CN115951683B - Artificial potential field path planning method for mixed gradient descent and longhorn beetle whisker search - Google Patents
Artificial potential field path planning method for mixed gradient descent and longhorn beetle whisker search Download PDFInfo
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Abstract
The invention provides a method for planning a path of an artificial potential field, which is used for mixing gradient descent and longhorn beetle whisker search. Firstly, establishing an artificial potential field to obtain the field intensity, gradient magnitude and gradient direction of each position in a map, converting a path planning problem into a problem of solving an optimal value of a function formed by a map environment and a distance, planning a path by adopting a gradient descent mode, and switching the gradient descent method into a longhorn beetle whisker method when the local optimum is sunk, so as to break through the sunk local optimum. The gradient descent method and the longhorn beetle whisker search method are mixed, so that the artificial potential field path planning method accords with the dynamic constraint of the robot, the path is smooth, the local optimum can be broken through, and the robot is guided to smoothly reach the end point.
Description
Technical Field
The invention relates to a path planning method of an artificial potential field for mixed gradient descent and longhorn beetle whisker search, which is a path planning method for obstacle avoidance of a mobile robot and belongs to the technical field of robots and path planning.
Background
As an unmanned carrier, the robot has the advantages of low cost, high safety, quick response, small volume and the like compared with other unmanned carriers. With the development of artificial intelligence, microelectronics, control theory, data processing and sensors, robots gradually overcome some barriers in the prior art, and are put into practical application in some fields, such as military robots, inspection and typing integrated unmanned vehicles, automatic driving robots, exploration robots, underwater robots and the like, so that the great application potential of the robots in military and civil fields is embodied. However, to enable the robot to perform tasks better, a good path planning algorithm is required to adapt to changing tasks and environments, enabling the robot to perform specified tasks quickly and autonomously. In order to improve the capability of the robot to autonomously execute tasks in a complex environment, obstacle avoidance path planning of the robot is one of key technologies. There have been many related studies and theoretical efforts on the technology of robot path planning, which mainly involves two kinds, global planning and local planning. Global planning can be divided into two types: search-based methods and sampling-based methods. The search-based method comprises the following steps: graph search-based methods, such as Dijkstra's algorithm (Dijkstra), a's algorithm, hybrid a's algorithm, and the like. The sampling-based method comprises the following steps: probability road mapping, RRT algorithm, informed RRT algorithm, etc. Classical methods in local planning include: artificial potential field method (APF), dynamic window method (DWA). The artificial potential field method is an efficient path planning method. The virtual force field method provided by Khatib considers the kinematics problem of the robot, has strong real-time performance of path planning, can dynamically avoid obstacles, and well realizes the path planning of the robot. But is prone to local optimization problems, and therefore, the artificial potential field method is improved by combining the artificial potential field method with a longhorn beetle whisker search algorithm (BAS).
Disclosure of Invention
The invention aims at overcoming the defects of the prior art, and provides an artificial potential field path planning method for mixing gradient descent and longhorn whisker search, wherein the path planning is carried out by adopting a mode of combining a gravitational field and a repulsive force field by an artificial potential field method, a gradient algorithm is utilized, a robot is guided to a target point through virtual attractive force generated by a target, and the robot avoids obstacles through virtual repulsive force of the obstacles. The path planning effect of the artificial potential field method is ideal, but the problem that the track falls into a local optimal solution exists, so that the robot falls into the obstacle groove to wander. And a longhorn beetle whisker search algorithm (BAS) is introduced, so that the problem of local optimum is broken through, and path planning is better realized.
The invention provides the following scheme: firstly, establishing an artificial potential field to obtain the field intensity, gradient magnitude and gradient direction of each position in a map. The path planning problem is converted into a problem of obtaining an optimal value of a function formed by a map environment and a distance, and path planning can be performed by adopting a gradient descent mode. When the local optimum is sunk, the switching gradient descent method is a longhorn beetle whisker method, and the sunk local optimum is broken through. Under the combined action of gradient descent and a longhorn beetle whisker search method, the kinematic constraint of a robot is fully considered, and a smooth track is generated, and the method specifically comprises the following steps:
step 1: and establishing an artificial potential field, and calculating to obtain the field intensity of each position in the map.
Step 2: and obtaining the field intensity gradient of each position through gradient calculation.
Step 3: based on the calculation results of step 1 and step 2, an optimal value of a function composed of the map environment and the distance is obtained.
Step 4: and (3) obtaining the path of the next step according to the optimal value calculated in the step (3).
Step 5: when the robot wanders in a small range area and does not reach the set end point, switching to a longhorn beetle whisker search algorithm to carry out the next path planning.
Step 6: and when the robot breaks through the semi-closed interval, returning to the step 1, switching to a gradient descent artificial potential field method, and continuing path planning.
Step 7: and when the robot reaches the set end point, the path planning is finished.
The beneficial effects are that:
1. the artificial potential field path planning method provided by the invention can dynamically avoid the obstacle.
2. According to the invention, an artificial potential field method of gradient descent is introduced, and a planned path accords with the dynamic constraint of the robot and is smoother.
3. The method can solve the problem that the artificial potential field path planning method is easy to fall into local optimum after introducing the longhorn beetle whisker path searching algorithm.
4. The gradient descent method and the longhorn beetle whisker search method are mixed, so that the artificial potential field path planning method accords with the dynamic constraint of the robot, the path is smooth, the local optimum can be broken through, and the robot is guided to smoothly reach the end point.
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FIG. 1 is a plot of the gravitational field profile of the present invention.
Fig. 2 is a repulsive force field distribution diagram of the present invention.
Fig. 3 is a plot of repulsive and attractive fields of the present invention.
Fig. 4 is a trace diagram of the gradient descent method of the present invention in a simple environment.
Fig. 5 is a trace diagram of the gradient descent method of the present invention in a complex environment.
Fig. 6 is a trace of the BAS method of the present invention in a simple environment.
Fig. 7 is a trace of the BAS process of the present invention in a complex environment.
Fig. 8 is a trace of the mixed gradient descent and BAS method of the present invention in a complex environment.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention.
The invention provides a method for planning a path of an artificial potential field, which is used for mixing gradient descent and longhorn beetle whisker search. The path planning effect of the artificial potential field method is ideal, but the problem that the track falls into a local optimal solution exists, so that the robot falls into the obstacle groove to wander. And a longhorn beetle whisker search algorithm (BAS) is introduced, so that the problem of local optimum is broken through, and path planning is better realized.
As shown in fig. 1-8.
(1) Artificial potential field establishment
The process of guiding a robot using an artificial potential field method can be understood as considering the robot as a "positively charged particle" moving in a negative gradient vector field. A negative gradient can be intuitively seen as a force acting on a positively charged particle robot that is attracted to a "negatively charged" target. Unlike the physical charge, the negative charge of the target point creates a negative gradient, creating an attractive force on the robot, causing the robot to approach the target point. The obstacle has a "positive charge" creating a field of positive gradient that creates a repulsive force on the robot forcing the robot away from the obstacle. The combination of the attractive force and the repulsive force can guide the robot to reach the target position from the start position while avoiding the obstacle. The robot can also be regarded as a sphere, rolling down from an uneven slope, the slope is a gravitational field generated by a target, the bottom end of the slope is the target point, and the convex part of the slope is a repulsive field generated by an obstacle. The sphere is pushed away by the repulsive force field generated by the obstacle in the process of sliding down to the target along the attractive force, so that the obstacle avoidance function is completed.
1) Gravitational field establishment
Gravitational field U for robot path planning att Should increase monotonically with the distance of the robot from the target point. By measuring the distance from the robot to the target point, a field function is constructed, namely:
U(x)＝ζd(p,p goal ) (1)
wherein p represents the current position of the robot, and the coordinates are (x, y); p is p goal Representing the position of the target point, the coordinates are (x goal ,y goal ) ζ is a parameter for controlling the strength of the gravitational field acting on the robot. d (p, p) goal ) Representing target pointsThe distance between the robot and the current position of the robot is obtained by the method that the gradient of the gravitational field is as follows:
when the method is implemented by a mathematical model, the gradient drop may have a "buffeting" problem due to the discontinuity of the gravitational gradient at the origin. It is therefore desirable to establish a continuously differentiable potential function so that the strength of the gravitational gradient decreases as the robot approaches the target point. The simplest potential energy function is a function which grows secondarily along with the distance between the robot and the target point, so as to eliminate the gradient discontinuity problem caused by denominator, namely:
the negative gradient function of the gravitational field constructed after squaring becomes:
it is apparent from the mathematical model that the gravitational field is a vector based on p, the direction from the target point to the target point is started, and the strength of the gravitational field is in proportional relation with the distance from the robot to the target point. The further the robot is from the target, the stronger the strength of the gravitational field effect, the robot can be quickly close to the target; as the robot approaches the target, the gravitational field effect becomes weaker. The mathematical model of the gravitational field is shown in FIG. 1, in which the Z-axis represents the potential field strength, the X-and Y-axes on the plane represent the areas where the potential field is generated, and the gravitational field is of formula (5), in which the parameters (X goal ,y goal )＝(-5,-5)，ζ＝0.125。
2) Repulsive field establishment
Repulsive field U rep Forcing the robot away from the obstacle. The strength of the repulsive force is related to the distance between the robot and the obstacle. And the characteristics of the negative gradient generated by the target point on the gravitational field generated by the robot are opposite, the obstacle generates a repulsive field with a positive gradient, and the closer the robot is to the obstacle, the stronger the repulsive force is. Therefore, the repulsive force is generally based on the distance D (x, y) of the robot from the nearest obstacle, the repulsive field U rep Can be expressed as:
thereby obtaining the gradient function of the repulsive field,
and rho in the mathematical model is used as an obstacle influence scale factor, and the robot is controlled to ignore the repulsive field generated by the obstacle with a longer distance through the factor. η is a parameter used to control the strength of the repulsive field acting on the robot. In (x) obs ,y obs ) Is the coordinates of the obstacle.
In the formula (8), the amino acid sequence of the compound,
setting parameters eta of three barriers to be eta 1 ＝η 2 ＝η 3 The coordinates of the three obstacles are (x) =20 obs1 ,y obs1 )＝(-2.05,1)，(x obs2 ,y obs2 )＝(4.05,-2)，(x obs3 ,y obs3 ) = (2, 3), the corresponding ρ are ρ respectively 1 ＝3，ρ 2 ＝3，ρ 3 =1. The repulsive force field mathematical model is shown in figure 2In the figure, the Z-axis represents the potential field strength, and the X-axis and Y-axis on the plane represent the region where the potential field is generated.
3) Attraction and repulsion field establishment
After the mathematical model of the gravitational field and the repulsive field is obtained, the two potential fields are overlapped to obtain the total potential field function.
U t ＝U att +U req (10)
U att The parameters of (2) are: ζ=0.125, (x) goal ,y goal )＝(-5,-5)；U req The parameters of (2) are: the parameter eta is eta 1 ＝η 2 ＝η 3 =20; the coordinates of the obstacle are (x) obs1 ,y obs1 )＝(-2.05,1)，(x obs2 ,y obs2 )＝(4.05,-2)，(x obs3 ,y obs3 ) = (2, 3); the corresponding ρ is ρ respectively 1 ＝3，ρ 2 ＝3，ρ 3 =1. FIG. 3 shows a gravitational field and a repulsive field U t Is a profile of (a). (2) Artificial potential field path planning based on gradient descent
After the field intensity, the gradient magnitude and the gradient direction of each position in the map are obtained by the step (1), the path planning problem is converted into the problem of solving the optimal value of a function formed by the map environment and the distance, and the path planning can be performed by adopting a gradient descent mode. Under the action of the gradient, the generated track is smooth, and the motion track of the robot fully considers the kinematic constraint of the robot.
The simulation adopts two map test algorithm performances, namely a simple environment map and a complex environment map, as shown in fig. 4 and 5, wherein in the two maps, a yellow point represents a target end point and a green point represents a starting point. The blue curve is the planned trajectory, the small arrow shows the gradient direction and the magnitude. The simulation parameters are respectively as follows:
simple environment starting point coordinate p start = (490,520), end point coordinate p dest = (50, 50), gravitational field U att Coefficient ζ=0.002; repulsive field U req The coefficient is η=1000, ρ=1.3.
Complex environment starting point coordinate p start = (430, 410), endpoint coordinate p dest = (50, 50), gravitational field U att Coefficient ζ=0.002; repulsive field U req The coefficient is η=1000, ρ=1.3.
Fig. 4 shows a path planning effect in a simple environment, which can successfully avoid obstacles, reach target points, and make the route smooth. FIG. 5 shows the path planning effect in a complex environment, where the final track is found to have a local optimum of the map distance function at the end point of the yellow spot in the map in an obstacle-dense environment, and the navigation fails. The gradient descent method can well complete the path planning problem under the condition of simpler environment, but when the environment becomes complex, the defects of the gradient descent method are exposed, and the defects are easy to sink into local optimal points in the region with complex gradient. To solve this problem, attempts have been made to perform trajectory planning in an artificial potential field using the longhorn beetle whisker search algorithm (BAS) instead of the gradient descent method.
(3) Artificial potential field method path planning based on longhorn beetle whisker search algorithm (BAS)
The BAS algorithm belongs to a heuristic algorithm, and the algorithm obtains the optimal value of the function by simulating the foraging process of the longhorns. The distribution of the objective function corresponds to the distribution of the food aroma in the space, and the values corresponding to different positions in the space of the function are different. The longhorn beetles move towards a certain direction according to the self perception, tentacles acquire smell information, namely the size of an objective function, as the basis of the next moving direction, and finally find the optimal value of the function.
1) Establishing a search model
Assuming that two tentacles of the longicorn are positioned at two sides of the mass center, the distance of each movement of the longicorn and the distance d between the two tentacles 0 Is a fixed constant c, i.e
step＝c×d 0 (11)
At the same time, assuming that the initial search direction is unknown, and the orientation after each movement is also unknown, i.e
Where rand (,) operation represents a random number function and k represents the dimension to be searched. It can be deduced that the range of detection of the longicorn to the left and right each time is of the size,
in the formula (13), x represents the current coordinate position of the longhorn beetle, and thus a model of the longhorn beetle as a search carrier is established.
2) Optimizing iteration step
For the objective function f (x), the calculation can be performed using a model of the search carrier. The current coordinates, i.e. the function values to the left and to the right of the current position of the simulated search carrier,
comparing the values to determine the orientation of the search carrier at the current iteration and the position of the search carrier at the next iteration, the process can be summarized as equation (15)
Where sign (,) represents a sign function.
In the iteration process, the moving step length and the searching range are not fixed, the parameter delta can be introduced as the attenuation of the step length, at the moment, the expression of the step length becomes,
step i ＝δ×step i-1 (16)
the distance of each search becomes the one,
the iterative process is changed to be a process of,
x i+1 ＝x i -step i ×dir×sign(f left -f right ) (18)
the amount of attenuation depends on the step size of the movement after each iteration and the size of the search range, as opposed to the size of the objective function domain range. For example, a fixed step strategy may be adopted when the size of the step per iteration is small and the domain of the objective function is very large.
The longhorn beetle whisker search algorithm has global optimizing capability and small calculated amount, and can realize the calculation of the optimal value of the function without knowing the specific gradient information of the function and the like. Meanwhile, the longhorn beetle whisker search algorithm has the capability of jumping out of the local optimal point, and is not easy to sink into the local optimal point.
3) BAS-based artificial potential field method path planning
The BAS algorithm is used to eliminate the need for function specific gradient information, so that the field intensity function is directly utilized for path planning. Since the objective function is determined by the map environment and distance, the field strength at the end point can be set to 0, i.e., f (x goal ) =0, and this is used as an iteration end condition.
The field intensity function is established by adopting the same expression as the artificial potential field adopted by the gradient descent method, and the gradient of the artificial potential field is not required to be calculated by adopting the BAS for planning.
An improved artificial potential field path planning method using BAS. The simulation uses the same simulation parameters and environment as the gradient descent method. Fig. 6 shows the effect of BAS path planning in a simple environment, and fig. 7 shows the effect of path planning in a complex environment.
In a simulation experiment of a complex environment, the paths planned by the traditional artificial potential sites using a gradient descent method are compared, so that the BAS method can be found to jump out of local optimum, and navigation tasks are completed. However, the path planned by the BAS does not conform to the dynamic constraint of the robot, the track is not smooth, and turning points are more. The problem can be solved by reducing the iteration step length, adding the coordinate point, and then using methods such as least square, ransac and the like to fit a track curve which better accords with the dynamic constraint of the robot.
(4) Gradient descent and BAS mixed artificial potential field path planning method
To further optimize the trajectory planned using the artificial potential field, an attempt was made to combine the gradient descent method with the longhorn whisker search algorithm (BAS) for path planning in the artificial potential field. The advantages of the two are combined, so that the planning algorithm has the capability of jumping out of local optimum, and the planned track can also accord with the kinematic constraint of the robot.
The method comprises the steps of firstly adopting a gradient descent method to conduct path planning in an artificial potential field, judging whether the position of a robot in the current iteration is at a local optimal point or whether the surrounding gradient environment is unfavorable for further iterative calculation of the gradient descent method, and if the conditions are met, adopting a longhorn beetle whisker search algorithm (BAS) to conduct navigation; and when the gradient environment is favorable for the gradient descent method to carry out iterative computation or the robot jumps out of the local optimal point, switching to carry out path planning by using the gradient descent method.
Setting a threshold alpha as a judgment standard, if the moving range of the robot in mu iterations is smaller than alpha, considering that the robot falls into a local optimal point, and adopting a gradient descent method to carry out path planning instead of using a longhorn beetle whisker search algorithm (BAS) to carry out path planning to try to jump out the local optimal point. When using the longhorn beetle whisker search (BAS), each iteration step is not more thanThe robot is fully far away from the unfavorable environment and then is switched to the gradient descent method navigation.
The following is a simulation of the artificial potential field path planning method that mixes gradient descent and BAS. The simulation parameters are as follows:
origin coordinate p under complex environment start = (430, 410), endpoint coordinate p dest = (50, 50), gravitational field U att Coefficient ζ=0.002; repulsive field U req The coefficient is η=1000, ρ=1.3. Fig. 8 is an effect of hybrid algorithm path planning in a complex environment.
As can be seen from comparison of simulation results, the track planned by the artificial potential field method using the hybrid algorithm not only jumps out of the local optimum point, but also is smoother, and accords with the kinematic constraint of the robot.
Claims (5)
1. The artificial potential field path planning method for mixed gradient descent and longhorn beetle whisker search is characterized by comprising the following steps of: firstly, establishing an artificial potential field to obtain the field intensity, gradient magnitude and gradient direction of each position in a map, converting a path planning problem into a problem of solving an optimal value of a function formed by a map environment and a distance, planning a path in a gradient descent mode, switching the gradient descent method into a longhorn beetle whisker method when the local optimum is sunk, breaking through the local optimum sunk, and generating a smooth track under the combined action of the gradient descent and the longhorn whisker method, wherein the method comprises the following specific steps of:
step 1: establishing an artificial potential field, and calculating to obtain the field intensity of each position in the map;
gravitational field U for robot path planning att Should monotonically increase with the distance of the robot from the target point, by measuring the distance of the robot from the target point, a field function is constructed, namely:
U(x)＝ζd(p,p goal ) Formula (1)
Wherein p represents the current position of the robot, and the coordinates are (x, y); p is p goal Representing the position of the target point, the coordinates are (x goal ,y goal ) ζ is a parameter for controlling the strength of the gravitational field acting on the robot, d (p, p goal ) Representing the distance between the target point and the current position of the robot, and obtaining the gravitational field gradient by the method is as follows:
step 2: obtaining the field intensity gradient of each position through gradient calculation;
step 3: based on the calculation results of the step 1 and the step 2, calculating an optimal value of a function formed by the map environment and the distance;
step 4: obtaining a path of the next step according to the optimal value calculated in the step 3;
step 5: when the robot wanders in a small-range area and does not reach the set end point, switching to a longhorn beetle whisker method, and planning a next path;
step 6: when the robot breaks through the semi-closed interval, returning to the step 1, switching to a gradient descent artificial potential field method, and continuing path planning;
step 7: and when the robot reaches the set end point, the path planning is finished.
2. The method for planning a path of an artificial potential field for mixed gradient descent and longhorn beetle whisker search according to claim 1, wherein the artificial potential field establishment of step 1 mainly comprises the following steps:
the robot is guided by using an artificial potential field method, namely the robot is regarded as a positive charge particle moving in a negative gradient vector field, the negative gradient is intuitively regarded as a force acting on the robot with positive charge particles, the robot is attracted to a target with negative charge, unlike the physical charge, the gradient generated by the negative charge of the target point is a negative gradient, attractive force is generated on the robot, the robot tends to the target point, an obstacle has positive charge, a positive gradient field is generated, repulsive force is generated on the robot, the robot is forced to be far away from the obstacle, the robot is guided to reach the target position from the starting position while avoiding the obstacle by combining the attractive force and the repulsive force, the robot is regarded as a sphere, the robot rolls down from an uneven slope, the slope is the gravitational field generated by the target, the bottom end of the slope is the target point, the convex part on the slope is the repulsive force field generated by the obstacle, and the sphere is pushed away by the repulsive force generated by the obstacle in the process of sliding down to the target along the attractive force, so that the obstacle is avoided;
1) Gravitational field establishment
When the method is realized through a mathematical model, because the gravity gradient is discontinuous at the original point, the gradient descent can have a buffeting problem, and therefore, a continuous and differentiable potential function is established, so that when the robot approaches a target point, the strength of the gravity gradient is reduced, and the simplest potential function is a function which grows secondarily along with the distance between the robot and the target point, so that the gradient discontinuity problem caused by denominator is eliminated, namely:
the negative gradient function of the gravitational field constructed after squaring becomes:
as can be seen from the mathematical model, the gravitational field is a vector based on p, the direction from the target point to the target point is started, the strength of the gravitational field is in proportional relation with the distance from the robot to the target point, the farther the robot is away from the target, the stronger the strength of the gravitational field acts, and the robot can quickly approach the target; when the robot approaches the target, the gravitational field effect becomes weak, the gravitational field being equation (5), where the parameter (x goal ,y goal )＝(-5,-5)，ζ＝0.125，
2) Repulsive field establishment
Repulsive field U rep Forcing the robot away from the obstacle, the strength of the repulsive force being related to the distance between the robot and the obstacle, the obstacle generating a positive gradient repulsive field against the characteristics of the gravitational field generated by the robot, the closer the robot is to the obstacle, the stronger the repulsive force, so that the repulsive force is generally based on the distance D (x, y) from the robot to the nearest obstacle, the repulsive field U rep Expressed as:
thereby obtaining the gradient function of the repulsive field,
ρ in the mathematical model is taken as an obstacle influence scale factor, the repulsive force field generated by the obstacle with a longer distance is controlled by the factor to be ignored by the robot, η is a parameter for controlling the acting strength of the repulsive force field on the robot, and the formula (x obs ,y obs ) As the coordinates of the obstacle,
in the formula (8), the expression "a",
setting parameters eta of three barriers to be eta 1 ＝η 2 ＝η 3 The coordinates of the three obstacles are (x) =20 obs1 ,y obs1 )＝(-2.05,1)，(x obs2 ,y obs2 )＝(4.05,-2)，(x obs3 ,y obs3 ) = (2, 3), the corresponding ρ are ρ respectively 1 ＝3，ρ 2 ＝3，ρ 3 ＝1；
3) Attraction and repulsion field establishment
After the mathematical model of the gravitational field and the repulsive field is obtained, the two potential fields are overlapped to obtain the total potential field function,
U t ＝U att +U req equation (10).
3. The method for planning a path of an artificial potential field for mixed gradient descent and longhorn beetle whisker search according to claim 1, wherein said step 2 specifically comprises the steps of:
after the field intensity, the gradient magnitude and the gradient direction of each position in the map are obtained based on the artificial potential field path planning of gradient descent, the path planning problem is converted into the problem of solving the optimal value of the function formed by the map environment and the distance, the path planning is carried out in a gradient descent mode, the generated track is smooth under the action of the gradient, the motion track of the robot fully considers the motion constraint of the robot,
the simulation adopts two map testing algorithm performances, namely a simple environment map and a complex environment map, and simulation parameters are respectively:
simple environment starting point coordinate p start = (490,520), end point coordinate p dest = (50, 50), gravitational field U att Coefficient ζ=0.002; repulsive field U req The coefficient is η=1000, ρ=1.3,
complex environment starting point coordinate p start = (430, 410), endpoint coordinate p dest = (50, 50), gravitational field U att Coefficient ζ=0.002; repulsive field U req The coefficient is η=1000, ρ=1.3.
4. The method for planning an artificial potential field path for mixed gradient descent and longhorn beetle whisker search according to claim 1, wherein the longhorn beetle whisker method specifically comprises the following steps:
the artificial potential field method path planning based on the longhorn beetle whisker method belongs to a heuristic algorithm, the algorithm obtains the optimal value of a function by simulating the foraging process of the longhorn beetles, the distribution of an objective function is equivalent to the distribution of food fragrance in space, the values corresponding to different positions of the function in space are different, the longhorn beetles move in a certain direction according to the perception of the longhorn beetles, tentacles acquire smell information, namely the size of the objective function, as the basis of the moving direction of the next step, and finally the optimal value of the function is found;
1) Establishing a search model
Assuming that two tentacles of the longicorn are positioned at two sides of the mass center, the step length of each movement of the longicorn is equal to twoDistance d between whiskers 0 Is a fixed constant c, i.e
step＝c×d 0 Formula (11)
At the same time, assuming that the initial search direction is unknown, and the orientation after each movement is also unknown, i.e
Wherein the rand (,) operation represents a random number function, k represents the dimension to be searched, and the range of each detection of the longicorn to the left and right is the size of the range,
in the formula (13), x represents the current coordinate position of the longhorn beetle, thereby establishing a model of the longhorn beetle serving as a search carrier;
2) Optimizing iteration step
For the objective function f (x), the current coordinates, i.e. the function values to the left and right of the current position of the simulated search carrier,
comparing the values to determine the orientation of the search carrier at the current iteration and the position of the search carrier at the next iteration, and summing this process into equation (15)
x i+1 ＝x i -step×dir×sign(f left -f right ) Formula (15)
Wherein sign (,) represents a sign function;
in the iterative process, the moving step and the searching range are not fixed, the parameter delta is introduced as the attenuation of the step, at this time, the expression of the distance of each movement becomes,
step i ＝δ×step i-1 formula (16)
The distance of each search becomes the one,
the iterative process is changed to be a process of,
x i+1 ＝x i -step i ×dir×sign(f left -f right ) Formula (18)
The attenuation amount depends on the moving step length after each iteration and the size of the searching range, and the relative size of the target function definition domain range;
the longhorn beetle whisker method has global optimizing capability and small calculated amount, can realize the calculation of the optimal value of the function without knowing the specific gradient information of the function and the like, and simultaneously has the capability of jumping out of the global optimal point and is not easy to fall into the global optimal point;
3) Artificial potential field method path planning based on longhorn beetle whisker method
The method uses the longhorn beetle whisker method without specific gradient information of the function, directly utilizes the field intensity function to carry out path planning, and because the objective function is determined by map environment and distance, the field intensity at the end point is set to be 0, namely f (x) goal ) =0, and this is used as an iteration end condition.
5. The method for planning an artificial potential field path for mixed gradient descent and longhorn beetle whisker search according to claim 1, wherein:
in order to further optimize the track planned by using the artificial potential field, a gradient descent method and a longhorn beetle whisker method are combined and used for carrying out path planning in the artificial potential field, and the advantages of the gradient descent method and the longhorn beetle whisker method are combined;
the method comprises the steps of firstly adopting a gradient descent method to conduct path planning in an artificial potential field, judging whether the position of a robot in the current iteration is at a local optimal point or whether the surrounding gradient environment is unfavorable for further iterative calculation of the gradient descent method, and if the conditions are met, navigating by adopting a longhorn beetle whisker method; when the gradient environment is favorable for the gradient descent method to carry out iterative computation or the robot jumps out of the local optimal point, switching to use the gradient descent method to carry out path planning;
setting a threshold alpha as a judgment standard, if the moving range of the robot in mu iterations is smaller than alpha, considering that the robot falls into a local optimal point, and the current environment is not suitable for path planning by adopting a gradient descent method, and instead, adopting a longhorn whisker method to carry out path planning to try to jump out the local optimal point, wherein when the longhorn whisker method is used, the step length of each iteration does not exceedSo that the robot is far away from the unfavorable mu
After the environment, the navigation is switched to the gradient descent method navigation;
the following is the simulation situation of the artificial potential field path planning method of the mixed gradient descent and the longhorn beetle whisker method, and the simulation parameters are as follows:
origin coordinate p under complex environment start = (430, 410), endpoint coordinate p dest = (50, 50), gravitational field U att Coefficient ζ=0.002; repulsive field U req The coefficient is η=1000, ρ=1.3.
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2017215044A1 (en) * | 2016-06-14 | 2017-12-21 | 广东技术师范学院 | Automatic path planning method for mobile robot and mobile robot |
| CN112344943A (en) * | 2020-11-20 | 2021-02-09 | 安徽工程大学 | Intelligent vehicle path planning method for improving artificial potential field algorithm |
| CN112817312A (en) * | 2020-12-31 | 2021-05-18 | 浙江工业大学 | Path planning method based on double search optimization algorithm |
| CN113687662A (en) * | 2021-09-08 | 2021-11-23 | 南京理工大学 | Four-rotor formation obstacle avoidance method based on cuckoo algorithm improved artificial potential field method |
| CN113985922A (en) * | 2021-11-10 | 2022-01-28 | 浙江建德通用航空研究院 | Unmanned aerial vehicle hierarchical path planning method under multi-target constraint |
| CN115328208A (en) * | 2022-09-21 | 2022-11-11 | 西华大学 | Unmanned aerial vehicle path planning method for realizing global dynamic path planning |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107037812A (en) * | 2017-03-31 | 2017-08-11 | 南京理工大学 | A kind of vehicle path planning method based on storage unmanned vehicle |
| CN110609552B (en) * | 2019-09-12 | 2022-08-02 | 哈尔滨工程大学 | Method for planning formation plane flight path of underwater unmanned aircraft |
| CN110766137A (en) * | 2019-10-18 | 2020-02-07 | 武汉大学 | Power electronic circuit fault diagnosis method based on longicorn whisker optimized deep confidence network algorithm |
| TWI756647B (en) * | 2020-03-18 | 2022-03-01 | 財團法人船舶暨海洋產業研發中心 | A vessel collision avoiding method and system based on artificial potential field |
-
2023
- 2023-01-29 CN CN202310043230.5A patent/CN115951683B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2017215044A1 (en) * | 2016-06-14 | 2017-12-21 | 广东技术师范学院 | Automatic path planning method for mobile robot and mobile robot |
| CN112344943A (en) * | 2020-11-20 | 2021-02-09 | 安徽工程大学 | Intelligent vehicle path planning method for improving artificial potential field algorithm |
| CN112817312A (en) * | 2020-12-31 | 2021-05-18 | 浙江工业大学 | Path planning method based on double search optimization algorithm |
| CN113687662A (en) * | 2021-09-08 | 2021-11-23 | 南京理工大学 | Four-rotor formation obstacle avoidance method based on cuckoo algorithm improved artificial potential field method |
| CN113985922A (en) * | 2021-11-10 | 2022-01-28 | 浙江建德通用航空研究院 | Unmanned aerial vehicle hierarchical path planning method under multi-target constraint |
| CN115328208A (en) * | 2022-09-21 | 2022-11-11 | 西华大学 | Unmanned aerial vehicle path planning method for realizing global dynamic path planning |
Non-Patent Citations (4)
| Title |
|---|
| Path planning with multiple constraints and path following based on model predictive control for robotic fish;Yizhuo Mu 等;《Information Processing in Agriculture》;第9卷(第1期);全文 * |
| 基于天牛须-粒子群混合算法的多分拣机器人任务调度;谭鹤毅 等;《机械设计与研究》;第38卷(第3期);全文 * |
| 基于深度学习的冗余机械臂无碰运动规划;季晓明 等;《组合机床与自动化加工技术》(第6期);全文 * |
| 天牛须搜索算法研究综述;廖列法 等;《计算机工程与应用》;第57卷(第12期);全文 * |
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