CN111487960A - Mobile robot path planning method based on positioning capability estimation - Google Patents
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Abstract
The invention relates to a mobile robot path planning method based on positioning capability estimation, which not only considers the influences of the distance of a path navigated to a target point, dynamic obstacles in the environment and the like on the path planning, but also considers the influences of different environmental characteristics and map noise on the robot positioning by fusing the positioning capability in a global map cost function. The path obtained by the invention can ensure that the mobile robot can navigate in an area with relatively strong positioning capability. Compared with the traditional path planning algorithm, the method can guide the robot to bypass dynamic obstacles or inform the robot that the robot cannot pass and needs to stop for waiting, and also enhances the positioning precision and the robustness in the navigation process of the mobile robot, thereby improving the moving performance. And finally, the algorithm is optimized by combining the actual navigation requirement of the robot, so that the algorithm can meet the real-time requirement when the path planning is carried out aiming at the large-range environment.
Description
Technical Field
The invention relates to a mobile robot path planning method based on positioning capacity estimation, which researches how to improve a path planning algorithm on the basis of considering the positioning capacity of a mobile robot in different navigation areas, and belongs to the technical field of mobile robot navigation planning.
Background
In the future, the mobile robot will work in increasingly complex dynamic and non-structural natural environments, and if the positioning accuracy of the mobile robot is reduced or even lost, the mobile robot cannot continue to effectively execute the autonomous navigation task. In conventional path planning, it has not been sufficient to consider only the shortest path without collision. Because if the shortest path is pursued, the influence of the complex environment is not considered, and more risks are brought to navigation, such as incapability of bypassing the area with poor locatability, loss of the position of the robot, task failure and the like. Therefore, the invention provides an algorithm for analyzing the positioning capacity of the mobile robot and optimizing the path planning by using the analysis result.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method solves the problem of how to effectively evaluate the influence of map features or mapping noise on robot positioning, namely the positioning capability, and can provide an analytic solution and introduce an analysis result into a path planning algorithm.
The technical solution of the invention is as follows:
firstly, the Fisher's information matrix and the CRB theorem are utilized to evaluate the influence of the known environment on positioning, the influence is expressed numerically, and the positioning capability is defined after normalization processing. Secondly, the influence brought by the positioning capacity, the Euler distance, the obstacle boundary and the sensor information of the robot is introduced into a gradient method cost distribution system together, and then a path planning algorithm is given according to a new cost function. And finally, the algorithm is optimized by combining the actual navigation requirement of the robot, so that the algorithm can meet the real-time requirement when the path planning is carried out aiming at the large-range environment.
Specifically, the invention provides a mobile robot path planning method based on positioning capability estimation, which comprises the following steps:
(1) evaluating and calculating the positioning capacity of the mobile robot;
(2) constructing a path planning cost function;
(3) performing path planning of the mobile robot through a path planning method based on positioning capacity estimation;
(4) and optimizing the real-time performance of the path planning method.
Further, the mobile robot uses an odometer and a laser range finder as sensors, and the map used is a probability grid map.
Further, the step (1) of evaluating and calculating the positioning capability of the mobile robot specifically comprises:
(1.1) estimating the positioning capacity of the mobile robot in the known environment by using a Fisher's information matrix and a CRB theorem; discretizing the influence based on the characteristics of the probability grid map to obtain a positioning capacity matrix;
and (1.2) reflecting the numerical positioning capacity of the robot in the position posture by using a determinant of the positioning capacity matrix.
Further, the positioning capability estimation is defined as:
estimating the influence of the known environment on positioning by using a Fisher's information matrix and a CRB theorem, numerically expressing the influence, and defining the influence as positioning capacity after normalization processing; the positioning capability reflects the influence of environmental characteristics and map noise on the positioning accuracy and robustness of the robot.
Further, the positioning capability matrix is specifically:
where p ═ x, y, θ denotes the position and attitude angle of the robot on the map,
is at that pointDesired measurement distance, σ, of ith laser rayi 2For the corresponding measured variance, NoThe number of laser beams is shown as,
the observation change of the laser range finder is observed after the robot moves a delta distance along each coordinate axis direction.
Using location capability matrices
The determinant of (a) reflects the numerical positioning capability of the mobile robot under the position attitude p, namely:
wherein,
is composed of
The greater the L (p) value is, the more useful positioning information the robot can acquire in the current pose is, the smaller the path cost corresponding to the position is, otherwise, the less useful positioning information the robot can acquire is, the larger the path cost is.
Furthermore, for any path P in the map space, a plurality of discrete points PiThe cost function C is defined as:
wherein the cost O represents when the robot moves to the adjacent point pi+1In time, the influence brought by the obstacle is increased by the point cost which is closer to the boundary of the obstacle; the cost D represents that the robot moves to the adjacent point pi+1The longer the moving distance is, the larger the cost is, and the cost L represents that the robot moves to the adjacent point pi+1Time, location capability bringsThe point cost is higher when the positioning capability is weaker; for the above cases, the cost is smaller in the opposite case.
Further, path planning is carried out according to the following steps:
(3.1) initializing a cost function value of each position point on the map: setting the initial cost at the target point to be 0, and setting the initial costs at other points to be infinite;
(3.2) traversal is performed starting from the target point: establishing a list to be traversed, taking a target point as a first point to be traversed, putting the target point into the list to be traversed, and detecting adjacent points of all points in the list to be traversed according to a first-in first-out principle;
(3.3) for the point p taken from the list to be traversediWith 8 adjacent points p around iti+1Respectively calculating from the target point to 8 adjacent points pi+1For any one adjacent pi+1If the calculated cost is less than the cost which is distributed at present, the point is indicated to have a path with lower cost when reaching the target point, and then the original cost of the point is replaced by the lower cost; meanwhile, the points subjected to cost replacement are put into a list to be traversed, and the paths passing through the points need to be traversed and detected again;
(3.4) if and only if the list to be traversed is empty, the algorithm jumps out of the loop.
Furthermore, when the algorithm completes traversal detection, the cost function values distributed by each point are the minimum cost of the path from the point to the target point; and backtracking is carried out from the initial point of the robot, a series of continuous points are found according to the direction that the cost function value is reduced most quickly, the target point can be backtracked finally, and the track formed by the continuous points is the planned optimal path.
Further, the step (4) optimizes the real-time performance of the path planning method, specifically: on the updated map, re-traversing the cost caused by the barrier boundary, and in the process of fusing sensor information and re-traversing the cost caused by the barrier boundary, setting a square area by taking a robot as a center according to the size and the moving speed of the robot, and re-traversing the cost caused by the barrier boundary only in the area; when the obstacle is outside the set area, the influence of the obstacle does not need to be introduced into the cost, namely, the path planning is not influenced; conversely, when an obstacle is within the set area, its effect is introduced into the cost, i.e., the planned path will bypass the obstacle.
Compared with the prior art, the invention has the following advantages:
(1) compared with the traditional path planning algorithm, the algorithm can guide the robot to bypass dynamic obstacles or inform the robot that the robot cannot pass and needs to stop for waiting, and can effectively ensure that the robot can navigate and move in an area with stronger positioning capacity, so that the positioning precision and the robustness in the navigation process of the mobile robot are enhanced, and the moving performance is improved. Meanwhile, the algorithm is optimized by combining with the actual navigation requirement of the robot, and the algorithm can meet the real-time requirement when the path planning is carried out aiming at the large-range environment.
(2) The method provided by the invention integrates the positioning capability in the global map cost function, and considers the influence of different environmental characteristics and map noise on the positioning of the robot.
(3) The method also considers the influence of the distance of the path navigated to the target point on the path planning.
(4) The method also considers the influence of dynamic obstacles in the environment on the path planning.
(5) The method utilizes Fisher's information matrix and CRB theorem to evaluate the influence of the known environment on positioning, numerically expresses the influence, and defines the influence as positioning capability after normalized processing. The positioning capability reflects the influence of environmental characteristics and map noise on the positioning accuracy and robustness of the robot.
(6) The method of the invention optimizes the algorithm by combining the actual navigation requirements of the robot, ensures that the algorithm can also meet the real-time requirement when planning the path aiming at the large-scale environment, and particularly comprises the following steps: in general, a dynamic obstacle far from the robot is not substantially dangerous to the robot, and for this reason, in consideration of the influence of the dynamic obstacle in the environment on the route planning, one map area is set with the robot center in accordance with the size, the moving speed, the control cycle, and the like of the robot, and the algorithm considers only the influence of the dynamic obstacle in the area.
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FIG. 1 is an overall scheme of the algorithm of the present invention;
FIG. 2 is a schematic diagram of a certain point and its neighboring points based on a grid map according to the present invention;
FIG. 3 is a schematic diagram of the steps of the planning algorithm of the present invention;
fig. 4 is a diagram illustrating a result of the improved path planning algorithm according to the present invention.
Detailed Description
The invention relates to a mobile robot path planning method based on positioning capacity estimation. The positioning capability reflects the influence of environmental characteristics and map noise on positioning accuracy and robustness, the invention not only considers the influence of the distance of a path navigated to a target point, dynamic obstacles in the environment and the like on path planning, but also considers the influence of different environmental characteristics and map noise on robot positioning by fusing the positioning capability in a global map cost function. The path obtained by the invention can ensure that the mobile robot can navigate in an area with relatively strong positioning capability. Compared with the traditional path planning algorithm, the method can guide the robot to bypass dynamic obstacles or inform the robot that the robot cannot pass and needs to stop for waiting, and also enhances the positioning precision and the robustness in the navigation process of the mobile robot, thereby improving the moving performance. And finally, the algorithm is optimized by combining the actual navigation requirement of the robot, so that the algorithm can meet the real-time requirement when the path planning is carried out aiming at the large-range environment.
As shown in fig. 1, the method for planning a path of a mobile robot based on estimation of positioning capability according to the present invention includes the following steps:
(1) evaluating and calculating the positioning capacity of the mobile robot;
(2) constructing a path planning cost function;
(3) performing path planning of the mobile robot through a path planning method based on positioning capacity estimation;
(4) and optimizing the real-time performance of the path planning method.
Firstly, evaluating and quantitatively calculating the positioning capability of the mobile robot
The mobile robot uses an odometer and a laser range finder as sensors, and the used map is a probability grid map. Firstly, estimating the influence of a known environment on the positioning of the mobile robot by using a Fisher's information matrix and a CRB (CrB) theorem; furthermore, the influence is discretized based on the characteristics of the probability grid map, and a positioning capacity matrix is obtained:
where p ═ x, y, θ denotes the position and attitude angle of the robot on the map,
is the desired measured distance, σ, of the ith laser ray at that pointi 2For the corresponding measured variance, NoThe number of laser beams is shown as,
the observation change of the laser range finder is observed after the robot moves a delta distance along each coordinate axis direction. The positioning capability matrix is essentially used for evaluating the uncertainty influence of expected observation information of the mobile robot in a certain position on a known map on positioning.
It is known that covariance ellipses can be used to represent the uncertainty of the variables, and therefore it can be used to evaluate the uncertainty of the position fix as well. For example, a larger area of the positioning covariance ellipse indicates that the possible poses of the robot are distributed over a larger area, i.e., their positioning uncertainty is higher, and vice versa. Of course, to plot the covariance ellipse, the covariance matrix is first obtained. According to the CRB theorem, the desired localization covariance matrix can be estimated by the localization capability matrix (1):
further, the long and short axes of the positioning covariance ellipse can be solved according to equation (2). Taking x-y covariance ellipse as an example, the major semi-axis is:
its minor semi-axis does:
the orientation angle of the major half axis is:
wherein, if
Andqxyis of opposite sign, then order
Order to
And
is composed of
The characteristic root of (1), then:
the area size of the covariance ellipse can measure the uncertainty of positioning, and the area of the ellipse area is in direct proportion to the characteristic root:
therefore, we can use
The determinant measures the positioning accuracy in the x-y direction under the current pose. By analogy, the x-theta and y-theta covariance ellipses can also be solved according to equations (2) - (5). In summary, we use the determinant of the positioning capability matrix to reflect the numerical positioning capability of the robot in the pose p, that is:
wherein, the larger the L (p) value is, the more useful positioning information that the robot can acquire in the current pose is, the smaller the path cost corresponding to the position is, otherwise, the less useful positioning information that can be acquired is, the larger the path cost is, wherein,
is composed of
The characteristic root of (2).
Second, the construction of the cost function of path planning
Generally, a two-dimensional laser range finder is not an omnidirectional sensor, so that when the robot faces different directions, the positioning capability at the same position is different. Therefore, in the path planning process, the robot positioning capability fused with the cost function needs to be calculated by combining the orientation of the robot. In order to ensure the real-time performance of the algorithm, the positioning capacity can be calculated in advance according to a known map and stored in advance, and in the actual execution process of the algorithm, a table look-up method is directly adopted to read a corresponding numerical value (when the calculation is carried out in advance, the direction of the robot is reflected to move from a certain grid on the map to a nearby grid).
In particular, for any path P (from several discrete points P) in the map spaceiComposition), we define its cost function C as:
wherein the cost O represents when the robot moves to the adjacent point pi+1In time, the influence of the obstacle is usually higher by the point closer to the boundary of the obstacle; the cost D represents that the robot moves to the adjacent point pi+1The influence of the distance is that the longer the moving distance is, the larger the cost is, and the cost L represents that the robot moves to the adjacent point pi+1In the time, the influence of the positioning capability is higher by the point cost of weaker positioning capability. For the above cases, the smaller the penalty is.
Third, path planning algorithm based on positioning capability estimation
In the navigation process, the robot can block dynamic obstacles, and detours the dynamic obstacles when planning paths. However, the dynamic obstacle does not exist on the initial map, which requires updating the map in real time according to the sensor information, and calculating the cost O caused by the obstacle boundary at each grid (i.e. location point), and then performing path planning according to the following steps.
Firstly, initializing a cost function value of each position point on a map: the initial cost at the target point is set to 0 and the initial costs at other points are set to infinity.
Second, traversal is performed starting from the target point. Establishing a list to be traversed, taking a target point as a first point to be traversed, putting the target point into the list to be traversed, and detecting adjacent points of all points in the list to be traversed according to a first-in first-out principle.
Thirdly, for a point p taken from the list to be traversediIt can be known that there are 8 neighboring points p around iti+1As shown in fig. 2. Calculating the orders of the eyes according to the formula (9)Punctuation to 8 neighboring points pi+1For any one adjacent pi+1If the calculated cost is less than the cost which is distributed at present, the point is indicated to have a path with lower cost when reaching the target point, and then the original cost of the point is replaced by the lower cost; meanwhile, the point subjected to cost replacement is put into a list to be traversed, and the path passing through the point needs to be traversed and detected again.
In the traversal process, the calculation of the cost O and the cost D is the same as the conventional method, and is not repeated, the cost L is calculated according to the formula (8), and it should be noted that the positioning capability is directional for a non-omnidirectional sensor.
Fourth, the algorithm jumps out of the loop if and only if the list to be traversed is empty.
Finally, it can be seen that, after the traversal detection is completed by the algorithm, the cost function values assigned to each point are the minimum cost of the path from the point to the target point. The backtracking is started from the initial point of the robot, a series of continuous points can be found according to the direction that the cost function value is reduced most rapidly, and finally the target point can be backtracked, the track formed by the continuous points is the planned optimal (minimum cost) path, and a simple and visual example is shown in fig. 3.
Fourth, algorithm real-time improvement
According to the path planning algorithm based on the positioning capability estimation, along with the fusion of sensor information, the cost caused by the barrier boundary needs to be re-traversed on the updated map, and thus the requirement is provided for the real-time performance of the algorithm.
Therefore, in the process of fusing sensor information and re-traversing the cost caused by the obstacle boundary, a square area is set by taking the robot as the center according to the size, the moving speed and the like of the robot, and the cost caused by the obstacle boundary is re-traversed only in the area. When the obstacle is outside the set area, although the robot can observe the existence of the obstacle, the influence of the obstacle does not need to be introduced into the cost, and therefore, the path planning is not influenced; conversely, when an obstacle is within the set area, its effect is introduced into the cost, and therefore the planned path bypasses the obstacle, as shown in fig. 4.
Fifth, conclusion
Compared with the traditional path planning algorithm, the algorithm can guide the robot to bypass dynamic obstacles or inform the robot that the robot cannot pass and needs to stop for waiting, and can effectively ensure that the robot can navigate and move in an area with stronger positioning capacity, so that the positioning precision and the robustness in the navigation process of the mobile robot are enhanced, and the moving performance is improved. Meanwhile, the algorithm is optimized by combining with the actual navigation requirement of the robot, and the algorithm can meet the real-time requirement when the path planning is carried out aiming at the large-range environment.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.
Claims (10)
1. A mobile robot path planning method based on positioning capability estimation is characterized by comprising the following steps:
(1) evaluating and calculating the positioning capacity of the mobile robot;
(2) constructing a path planning cost function;
(3) performing path planning of the mobile robot through a path planning method based on positioning capacity estimation;
(4) and optimizing the real-time performance of the path planning method.
2. The method for planning the path of the mobile robot based on the estimation of the positioning capability of claim 1, wherein: the mobile robot uses an odometer and a laser range finder as sensors, and the map used is a probability grid map.
3. The method for planning the path of the mobile robot based on the estimation of the positioning capability of claim 1, wherein: the step (1) of evaluating and calculating the positioning capability of the mobile robot specifically comprises the following steps:
(1.1) estimating the positioning capacity of the mobile robot in the known environment by using a Fisher's information matrix and a CRB theorem; discretizing the influence based on the characteristics of the probability grid map to obtain a positioning capacity matrix;
and (1.2) reflecting the numerical positioning capacity of the robot in the position posture by using a determinant of the positioning capacity matrix.
4. The method of claim 3, wherein the method comprises: the location capability estimate defined as:
estimating the influence of the known environment on positioning by using a Fisher's information matrix and a CRB theorem, numerically expressing the influence, and defining the influence as positioning capacity after normalization processing; the positioning capability reflects the influence of environmental characteristics and map noise on the positioning accuracy and robustness of the robot.
5. The method of claim 3, wherein the method comprises: the positioning capability matrix is specifically:
where p ═ x, y, θ denotes the position and attitude angle of the robot on the map,
is the desired measured distance, σ, of the ith laser ray at that pointi 2For the corresponding measured variance, NoThe number of laser beams is shown as,
the observation change of the laser range finder is observed after the robot moves a delta distance along each coordinate axis direction.
6. A location based capability as claimed in claim 5The estimated mobile robot path planning method is characterized by comprising the following steps: using location capability matrices
The determinant of (a) reflects the numerical positioning capability of the mobile robot under the position attitude p, namely:
wherein,
is composed of
The greater the L (p) value is, the more useful positioning information the robot can acquire in the current pose is, the smaller the path cost corresponding to the position is, otherwise, the less useful positioning information the robot can acquire is, the larger the path cost is.
7. The method for planning the path of the mobile robot based on the estimation of the positioning capability of claim 1, wherein: for any path P in the map space, a plurality of discrete points PiThe cost function C is defined as:
wherein the cost O represents when the robot moves to the adjacent point pi+1In time, the influence brought by the obstacle is increased by the point cost which is closer to the boundary of the obstacle; the cost D represents that the robot moves to the adjacent point pi+1The longer the moving distance is, the larger the cost is, and the cost L represents that the robot moves to the adjacent point pi+1In time, the point cost is higher when the positioning capability is weaker; for the above cases, the cost is smaller in the opposite case.
8. The method for planning the path of the mobile robot based on the estimation of the positioning capability of claim 1, wherein: path planning is performed according to the following steps:
(3.1) initializing a cost function value of each position point on the map: setting the initial cost at the target point to be 0, and setting the initial costs at other points to be infinite;
(3.2) traversal is performed starting from the target point: establishing a list to be traversed, taking a target point as a first point to be traversed, putting the target point into the list to be traversed, and detecting adjacent points of all points in the list to be traversed according to a first-in first-out principle;
(3.3) for the point p taken from the list to be traversediWith 8 adjacent points p around iti+1Respectively calculating from the target point to 8 adjacent points pi+1For any one adjacent pi+1If the calculated cost is less than the cost which is distributed at present, the point is indicated to have a path with lower cost when reaching the target point, and then the original cost of the point is replaced by the lower cost; meanwhile, the points subjected to cost replacement are put into a list to be traversed, and the paths passing through the points need to be traversed and detected again;
(3.4) if and only if the list to be traversed is empty, the algorithm jumps out of the loop.
9. The method of claim 8, wherein the method comprises: when the algorithm finishes traversal detection, the cost function values distributed by each point are the minimum cost of the path from the point to the target point; and backtracking is carried out from the initial point of the robot, a series of continuous points are found according to the direction that the cost function value is reduced most quickly, the target point can be backtracked finally, and the track formed by the continuous points is the planned optimal path.
10. The method for planning the path of the mobile robot based on the estimation of the positioning capability of claim 1, wherein: the step (4) of optimizing the real-time performance of the path planning method specifically comprises the following steps: on the updated map, re-traversing the cost caused by the barrier boundary, and in the process of fusing sensor information and re-traversing the cost caused by the barrier boundary, setting a square area by taking a robot as a center according to the size and the moving speed of the robot, and re-traversing the cost caused by the barrier boundary only in the area; when the obstacle is outside the set area, the influence of the obstacle does not need to be introduced into the cost, namely, the path planning is not influenced; conversely, when an obstacle is within the set area, its effect is introduced into the cost, i.e., the planned path will bypass the obstacle.
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