CN111207756A - Mobile robot path planning method based on improved artificial potential field algorithm - Google Patents
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Abstract
The invention provides a mobile robot path planning method based on an improved artificial potential field algorithm. The method comprises the following specific steps: firstly, constructing an attractive force potential field function according to the distance from a mobile robot to a target point, and constructing a repulsive force potential field function according to the distance from the mobile robot to the target point and the distance from an obstacle; then, respectively solving a negative gradient of the attraction force potential field function and the repulsion force potential field function to obtain the attraction force and the repulsion force applied to the mobile robot; and finally, the mobile robot avoids the obstacle to advance to the target point under the combined action of the attraction force and the repulsion force, and a forced interference force is generated midway to enable the robot to escape from the local minimum point influence range. Experimental results in an indoor multi-obstacle environment show that: compared with other methods, the method has higher success rate of path planning and meets the requirement of practical application.
Description
Technical Field
The invention belongs to the field of autonomous navigation of mobile robots, and particularly relates to a mobile robot path planning method based on an improved artificial potential field algorithm.
Background
Path planning is an important step in the autonomous navigation process of a mobile robot, and refers to: the mobile robot plans a safe collision-free path from the starting point to the target point according to the actual situation. The path planning of the mobile robot in the working environment needs to reach the following three standards: (1) the planned path can connect the starting point and the target point; (2) the planned path must effectively avoid obstacles in the environment; (3) the planned path meets the requirements in terms of length, smoothness and the like.
The standard artificial potential field method has the advantages of simple principle, easy realization, small calculated amount and strong real-time property, so the method is widely applied to the field of path planning of the mobile robot. However, when path planning is performed in an indoor multi-obstacle environment using standard artificial potential field methods, target unreachability problems and the problem of falling into local minima often occur. The target unreachable problem is as follows: when the target point is within the obstacle influence range, the mobile robot loiters around the target point without staying at the target point position. The problem of trapping local minimum points is that: when the force of the mobile robot is balanced at a certain non-target point position, the robot stops moving and does not continue to advance to the target point. The occurrence of these two problems can have a serious impact on the whole path planning process of the mobile robot, and eventually lead to the failure of the path planning operation.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A mobile robot path planning method based on an improved artificial potential field method and suitable for an indoor multi-obstacle environment is provided. The method comprises the following steps:
and S1, constructing an attractive force potential field function according to the distance from the mobile robot to the target point.
And S2, constructing a repulsive potential field function according to the distance from the mobile robot to the target point and the distance from the mobile robot to the obstacle.
And S3, obtaining the current attractive force of the mobile robot by solving a negative gradient of the attractive force potential field function based on the current position of the mobile robot.
And S4, obtaining the currently applied repulsive force of the mobile robot by solving a negative gradient of the repulsive force potential field function based on the current position of the mobile robot.
S5, guiding the mobile robot to advance to the target point using the attractive force and the repulsive force calculated in steps S3 and S4, including:
if the resultant force of the current attractive force and the current repulsive force is 0 and the current position of the mobile robot is the target point, path planning is finished;
if the resultant force of the current attractive force and the current repulsive force is 0 and the current position of the mobile robot is not a target point, the mobile robot falls into a local minimum value point, a forced interference force is generated to enable the mobile robot to escape from the position influence range to reach a new position, and then path planning operation is continuously executed;
if the resultant force of the current attractive force and the current repulsive force is not 0, the mobile robot moves one step to a new position under the combined action of the current attractive force and the current repulsive force, and then the step S3 is continuously executed.
The invention has the following advantages and beneficial effects:
the invention provides a mobile robot path planning method based on an improved artificial potential field method, aiming at the problems that targets are not reachable and fall into local minimum points which often occur when a standard artificial potential field method is used for path planning in an indoor multi-obstacle environment. The method introduces the distance from the mobile robot to the target point processed by the arctangent function into the repulsive potential field function of the standard artificial potential field method to solve the problem that the target cannot be reached. Wherein the arctan function exists in the sense that: the deformation of the repulsive force potential field function caused by introducing the distance from the mobile robot to the target point is reduced, and the quality of the planned path is further ensured not to be reduced. In addition, the method solves the problem that the vehicle can not escape due to the fact that the vehicle falls into a local minimum value point by breaking the stress balance through the forced interference force constructed on the basis of the attraction force. The invention introduces the distance between the mobile robot and the target point processed by the arc tangent function and the forced interference force generated by the attraction, and the two factors act synergistically, thereby improving the success rate of path planning of the mobile robot in the indoor multi-obstacle environment and simultaneously ensuring that the path planned by the mobile robot is shorter.
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FIG. 1 is a mobile robot path planning implementation framework based on an improved artificial potential field method according to a preferred embodiment of the invention;
FIG. 2 is an exploded schematic view of an attractive force;
fig. 3 is a schematic diagram of forced disturbance force generation.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
Referring to fig. 1, the main steps of the present invention are:
s1, initializing relevant parameters, and setting a path planning starting point and a target point;
s2, constructing an attraction potential field function according to the distance from the mobile robot to the target point;
s3, constructing a repulsive potential field function according to the distance from the mobile robot to the target point and the distance from the mobile robot to the obstacle;
s4, obtaining the current attractive force of the mobile robot by solving the negative gradient of the attractive force potential field function based on the current position of the mobile robot;
s5, obtaining the repulsive force currently applied to the mobile robot by solving a negative gradient of the repulsive force potential field function based on the current position of the mobile robot;
and S6, if the resultant force of the current attractive force and the current repulsive force is 0 and the current position of the mobile robot is the target point, the path planning is completed. And if the resultant force of the current attractive force and the current repulsive force is 0 and the current position of the mobile robot is not the target point, generating a forced interference force to enable the mobile robot to escape from the position influence range to reach a new position, and then continuing to execute the path planning operation. And if the resultant force of the current attractive force and the current repulsive force is not 0, the mobile robot moves one step to a new position under the combined action of the current attractive force and the current repulsive force, and then the path planning operation is continuously executed.
The specific implementation process of step S2 is:
constructing an attractive force potential field function U according to the distance from the mobile robot to a target pointattThe concrete formula is as follows:
in the above equation, k represents an attraction gain coefficient.Representing the distance of the mobile robot to the target point. Wherein (x)R,yR) World coordinates representing the mobile robot; (x)G,yG) Representing world coordinates of the target point.
The specific implementation process of step S3 is:
constructing a repulsive force potential field function U according to the distance from the mobile robot to a target point and the distance from the mobile robot to an obstaclerepThe specific formula is as follows:
in the above equation, η denotes the repulsion gain factor.Indicating the distance of the mobile robot to the obstacle. Wherein (x)o,yo) Representing world coordinates of the obstacle. RhooRepresenting the maximum impact distance of the obstacle.Representing the arctan restriction function. n represents a distance adjustment coefficient.
The specific implementation process of step S4 is:
s41: according to the current position of the mobile robot, the gravitational potential field function U is selectedattObtaining the current attractive force F 'received by the mobile robot by solving the negative gradient'attThe concrete formula is as follows:
F′att=-grad(Uatt)=-k·(x′R-xG)i-k·(y′R-yG)j
in the above formula, (x'R,y′R) World coordinates representing the current position of the mobile robot. i and j respectively denote square along the horizontal axis of the world coordinate systemUnit vectors in the positive direction of the vertical axis.
S42: obtaining attractive force F'attIs of a size ofThe direction is directed by the mobile robot to a target point.
The specific implementation process of step S5 is:
s51: according to the current position of the mobile robot to the repulsive force potential field function UrepObtaining the current attractive force F 'received by the mobile robot by solving the negative gradient'repThe concrete formula is as follows:
wherein, F'x,repAnd F'y,repThe specific expressions of (A) are as follows:
in the above two formulas, the first and second groups,indicating the distance of the current mobile robot to the target point.Indicating the distance of the current mobile robot to the obstacle.
S52: obtaining repulsive force F'repIs of a size ofThe direction is directed by the mobile robot to a target point.
The specific implementation process of step S6 is:
s61: if the resultant force of the current attractive force and the current repulsive force is 0 and the current position of the mobile robot is the target point, path planning is finished;
s62: and if the resultant force of the current attractive force and the current repulsive force is 0 and the current position of the mobile robot is not the target point, the mobile robot sinks into a local minimum value point. At this time, (1) to (8) are executed in order;
(1) storing the current position (i.e. the local minimum point position) of the mobile robot in a world coordinate system XwOwYwThe coordinate of (5) is marked as a;
(2) using the current position of the mobile robot as an origin and the current attraction force F'attThe direction deviation (including left deviation and right deviation) theta is the positive direction of the horizontal axis, and a rectangular coordinate system X is establishedNONYN. Wherein theta is in the value range ofRandom angle of (2). In this embodiment, a rectangular coordinate system X is established with the right deviation θ as the positive direction of the horizontal axisNONYN. The same holds true to the left.
(3) In rectangular coordinate system XNONYNIn (c), attraction force F'attDecomposed along the horizontal and vertical coordinate axes to obtain two component attractive forces which are respectively marked as F'X,attAnd F'Y,att. Wherein, F'X,attIs expressed as (| F'att|cosθ,0),F′Y,attIs expressed as (0, | F'att|sinθ)。
(4) Utilizing random coefficient to F'X,attAnd F'Y,attThe modification is carried out to obtain two new component attractive forces,and is represented by the coordinates of (α | F'att|cosθ,0),Is expressed as (0, β | F'attI sin θ), wherein α and β both represent a value range of 0.5,1.5]The random coefficient of (2). Note that two random coefficients cannot take the same value at the same time;
(5) will be provided withAndsynthesized to obtain a new attractive force which is recorded asThe attraction is the key to the mobile robot to escape from the local minimum point, and is called forced interference force. In a rectangular coordinate system XNONYNCoordinate of (D) is represented by (α | F'att|cosθ,β|F′att|sinθ)。
(6) According toIn rectangular coordinate system XNONYNThe coordinate representation in (1) is calculated to be the coordinate representation in the world coordinate systemThe specific formula is as follows:
in the above formula, ∠ F'attDenotes the current attractive force F'attDeflection angle in the world coordinate system.
(7) Determination of the force of the forced disturbanceThe size in the world coordinate system isHas a deflection angle of
(8) Keeping the magnitude and the deflection angle of the forced interference force unchanged, enabling the mobile robot to move 5 steps under the combined action of the force, the received attractive force and the repulsive force to reach a certain position point, and recording the world coordinate of the position point as b. At this time, the total force received by the mobile robot at the b position is calculated without considering the influence of the forcible interference force. If the resultant force and the vectorIs greater thanThe mobile robot has jumped out of the local minimum point. And then, removing the forced interference force, and continuing executing the path planning operation by the mobile robot. If the resultant force and the vectorIs less than or equal toThe forcible interference force is canceled and the process returns to (2) to regenerate the forcible interference force.
S63: and if the resultant force of the current attractive force and the current repulsive force is not 0, the mobile robot moves one step along the direction of the resultant force to reach a new position, and then the path planning operation is continuously executed.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.
Claims (8)
1. A mobile robot path planning method based on an improved artificial potential field algorithm is characterized by comprising the following steps:
s1, constructing an attraction potential field function according to the distance from the mobile robot to the target point;
s2, constructing a repulsive potential field function according to the distance from the mobile robot to the target point and the distance from the mobile robot to the obstacle;
s3, obtaining the current attractive force of the mobile robot by solving the negative gradient of the attractive force potential field function based on the current position of the mobile robot;
s4, obtaining the repulsive force currently applied to the mobile robot by solving a negative gradient of the repulsive force potential field function based on the current position of the mobile robot;
s5, guiding the mobile robot to advance toward the target point using the attractive force and the repulsive force calculated in steps S3 and S4, including,
if the resultant force of the current attractive force and the current repulsive force is 0 and the current position of the mobile robot is the target point, path planning is finished;
if the resultant force of the current attractive force and the current repulsive force is 0 and the current position of the mobile robot is not a target point, the mobile robot falls into a local minimum value point, a forced interference force is generated to enable the mobile robot to escape from the position influence range to reach a new position, and then path planning operation is continuously executed;
if the resultant force of the current attractive force and the current repulsive force is not 0, the mobile robot moves one step to a new position under the combined action of the current attractive force and the current repulsive force, and then the step S3 is continuously executed.
2. The method for planning the path of the mobile robot based on the improved artificial potential field algorithm according to claim 1, is characterized in that: step S1 is the attraction potential field function UattThe specific formula of (A) is as follows:
3. The method for planning the path of the mobile robot based on the improved artificial potential field algorithm according to claim 1, is characterized in that: repulsive potential field function U of step S2repThe specific formula of (A) is as follows:
where η denotes the rejection gain factor,represents the distance from the mobile robot to the obstacle, (x)o,yo) World coordinate, p, representing an obstacleoThe maximum influence distance of the obstacle is represented,represents an arctangent limiting function and n represents a distance adjustment coefficient.
4. The method for planning the path of the mobile robot based on the improved artificial potential field algorithm according to claim 1, is characterized in that: step S3 shows that the mobile robot is currently attracted by attractive force F'attThe method is calculated by the following method, and the specific formula is as follows:
F′att=-grad(Uatt)=-k·(x′R-xG)i-k·(y′R-yG)j
wherein (x'R,y′R) The world coordinate system comprises world coordinates representing the current position of the mobile robot, and i and j respectively represent unit vectors along the positive direction of a horizontal axis and the positive direction of a vertical axis of the world coordinate system;
5. The method for planning the path of the mobile robot based on the improved artificial potential field algorithm according to claim 1, is characterized in that: repulsive force F 'currently applied to the mobile robot in step S4'repThe concrete formula is as follows:
wherein, F'x,repAnd F'y,repThe specific expressions of (A) are as follows:
in the above two formulas, the first and second groups,indicating the distance of the current mobile robot to the target point,indicating a distance from the current mobile robot to the obstacle;
6. The method for planning the path of the mobile robot based on the improved artificial potential field algorithm according to any one of claims 1 to 5, characterized in that: s, when the mobile robot falls into the local minimum value point, the following operations are carried out:
(1) saving the current position of the mobile robot in the world coordinate system XwOwYwThe coordinate of (5) is marked as a;
(2) constructing a forced interference force by using the current attraction force;
(3) keeping the magnitude and the deflection angle of the forced interference force unchanged, enabling the mobile robot to move 5 step lengths under the combined action of the force, the received attraction force and the repulsive force to reach a certain position point, and recording the world coordinate of the position point as b;
(4) the influence of the forced interference force is not considered, and the resultant force of the attractive force and the repulsive force of the mobile robot at the position b is calculated; if the resultant force and the vectorIs greater thanCanceling the forced interference force, and continuing to execute path planning operation by the mobile robot; if the resultant force and the vectorIs less than or equal toThe forcible interference force is cancelled and the step (2) is returned to regenerate the forcible interference force.
7. The method for planning the path of the mobile robot based on the improved artificial potential field algorithm according to claim 6, characterized in that: the step of constructing the forced interference force comprises the following steps:
(2.1) with the current position of the mobile robot as the origin and the current attraction force F'attThe direction deviation theta is the positive direction of the horizontal axis, and a rectangular coordinate system X is establishedNONYNTheta is in the value rangeRandom angle of (d);
(2.2) in a rectangular coordinate system XNONYNIn (c), attraction force F'attDecomposed along the horizontal and vertical coordinate axes to obtain two component attractive forces which are respectively marked as F'X,attAnd F'Y,att,F′X,attIs expressed as (| F'att|cosθ,0),F′Y,attIs expressed as (0, | F'att|sinθ);
(2.3) pairing F 'by random coefficient'X,attAnd F'Y,attThe modification is carried out to obtain two new component attractive forces,and is represented by the coordinates of (α | F'att|cosθ,0),Is expressed as (0, β | F'attI sin θ), wherein α and β both represent a value range of 0.5,1.5]The random coefficient of (a);
(2.4) mixingAndsynthesized to obtain a new attractive force, which is recorded as a forced interference forceIn a rectangular coordinate system XNONYNCoordinate of (D) is represented by (α | F'att|cosθ,β|F′att|sinθ);
(2.5) according toIn rectangular coordinate system XNONYNThe coordinate representation in (1) is calculated to be the coordinate representation in the world coordinate systemThe specific formula is as follows:
in the above formula, ∠ F'attDenotes the current attractive force F'attA yaw angle in a world coordinate system;
8. The method for planning the path of the mobile robot based on the improved artificial potential field algorithm as claimed in claim 7, wherein the two random coefficients α and β cannot take the same value at the same time.
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CN112068560A (en) * | 2020-08-28 | 2020-12-11 | 的卢技术有限公司 | Robot path planning method based on improved artificial potential field method |
CN112907187A (en) * | 2021-03-13 | 2021-06-04 | 深圳市土地公网络科技有限公司 | Distribution route planning method and device, electronic equipment and storage medium |
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CN117369482B (en) * | 2023-12-06 | 2024-03-12 | 华润数字科技有限公司 | Path planning method, device and equipment for mobile robot and storage medium |
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