CN112509114A - Path planning method, system and medium - Google Patents

Path planning method, system and medium Download PDF

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CN112509114A
CN112509114A CN202011329567.5A CN202011329567A CN112509114A CN 112509114 A CN112509114 A CN 112509114A CN 202011329567 A CN202011329567 A CN 202011329567A CN 112509114 A CN112509114 A CN 112509114A
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list
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李杏
苏建
张鹏翼
王坤福
冯炜
毛万峰
张鹏
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CSSC Systems Engineering Research Institute
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Abstract

The invention provides a path planning method, a system and a medium, wherein the path planning is used for a hexagonal checkerboard map, and the method comprises the following steps: step S1, obtaining initial data of the path planning, and initializing the initial data; step S2, defining an obstacle area, and taking a point in the obstacle area as an obstacle point; step S3, based on the initialized initial data and the obstacle area, traversing all estimation points on the hexagonal checkerboard map by using an A-x algorithm and an estimation function to obtain a traversal result; and step S4, generating the planning path according to the traversal result. The method can quickly obtain the shortest path and successfully avoid the obstacle, so that the operator intelligent agent can win the opposite cube in the hexagonal checkerboard map.

Description

Path planning method, system and medium
Technical Field
The present invention relates to the field of path planning, and in particular, to a method, a system, and a medium for path planning.
Background
The war game deduction system is an important means for colleges and universities to develop education training, innovation theory and participate in argumentation and other operations. The chessboard map in the chess deduction system generally uses a hexagonal grid chessboard. The intelligent operator decision-making body in the system is an intelligent body which can substitute human beings in the war game deduction system and can make the war game operators execute the actions of war games. A chess pursuing system typically includes a plurality of chess operators. Wherein, each type of operator in the chess participants can be used as an intelligent agent to automatically execute the predefined chess actions. For each type of intelligent agent, the functions of path planning and obstacle avoidance are required to be realized based on the hexagonal box military chess map.
A common path search algorithm is generally Dijkstra algorithm, a-algorithm. The Dijkstra search algorithm is a blind search, and although the optimal solution can be obtained by the Dijkstra search algorithm, the Dijkstra search algorithm is not suitable for meeting the requirement that game confrontation in a war game deduction system has the highest timeliness for an operator intelligent agent as much as possible due to the fact that the traversed nodes are multiple and the calculation amount is large. The A-star algorithm is an heuristic algorithm, is high in timeliness and short in path, and lacks estimation definition and application suitable for marine military chess deduction of the hexagonal map.
Disclosure of Invention
In view of the above problems, the present invention provides a path planning scheme to solve the above technical problems. The scheme provides an improved A-x algorithm aiming at the requirements of independent path search and obstacle avoidance of a military chess operator intelligent body in a military chess deduction system based on the characteristics of a hexagonal checkerboard map, avoids an opposite-direction obstacle area in a chessboard, implements independent path planning, obtains a shortest path in the shortest time and strives for precious opportunities for the military chess operator game.
In a first aspect, there is provided a path planning method for a checkerboard map, the method comprising: step S1, obtaining initial data of the path planning, and initializing the initial data; step S2, defining an obstacle area, and taking a point in the obstacle area as an obstacle point; step S3, based on the initialized initial data and the obstacle area, traversing all estimation points on the hexagonal checkerboard map by using an A-x algorithm and an estimation function to obtain a traversal result; and step S4, generating the planning path according to the traversal result.
Specifically, the start data includes a start point S, an end point E, an obstacle center point of the obstacle area, and an obstacle radius for the path planning.
Specifically, in step S2, the obstacle point is determined to be the obstacle point by traversing the neighborhood of the obstacle center point of the obstacle region and setting the obstacle flags of the obstacle center point and the point within the obstacle radius to true.
Specifically, the step S3 includes:
step S31, creating an open _ list, assigning a value to be null, and adding all the estimated value points into the null;
and step S32, creating a close _ list, assigning a value to be null, and adding the planned path point into the list.
And step S33, adding the starting point S into the open _ list, and taking the starting point S as a father node P.
Step S34, create CnThe list comprises:
neighbor point C of the parent node PnAdding CnA list;
if the neighboring point CnIn the close _ list, from the CnDeleting the neighboring point C from the listn(ii) a And
if the neighboring point CnIs true, from said CnDeleting the neighboring point C from the listn；
Step S35, traverseSaid C isnList of _ list when said CnNeighbor point P in list with the smallest F valuefWhen the point is the same as the end point E, ending the traversal, and enabling the adjacent point P to be adjacentfRemoving and adding the close _ list from the open _ list, otherwise, repeating the steps;
the calculation formula of the F value is as follows:
F(Cn)＝G(Cn)+H(Cn)
wherein G (C)n) The calculation formula of (2) is as follows:
G(Cn)＝DC(n)P(n)*a+GP(n)S
GP(n)S＝DP(n)P(n-1)*a+GP(n-1)S
DC(n)P(n)is the adjacent point CnTo the parent node PnDistance of (G)P(n)SValue G, D for parent node P to starting point SP(n)P(n-1)Is a parent node PnTo the previous parent node Pn-1Distance of (G)P(n-1)SFor the previous parent node Pn-1The value G to the starting point S, a is a first adjusting coefficient;
wherein H (C)n) The calculation formula of (2) is as follows:
H(Cn)＝DP(n)E*β
DP(n)Eis a neighboring point CnThe distance β from the end point E is a second adjustment factor.
Specifically, the first adjustment coefficient and the second adjustment coefficient are determined as follows: acquiring a three-dimensional surface graph of a training data set; determining values of the point having the maximum value on the z-axis on the x-axis and the y-axis as the first adjustment coefficient and the second adjustment coefficient, respectively.
Specifically, the step S4 includes: reading the close _ list; acquiring all points from the starting point S to the end point E to generate the planned path.
In a second aspect, there is provided a path planning system for a checkerboard map, the system comprising: an initialization unit configured to: acquiring initial data of the path planning, and initializing the initial data; a definition unit configured to: defining an obstacle area, and taking a point in the obstacle area as an obstacle point; a traversal unit configured to: based on the initialized initial data and the obstacle area, traversing all estimation points on the hexagonal checkerboard map by using an A-x algorithm and an estimation function to obtain a traversal result; and a generation unit configured to: and generating the planning path according to the traversal result.
Specifically, the start data includes a start point S, an end point E, an obstacle center point of the obstacle area, and an obstacle radius for the path planning.
In particular, the defining unit is further configured to: setting the obstacle flag of the obstacle center point and a point within the obstacle radius to true as the obstacle point by traversing a neighborhood of the obstacle center point of the obstacle region.
Specifically, the traversal unit is further configured to:
creating an open _ list, assigning a value to be null, and adding all the estimated value points into the list;
and creating a close _ list, assigning the list to be null, and adding the planned path point into the list.
And adding the starting point S into the open _ list, and taking the starting point S as a parent node P.
Creation CnThe list comprises:
neighbor point C of the parent node PnAdding CnA list;
if the neighboring point CnIn the close _ list, from the CnDeleting the neighboring point C from the listn(ii) a And
if the neighboring point CnIs true, from said CnDeleting the neighboring point C from the listn；
Traverse the CnList of _ list when said CnNeighbor point P in list with the smallest F valuefAnd the placeWhen the end point E is the same point, ending the traversal, and enabling the adjacent points PfRemoving and adding the close _ list from the open _ list, otherwise, repeating the steps;
the calculation formula of the F value is as follows:
F(Cn)＝G(Cn)+H(Cn)
wherein G (C)n) The calculation formula of (2) is as follows:
G(Cn)＝DC(n)P(n)*a+GP(n)S
GP(n)S＝DP(n)P(n-1)*a+GP(n-1)S
DC(n)P(n)is the adjacent point CnTo the parent node PnDistance of (G)P(n)SValue G, D for parent node P to starting point SP(n)P(n-1)Is a parent node PnTo the previous parent node Pn-1Distance of (G)P(n-1)SFor the previous parent node Pn-1The value G to the starting point S, a is a first adjusting coefficient;
wherein H (C)n) The calculation formula of (2) is as follows:
H(Cn)＝DP(n)E*β
DP(n)Eis a neighboring point CnThe distance β from the end point E is a second adjustment factor.
Specifically, the traversal unit is further configured to: determining the first adjustment factor and the second adjustment factor using: acquiring a three-dimensional surface graph of a training data set; determining values of the point having the maximum value on the z-axis on the x-axis and the y-axis as the first adjustment coefficient and the second adjustment coefficient, respectively.
In particular, the generating unit is further configured to: reading the close _ list; acquiring all points from the starting point S to the end point E to generate the planned path.
In a third aspect, there is provided a non-transitory computer readable medium having stored thereon instructions which, when executed by a processor, perform the steps of the first aspect.
Drawings
Fig. 1 is a schematic flow chart of a path planning method according to an embodiment of the present invention; and
fig. 2 is a schematic structural diagram of a path planning system according to an embodiment of the present invention;
Detailed Description
A first aspect of the present invention provides a path planning method, and fig. 1 is a schematic flow chart of the path planning method according to the embodiment of the present invention; as shown in fig. 1, the method includes: step S1, obtaining initial data of the path planning, and initializing the initial data; step S2, defining an obstacle area, and taking a point in the obstacle area as an obstacle point; step S3, based on the initialized initial data and the obstacle area, traversing all estimation points on the hexagonal checkerboard map by using an A-x algorithm and an estimation function to obtain a traversal result; and step S4, generating the planning path according to the traversal result. The starting data includes a starting point S, an end point E, a barrier center point of the barrier area, and a barrier radius for the path planning.
In step S1, acquiring initial data of the path plan, and initializing the initial data; the starting data includes a starting point S, an end point E, a barrier center point of the barrier area, and a barrier radius for the path planning.
Specifically, a hexagonal checkerboard map of the chess deduction system is analyzed, the length value L and the width value W of the map are obtained, and a map data list is set from [0, 0]]To [ L-1, W-1]. Obtaining initial data of path planning, the initial data includes initial point S [ x ] of path plannings,ys]End point E [ x ]e,ye]Center point of obstacle area O [ x ]o,yo]And an obstacle area radius Z. Initializing route planning initial data, and assigning a value of 0 to the initialized map data state mark at the beginning of each turn. Converting the path planning data according to the characteristics of the hexagonal checkerboard map, and resetting the path planning data to the starting point Sxs-1,ys-1]End point E [ x ]e-1,ye-1]And center point of obstacle area O [ x ]o-1,yo-1]。
In step S2, an obstacle area is defined, and a point within the obstacle area is set as an obstacle point. Setting the obstacle flag of the obstacle center point and a point within the obstacle radius to true as the obstacle point by traversing a neighborhood of the obstacle center point of the obstacle region.
Specifically, the obstacle area includes a map obstacle area and an opposite chess operator obstacle area. The map obstacle area includes an island terrain area, a sea-limited terrain area, and the like. The opposite war chess operator obstacle area comprises an air airplane operator early warning visual range, a water surface operator investigation detection visual range, a firepower attack range, an underwater operator underwater detection visual range and the like. And respectively setting an area center point O and an obstacle area radius Z for the obstacle area, converting data according to the characteristic of the hexagonal grid map, and setting an obstacle sign of the center point of the obstacle area to be true. And traversing adjacent points (comprising an upper coordinate, a lower coordinate, an upper left coordinate, a lower left coordinate, an upper right coordinate and a lower right coordinate) of the central point of the obstacle area, and setting the obstacle marks of the adjacent points to be true. For each neighboring point, the neighboring points of the point (including the top coordinate, the bottom coordinate, the top left coordinate, the bottom left coordinate, the top right coordinate, and the bottom right coordinate) are traversed, and the further neighboring point obstacle flag is set to true. Finally, traverse Z (obstacle radius) times, all obstacle points within the obstacle area.
In step S3, based on the initialized start data and the obstacle region, all estimation points on the hexagonal checkerboard map are traversed by using the a-x algorithm and the estimation function to obtain a traversal result.
The a-Star algorithm is the most effective direct search method for solving the shortest path in the static road network, and is also a common heuristic algorithm for many other problems. The formula is expressed as: (n) g (n) + h (n), where f (n) is the cost estimate from the initial state to the target state via state n, g (n) is the actual cost from the initial state to state n in the state space, and h (n) is the estimated cost of the best path from state n to the target state.
Step S3 specifically includes the following steps:
in step S31, an open _ list is created, assigned null, and all evaluation points are added.
In step S32, a close _ list is created, the assignment is null, and the planned waypoint is added thereto.
In step S33, the start point S is added to the open _ list, and the start point S is used as the parent node P.
In step S34, create CnList _ list. In particular, the neighboring point C of the parent node Pn(including upper, lower, upper left, lower left, upper right, and lower right) add CnA _ list is added into the open _ list; if the neighboring point CnIn the close _ list, from the CnDeleting the neighboring point C from the listn(ii) a And if said neighboring point CnIs true, from said CnDeleting the neighboring point C from the listn；
In step S35, traverse the CnList of _ list when said CnNeighbor point P in list with the smallest F valuefWhen the point is the same as the end point E, ending the traversal, and enabling the adjacent point P to be adjacentfAnd removing and adding the close _ list from the open _ list, otherwise, repeating the steps. Wherein the calculation formula of the F value is as follows:
F(Cn)＝G(Cn)+H(Cn)
wherein G (C)n) The calculation formula of (2) is as follows:
G(Cn)＝DC(n)P(n)*a+GP(n)S
GP(n)S＝DP(n)P(n-1)*a+GP(n-1)S
DC(n)P(n)is the adjacent point CnTo the parent node PnDistance of (G)P(n)SValue G, D for parent node P to starting point SP(n)P(n-1)Is a parent node PnTo the previous parent node Pn-1Distance of (G)P(n-1)SFor the previous parent node Pn-1The value of G to the starting point S, a is the first adjustment factor.
Wherein H (C)n) The calculation formula of (2) is as follows:
H(Cn)＝DP(n)E*β
DP(n)Eis a neighboring point CnThe distance β from the end point E is a second adjustment factor.
Determining the first adjustment factor and the second adjustment factor using: acquiring a three-dimensional surface graph of a training data set; determining values of the point having the maximum value on the z-axis on the x-axis and the y-axis as the first adjustment coefficient and the second adjustment coefficient, respectively. For example, the training data S is set to [0, 0]]E is [ R-1, C-1 ]]，CnIs [ R//2, C//2]；
Constructing a training data set of [0,1], [0,100] for a and beta, and constructing a three-dimensional surface map (x, y, z) under 4 types of combined data sets:
x is a and the range is [0,1], y is beta and the range is [0,1 ];
x is a and the range is [0,100], y is beta and the range is [0,1 ];
x is a and the range is [0,1], y is beta and the range is [0,100 ];
x is a, a ranges from [0,100], y is beta, and ranges from [0,100 ];
calculation of F (C)n) Assigning a value of F (C) to the z valuen)。
Then drawing a three-dimensional curved surface; and acquiring the highest point of the z value of the three-dimensional curved surface, and acquiring x and y values below the highest point as optimal parameter solutions of a and beta respectively.
While the foregoing has been made several times with reference to calculating the distance between two points on the checkerboard map, in some embodiments, the following method may be employed to calculate the distance between two points on the checkerboard map (point a (x)1，y1) And point B (x)2，y2) For example:
max(abs(du),abs(dv))if((du>＝0anddv>＝0)or(du<0anddv<0))elseabs(du)+abs(dv)
du＝x2-x1；dv＝(y2+x2//2)-(y1+x1//2)
if du and dv are both positive numbers or both negative numbers, returning the maximum values of the du absolute value and the dv absolute value; otherwise, the sum of the du absolute value and the dv absolute value is returned.
In step S4, the planned path is generated according to the traversal result. The step S4 specifically includes: reading the close _ list; acquiring all points from the starting point S to the end point E to generate the planned path.
A second aspect of the present invention provides a path planning system, where the path planning system is used for a checkerboard map, and the system includes: an initialization unit configured to: acquiring initial data of the path planning, and initializing the initial data; a definition unit configured to: defining an obstacle area, and taking a point in the obstacle area as an obstacle point; a traversal unit configured to: based on the initialized initial data and the obstacle area, traversing all estimation points on the hexagonal checkerboard map by using an A-x algorithm and an estimation function to obtain a traversal result; and a generation unit configured to: and generating the planning path according to the traversal result.
Specifically, the start data includes a start point S, an end point E, an obstacle center point of the obstacle area, and an obstacle radius for the path planning.
In particular, the defining unit is further configured to: setting the obstacle flag of the obstacle center point and a point within the obstacle radius to true as the obstacle point by traversing a neighborhood of the obstacle center point of the obstacle region.
Specifically, the traversal unit is further configured to:
creating an open _ list, assigning a value to be null, and adding all the estimated value points into the list;
and creating a close _ list, assigning the list to be null, and adding the planned path point into the list.
And adding the starting point S into the open _ list, and taking the starting point S as a parent node P.
Creation CnThe list comprises:
neighbor point C of the parent node PnAdding CnA list;
if the neighboring point CnIn the close _ list, from the CnDeleting the neighboring point C from the listn(ii) a And
if the neighboring point CnIs true, from said CnDeleting the neighboring point C from the listn；
Traverse the CnList of _ list when said CnNeighbor point P in list with the smallest F valuefWhen the point is the same as the end point E, ending the traversal, and enabling the adjacent point P to be adjacentfRemoving and adding the close _ list from the open _ list, otherwise, repeating the steps;
the calculation formula of the F value is as follows:
F(Cn)＝G(Cn)+H(Cn)
wherein G (C)n) The calculation formula of (2) is as follows:
G(Cn)＝DC(n)P(n)*a+GP(n)S
GP(n)S＝DP(n)P(n-1)*a+GP(n-1)S
DC(n)P(n)is the adjacent point CnTo the parent node PnDistance of (G)P(n)SValue G, D for parent node P to starting point SP(n)P(n-1)Is a parent node PnTo the previous parent node Pn-1Distance of (G)P(n-1)SFor the previous parent node Pn-1The value G to the starting point S, a is a first adjusting coefficient;
wherein H (C)n) The calculation formula of (2) is as follows:
H(Cn)＝DP(n)E*β
DP(n)Eis a neighboring point CnThe distance β from the end point E is a second adjustment factor.
Specifically, the traversal unit is further configured to: determining the first adjustment factor and the second adjustment factor using: acquiring a three-dimensional surface graph of a training data set; determining values of the point having the maximum value on the z-axis on the x-axis and the y-axis as the first adjustment coefficient and the second adjustment coefficient, respectively.
In particular, the generating unit is further configured to: reading the close _ list; acquiring all points from the starting point S to the end point E to generate the planned path.
A third aspect of the invention provides a non-transitory computer readable medium having stored thereon instructions which, when executed by a processor, perform the steps of the first aspect.
In conclusion, the technical scheme of the invention provides an improved A-x algorithm based on the characteristics of a hexagonal checkerboard map aiming at the requirements of military chess operator intelligent body autonomous path search and obstacle avoidance in a military chess deduction system, avoids an opposite-direction obstacle area in a checkerboard, implements autonomous path planning, obtains the shortest path in the shortest time and strives for precious opportunities for military chess operator games.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. A method of path planning for a checkerboard map, the method comprising:
step S1, obtaining initial data of the path planning, and initializing the initial data;
step S2, defining an obstacle area, and taking a point in the obstacle area as an obstacle point;
step S3, based on the initialized initial data and the obstacle area, traversing all estimation points on the hexagonal checkerboard map by using an A-x algorithm and an estimation function to obtain a traversal result; and
and step S4, generating the planning path according to the traversal result.
2. The path planning method according to claim 1, wherein the start data includes a start point S, an end point E, an obstacle center point of the obstacle area, and an obstacle radius for the path planning.
3. The path planning method according to claim 2, wherein in step S2, the obstacle point is determined by traversing a neighborhood of obstacle center points of the obstacle region, and setting obstacle flags of the obstacle center points and points within the obstacle radius to true.
4. The path planning method according to claim 3, wherein the step S3 specifically includes:
step S31, creating an open _ list, assigning a value to be null, and adding all the estimated value points into the null;
and step S32, creating a close _ list, assigning a value to be null, and adding the planned path point into the list.
And step S33, adding the starting point S into the open _ list, and taking the starting point S as a father node P.
Step S34, create CnThe list comprises:
neighbor point C of the parent node PnAdding CnA list;
if the neighboring point CnIn the close _ list, from the CnDeleting the neighboring point C from the listn(ii) a And
if the neighboring point CnIs true, from said CnDeleting the neighboring point C from the listn；
Step S35, traversing the CnList of _ list when said CnNeighbor point P in list with the smallest F valuefWhen the point is the same as the end point E, ending the traversal, and enabling the adjacent point P to be adjacentfRemoving and adding the close _ list from the open _ list, otherwise, repeating the steps;
the calculation formula of the F value is as follows:
F(Cn)＝G(Cn)+H(Cn)
wherein G (C)n) The calculation formula of (2) is as follows:
G(Cn)＝DC(n)P(n)*a+GP(n)S
GP(n)S＝DP(n)P(n-1)*a+GP(n-1)S
DC(n)P(n)is the adjacent point CnTo the parent node PnDistance of (G)P(n)SValue G, D for parent node P to starting point SP(n)P(n-1)Is a parent node PnTo the previous parent node Pn-1Distance of (G)P(n-1)SFor the previous parent node Pn-1The value G to the starting point S, a is a first adjusting coefficient;
wherein H (C)n) The calculation formula of (2) is as follows:
H(Cn)＝DP(n)E*β
DP(n)Eis a neighboring point CnThe distance β from the end point E is a second adjustment factor.
5. The path planning method according to claim 4, wherein the first adjustment factor and the second adjustment factor are determined by:
acquiring a three-dimensional surface graph of a training data set;
determining values of the point having the maximum value on the z-axis on the x-axis and the y-axis as the first adjustment coefficient and the second adjustment coefficient, respectively.
6. The path planning method according to claim 4, wherein the step S4 specifically includes:
reading the close _ list;
acquiring all points from the starting point S to the end point E to generate the planned path.
7. A path planning system for a checkerboard map, the system comprising:
an initialization unit configured to: acquiring initial data of the path planning, and initializing the initial data;
a definition unit configured to: defining an obstacle area, and taking a point in the obstacle area as an obstacle point;
a traversal unit configured to: based on the initialized initial data and the obstacle area, traversing all estimation points on the hexagonal checkerboard map by using an A-x algorithm and an estimation function to obtain a traversal result; and
a generation unit configured to: and generating the planning path according to the traversal result.
8. The path planning system according to claim 7, wherein:
the starting data comprises a starting point S and an end point E for the path planning, and a barrier central point and a barrier radius of the barrier area; and
the defining unit is further configured to: setting the obstacle flag of the obstacle center point and a point within the obstacle radius to true as the obstacle point by traversing a neighborhood of the obstacle center point of the obstacle region.
9. The path planning system of claim 8 wherein the traversal unit is further configured to:
creating an open _ list, assigning a value to be null, and adding all the estimated value points into the list;
and creating a close _ list, assigning the list to be null, and adding the planned path point into the list.
And adding the starting point S into the open _ list, and taking the starting point S as a parent node P.
Creation CnThe list comprises:
neighbor point C of the parent node PnAdding CnA list;
if the neighboring point CnIn the close _ list, from the CnDeleting the neighboring point C from the listn(ii) a And
if the neighboring point CnIs true, from said CnDeleting the neighboring point C from the listn；
Traverse the CnList of _ list when said CnNeighbor point P in list with the smallest F valuefWhen the point is the same as the end point E, ending the traversal, and enabling the adjacent point P to be adjacentfRemoving and adding the close _ list from the open _ list, otherwise, repeating the steps;
the calculation formula of the F value is as follows:
F(Cn)＝G(Cn)+H(Cn)
wherein G (C)n) The calculation formula of (2) is as follows:
G(Cn)＝DC(n)P(n)*a+GP(n)S
GP(n)S＝DP(n)P(n-1)*a+GP(n-1)S
DC(n)P(n)is the adjacent point CnTo the parent node PnDistance of (G)P(n)SValue G, D for parent node P to starting point SP(n)P(n-1)Is a parent node PnTo the previous parent node Pn-1Distance of (G)P(n-1)SFor the previous parent node Pn-1The value G to the starting point S, a is a first adjusting coefficient;
wherein H (C)n) The calculation formula of (2) is as follows:
H(Cn)＝DP(n)E*β
DP(n)Eis a neighboring point CnThe distance β from the end point E is a second adjustment factor.
10. A non-transitory computer readable medium having stored thereon instructions which, when executed by a processor, perform the steps in the path planning according to any of claims 1-6.
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