static obstacles at an initial moment so (ii) a O = [ P ] when the optimal target pattern is re-solved in the iterative control so ；P do ]In which P is do A set of locations representing a plurality of dynamic obstacles;
robot i selects RVO i Outer closest to the preferred speed of robot i
Figure FDA0003873757250000024
Speed of as an optimum collision avoidance speed
Figure FDA0003873757250000025
Figure FDA0003873757250000026
Wherein: AV (Audio video) i The speed of the robot i does not exceed V p The velocity set of (a); v p Is the maximum velocity of the robot.
2. The iterative optimization method for multi-robot pattern formation in obstacle environment according to claim 1, characterized in that: the pattern formed by the multiple robots is a rectangular, circular or letter pattern.
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