CN113847924B - Navigation path planning method and system based on parameter curve optimization - Google Patents
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Abstract
The invention discloses a navigation path planning method and system based on parameter curve optimization, which comprises the following specific processes: generating planning configuration according to the positioning, the laser radar and the map information; according to the planning configuration, performing initial path search by using a Lazy Theta star algorithm to obtain an initial path; performing geometric analysis on the initial path to obtain a part of key points, and amplifying the key points to obtain the rest key points; performing cubic spline interpolation on all key points to obtain a parameter curve; defining an optimized objective function, inputting the parameter curve as the objective function, taking key points as decision variables, and outputting the key points as measurement values of collision risk and smoothness of the parameter curve; performing numerical optimization on the objective function by a numerical optimization method to obtain a navigation path; and optimizing collision risk and smoothness of the path to obtain a final path, and combining numerical optimization and geometric optimization in the optimization process to improve the optimization effect.
Description
Technical Field
The invention belongs to the technical field of autonomous mobile robots, and particularly relates to a navigation path planning method and system based on parameter curve optimization.
Background
Global path planning is one of the important modules in an autonomous mobile robot system. The purpose of this is to generate a path that can guide the robot from the current position to the destination, providing navigation for the local behavior planning. There are two key elements of global path planning, first collision risk and second smoothness.
Conventional global path planning methods are divided into two categories, a graph search-based planning method and a sampling-based planning algorithm. These methods can generate paths from the current location to the end point, but the generated paths cannot meet the requirements of high smoothness and minimized collision risk, requiring further path smoothing and optimization.
Current researchers propose to generate an initial path using a planning algorithm for graph search, then construct an optimization objective function, and optimize the collision risk and smoothness of the path using a conjugate gradient descent method. Although these methods have good effects, there are still problems that the path cannot be stably optimized, and sometimes the path smoothness may be even reduced.
The reason for this problem is that these methods construct an objective function using the coordinates of all points on the path as decision variables. This results in a defined optimization problem that is highly dimensional and difficult to solve. At the same time, excessive redundancy of decision variables also results in some variables that may adversely affect the optimization process.
But these methods have difficulty in stably improving smoothness while minimizing collision risk of the path. As it takes all the sampling point coordinates of the path as optimization targets, resulting in an excessively high dimensionality of the constructed optimization problem.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a new global path planning method and system, which are characterized in that firstly, a Lazy Theta star algorithm is utilized to search an initial path, after the initial path is obtained, key points are extracted from the path, a parameter path is constructed according to the key points, and an optimized objective function is further obtained, so that the collision risk and smoothness of the path are optimized, and a final path is obtained, and in the optimization process, not only the coordinates of the key points are adjusted (numerical optimization), but also the addition and deletion (geometric optimization) of the key points are performed, so that the optimization effect is improved.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: a navigation path planning method based on parameter curve optimization comprises the following specific processes:
Generating planning configuration according to the positioning, the laser radar and the map information;
According to the planning configuration, performing initial path search by using a Lazy Theta star algorithm to obtain an initial path;
Performing geometric analysis on the initial path to obtain a part of key points, and amplifying the key points to obtain the rest key points;
performing cubic spline interpolation on all key points to obtain a parameter curve;
Defining an objective function, taking the parameter curve as input of the objective function, taking key points as decision variables, and outputting the key points as measurement values of collision risk and smoothness of the parameter curve; and optimizing the objective function through geometric optimization and numerical optimization to obtain the navigation path.
When the initial path is geometrically analyzed to obtain a part of key points, a Fabry-Perot algorithm is used.
The key point amplification is specifically as follows:
calculating each section of parameter curve S i (u) and corresponding straight line section Maximum Euclidean distance d i of the two-dimensional coordinate system, and simultaneously obtaining a straight line segmentThe point of maximum distance from curve segment S i (u)If d i is greater than a given deviation tolerance sigma, then the point is takenInserting keypoints as new keypointsAndBetween them;
the above process is repeated until no new key points need to be inserted Obtaining key point pointsAnd parameter curve
According to the current key pointPerforming cubic spline interpolation to obtain a parameter curveIs a piecewise function of the parameter u, the parameter curveThe expression of the i-th segment S i (u) is shown in formula (1):
Wherein, Representing two key pointsAndThe euclidean distance between them, i 0 = 0,AndThe same is a parameter curveUnknown parameters of (a); after solving the unknown parameters, the exact expression of the parameter curve can be obtained.
The objective function is specifically:
Wherein, Is a parameter curveMeasurement of the risk of collision,Is a parameter curveThe measurement of the smoothness of the object is carried out,Is a parameter curveThe offsets of the two endpoints from the planned start and end points, w c,ws and w o, are preset weights.
For parameter curveDiscretizing: through sampling pointsTo represent a parameter curve, wherein t+1 is the number of sampling points; calculating collision risk measurementsThe calculation of (2) is shown in the formula (3)
Wherein,Indicating separationThe nearest obstacle point FILTERMEAN is a custom function, and gamma is a preset parameter, so that gamma is more than or equal to 0 and less than or equal to 1;
Number curve Measurement of smoothnessThe calculation of (2) is shown in formula (4):
The Euclidean distance between each sampling point and the connecting line central point of the front sampling point and the rear sampling point is calculated by the formula (4);
Parameter curve Offset of two endpoints from the start and end of the planThe calculation of (2) is shown in formula (5):
Wherein, AndRespectively, initial pathsΤ (s) and τ (g) are the start and end tolerant offsets, respectively.
The parameter curve is optimized by a method combining numerical optimization and geometric optimization, and the method comprises the following steps: firstly, utilizing a numerical optimization method to carry out key pointOptimizing, judging the distance between the optimized key points, deleting the corresponding key points if the distance is smaller than a preset value, and performing cubic spline interpolation on the rest key points to obtain a new parameter curveIf the obtained parameter curve has no collision, ending the optimization process, otherwise, judging whether each section S i (u) of the parameter curve has collision, if so, finding the nearest point of S i (u) and the obstacleInsert it into the key pointIn (a) and (b); the above process is repeated until the maximum iteration number it is reached, and an optimized parameter curve is obtainedI.e. the final global path.
On the other hand, the invention provides a navigation path planning system based on parameter curve optimization, which comprises a planning configuration generation module, an initial path acquisition module, a key point acquisition module, a parameter curve acquisition module and a path calculation module;
the planning configuration generation module is used for generating planning configuration according to the positioning, the laser radar and the map information;
The initial path acquisition module is used for carrying out initial path search by using a Lazy Theta star algorithm according to planning configuration to obtain an initial path;
The key point acquisition module is used for performing geometric analysis on the initial path to obtain a part of key points, and amplifying the key points to obtain the rest key points;
The parameter curve acquisition module is used for carrying out cubic spline interpolation on all the key points to obtain a parameter curve;
defining a defined objective function by a path calculation module, taking the parameter curve as the input of the objective function, taking a key point as a decision variable, and outputting the key point as a measured value of collision risk and smoothness of the parameter curve; and optimizing the objective function through geometric optimization and numerical optimization to obtain the navigation path.
The computer equipment comprises a processor and a memory, wherein the memory is used for storing a computer executable program, the processor reads the computer executable program from the memory and executes the computer executable program, and the navigation path planning method based on parameter curve optimization can be realized when the processor executes the computer executable program.
A computer readable storage medium, in which a computer program is stored, which when being executed by a processor, can implement the navigation path planning method based on parameter curve optimization according to the present invention.
Compared with the prior art, the invention has at least the following beneficial effects:
The method can effectively reduce collision risk of the path and improve the smoothness of the path by optimizing the parameterized global path; a new optimization objective function is defined, so that the numerical optimization of the objective function can fully improve the performance of a path, the numerical optimization and the geometric optimization are combined in the path optimization process, the new optimization objective function is provided, and the optimization effect is improved; based on the method, the global path is not re-planned in real time, and the global path is updated only when the current global path collides or the current global path is evaluated inferior to the newly planned global path.
Drawings
FIG. 1 is a schematic diagram of a path navigation and planning method framework.
Fig. 2 is a schematic diagram of adding and deleting key points.
Fig. 3 is a diagram of a mobile robot and a system architecture thereof.
Detailed Description
The flow of the method proposed by the invention is shown in figure 1 and can be divided into four steps. First, a planned configuration is generated from the positioning, the lidar, and the map information. And secondly, according to the planning configuration, performing initial path search by using a Lazy Theta star algorithm to obtain an initial path shown by a red line in fig. 1. And thirdly, performing geometric analysis on the initial path to obtain a part of key points, and amplifying the key points to obtain the rest key points. All key points obtained in the third step are shown as red points in fig. 1. The key points are subjected to cubic spline interpolation, and the obtained parameter curve is shown as a green curve in fig. 1. And fourthly, defining an optimization objective function, inputting a parameter curve as the objective function, taking key points as decision variables, and carrying out numerical optimization. In the optimization process, the insertion and deletion of key points are performed simultaneously: judging whether a new key point needs to be inserted between two key points; and judging whether each key point is redundant or not, and deleting the key points if the key points are redundant. The above process is repeated until the termination condition is met. The adjusted key points are shown as blue points in fig. 1, and the optimized curves are shown as blue curves in fig. 1.
After using the Lazy Theta star algorithm, an initial path can be obtainedBut the route obtained at this timeRather than being curvature-continuous, the present invention contemplates obtaining a path that is consistent with the original pathSimilarly, and meets the curvature continuity requirement. The method adopted by the invention is that in the initial pathExtracting key points on the basis of (1)By means of key pointsPerforming cubic spline interpolation to obtain a parameter curveThe above process requires the obtained parameter curveAnd pathSimilar (preventing the initial values of the subsequent path optimizations from being too bad), and the smaller the number of keypoints, the better (reducing the problem of the subsequent optimizations).
To achieve the above object, the method used in the present invention is shown in algorithm 1. The algorithm is divided into two parts: initial path geometry analysis (GeometryAnalysis) and keypoint amplification (KeyPointsIncrement). The former is to use as few key points as possible for the characterization of the initial path, and the latter is to prevent the parameter curve obtained by interpolation from being too different from the initial path.
The geometry analysis uses the douglas-poder algorithm, and the key point amplification is shown in algorithm 2.
According to the current key pointPerforming cubic spline interpolation to obtain a parameter curveIs a piecewise function with respect to the parameter u. Parameter curveThe expression of the i-th segment S i (u) is shown in formula 1.
Wherein,Representing two key pointsAndThe euclidean distance between them, i 0 = 0,AndThe same is a parameter curveIs a parameter unknown to the user. After solving the unknown parameters, the exact expression of the parameter curve can be obtained, and the solving method is to solve the equation set shown in the formula 2.
Wherein l i has the same meaning as in formula 1.
Obtaining a parameter curveThen, calculate each section of parameter curve S i (u) and the corresponding straight line sectionIs a maximum euclidean distance d i. At the same time, a straight line segment is obtainedThe point of maximum distance from curve segment S i (u)If d i is greater than a given deviation tolerance sigma, then the point is takenInserting keypoints as new keypointsAndBetween them. The above process is repeated until no new key points need to be insertedIn (3), the key point amplification is finished. Thus, the key points shown in the midpoint of FIG. 1 can be obtainedAnd a parameter curve shown in the curve
The parameter curve obtained in the last stepAlthough approximately optimal in efficiency and satisfying curvature continuity. But it is not optimal in terms of collision risk and smoothness. In order to optimize the collision risk and smoothness of the parameter curves, a classical idea is to perform numerical optimization.
In detail, an objective function is definedObjective functionIs input as a parametric curveObjective functionThe output of (a) is a measure of the risk of collision and smoothness of the parametric curve. The invention only needs to optimize the objective function by a numerical valueOptimizing the parameter curveCollision risk and smoothness of (c). Furthermore, due to the parameter curveIs composed of key pointsThe decision variables uniquely determined for the above-mentioned optimization problem are in factThus, the objective functionCan also be recorded as
The final objective function is shown in formula 3 after theoretical calculation analysis, multiple experiments and tests.
Wherein,Is a parameter curveMeasurement of the risk of collision,Is a parameter curveThe measurement of the smoothness of the object is carried out,Is a parameter curveThe offsets of the two endpoints from the planned start and end points, w c,ws and w o, are preset weights. To simplify the calculation of the objective function, the parameter curve is calculatedDiscretization is performed: representing the parametric curve by some sampling points, i.e. assumingWhere t+1 is the number of sampling points.
The calculation of (2) is shown in equation 4.
Wherein,Indicating separationThe nearest obstacle point. FILTERMEAN is a custom function, as shown in algorithm 3. Gamma is a preset parameter, and is more than or equal to 0 and less than or equal to 1.
Using FILTERMEAN functions, in calculating collision risk measurementsIn the course of (2), only the influence of a part of the obstacle closest to the curve on the curve is considered, but not all the obstacles. The reason for this is that the collision risk mainly originates from close obstacles. If all the obstacles are considered, the curve may not be far away from the close-range obstacle in the optimization process, but rather far away from the far-range obstacle, which violates our expectations. The current approach solves this problem by setting a safe distance threshold, and once the obstacle is greater than the threshold, no consideration is given. This approach is problematic: if the threshold value is set too large, the effect is difficult to be achieved in a narrow scene; if the threshold value is set too small, the optimization is limited by the threshold value, and the ideal situation is difficult to achieve. In contrast, the method of the present invention does not have the above-described problems.
Number curveMeasurement of smoothnessThe calculation of (2) is shown in equation 5.
Equation (5) calculates the euclidean distance between each sampling point and the center point of the line connecting the front sampling point and the back sampling point. That is, when the sampling point is at the center point of the line connecting the front and rear sampling points, the ideal smoothness is considered to be achieved, and the purpose of using FILTERMEAN functions is to focus the optimization on the least smooth part of the curve.
Parameter curveOffset of two endpoints from the start and end of the planThe calculation of (2) is shown in equation 6.
Wherein,AndRespectively, initial pathsΤ (s) and τ (g) are the start and end tolerant offsets, respectively. In the optimization process, the starting point and the end point are not regarded as constraints, but are regarded as optimization items, so that the influence of the too bad conditions of the starting point or the end point on the optimization of the whole parameter curve can be avoided.
To this end, the objective function is given in its entiretyIs a calculation method of (a). The optimization for the objective function is a nonlinear unconstrained optimization problem, and there is no analytical solution to the derivative of the objective function. Thus, the COBYLA algorithm can be used for optimization.
But it is not sufficient to optimize the parameter curve by means of numerical optimization only. For example, in the scenario shown above in fig. 2, it is difficult to achieve a desired planned path using only a numerical optimization method to adjust the coordinates of the keypoints. In the scenario shown below in fig. 2, too close a keypoint may cause curve jitter, which is also difficult to solve by numerical optimization. In solving these problems, the insertion and deletion of key points is a great help to solve this problem, as shown in fig. 2.
Therefore, the invention provides a method for combining numerical optimization and geometric optimization (inserting and deleting key points) to optimize a parameter curve, and the process is shown as an algorithm 4. Firstly, utilizing a numerical optimization method to carry out key pointAnd (5) optimizing. And judging the distance between the optimized key points, and deleting the corresponding key points if the distance is too small. Performing cubic spline interpolation on the rest key points to obtain a new parameter curveAnd if the obtained parameter curve has no collision, ending the optimization process. Otherwise, it is determined whether each segment S i (u) of the parametric curve collides. If a collision, find S i (u) the nearest point to the obstacleInsert it into the key pointIs a kind of medium. The above process is repeated until the maximum iteration number it is reached, and the optimization process is ended. At this time, an optimized parameter curve can be obtainedI.e. the final global path.
The method is realized on a self-developed mobile robot and is integrated into the whole robot system. The robot and system used in the present invention is shown in fig. 3. The robot chassis is provided with a wheel speed meter and a single-line laser radar, and a calculation unit of the robot uses NVIDIA Xavier NX. The system of the robot uses AMCL for localization, TEB planner for local planning, and smoothing the speed of the local planning output, as shown in fig. 3. In this framework, the global planner is not re-planned in real time. The global path is updated only if a collision occurs to the current global path or the current global path evaluates less than the newly planned global path.
In addition, the invention provides a navigation path planning system based on parameter curve optimization, which comprises a planning configuration generation module, an initial path acquisition module, a key point acquisition module, a parameter curve acquisition module and a path calculation module;
the planning configuration generation module is used for generating planning configuration according to the positioning, the laser radar and the map information;
The initial path acquisition module is used for carrying out initial path search by using a Lazy Theta star algorithm according to planning configuration to obtain an initial path;
The key point acquisition module is used for performing geometric analysis on the initial path to obtain a part of key points, and amplifying the key points to obtain the rest key points;
The parameter curve acquisition module is used for carrying out cubic spline interpolation on all the key points to obtain a parameter curve;
defining a defined objective function by a path calculation module, taking the parameter curve as the input of the objective function, taking a key point as a decision variable, and outputting the key point as a measured value of collision risk and smoothness of the parameter curve; and optimizing the objective function through geometric optimization and numerical optimization to obtain the navigation path.
The invention also provides a computer device, which comprises a processor and a memory, wherein the memory is used for storing computer executable programs, the processor reads part or all of the computer executable programs from the memory and executes the computer executable programs, and the navigation path planning method based on parameter curve optimization can be realized when the processor executes part or all of the computer executable programs.
In another aspect, the present invention provides a computer readable storage medium, where a computer program is stored, where the computer program, when executed by a processor, can implement the navigation path planning method based on parameter curve optimization according to the present invention.
The computer device may be an in-vehicle computer, a notebook computer, a desktop computer, or a workstation.
The processor may be a Central Processing Unit (CPU), a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), or an off-the-shelf programmable gate array (FPGA).
The memory can be an internal memory unit of a notebook computer, a desktop computer or a workstation, such as a memory and a hard disk; external storage units such as removable hard disks, flash memory cards may also be used.
Computer readable storage media may include computer storage media and communication media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. The computer readable storage medium may include: read Only Memory (ROM), random access Memory (RAM, random Access Memory), solid state disk (SSD, solid STATE DRIVES), or optical disk, etc. The random access memory may include resistive random access memory (ReRAM, RESISTANCE RANDOM ACCESS MEMORY) and dynamic random access memory (DRAM, dynamic Random Access Memory), among others.
Claims (5)
1. The navigation path planning method based on parameter curve optimization is characterized by comprising the following specific processes:
Generating planning configuration according to the positioning, the laser radar and the map information;
According to the planning configuration, performing initial path search by using a Lazy Theta star algorithm to obtain an initial path;
performing geometric analysis on the initial path to obtain a part of key points, and amplifying the key points to obtain the rest key points; when the initial path is geometrically analyzed to obtain a part of key points, a Fabry-Perot algorithm is used; the key point amplification is specifically as follows: calculating each section of parameter curve S i (u) and corresponding straight line section Maximum Euclidean distance d i of the two-dimensional coordinate system, and simultaneously obtaining a straight line segmentThe point of maximum distance from curve segment S i (u)If d i is greater than a given deviation tolerance sigma, then the point is takenInserting keypoints as new keypointsAndBetween them;
the above process is repeated until no new key points need to be inserted Obtaining key point pointsAnd parameter curve
Performing cubic spline interpolation on all key points to obtain a parameter curve; performing cubic spline interpolation on all key points to obtain a parameter curveIs a piecewise function of the parameter u, the parameter curveThe expression of the i-th segment S i (u) is shown in formula (1):
Wherein, Representing two key pointsAndThe euclidean distance between them, i 0 = 0,AndThe same is a parameter curveUnknown parameters of (a); solving the unknown parameters to obtain an expression with exact parameter curve;
Defining an objective function, taking the parameter curve as input of the objective function, taking key points as decision variables, and outputting the key points as measurement values of collision risk and smoothness of the parameter curve; optimizing the objective function through geometric optimization and numerical optimization to obtain a navigation path; the objective function is specifically:
Wherein, Is a parameter curveMeasurement of the risk of collision,Is a parameter curveThe measurement of the smoothness of the object is carried out,Is a parameter curveThe offsets of the two endpoints from the planned start and end points, w c,ws and w o, are preset weights.
2. The navigation path planning method based on parameter curve optimization according to claim 1, wherein the method of combining numerical optimization and geometric optimization optimizes the parameter curve, specifically as follows: firstly, utilizing a numerical optimization method to carry out key pointOptimizing, judging the distance between the optimized key points, deleting the corresponding key points if the distance is smaller than a preset value, and performing cubic spline interpolation on the rest key points to obtain a new parameter curveIf the obtained parameter curve has no collision, ending the optimization process, otherwise, judging whether each section S i (u) of the parameter curve has collision, if so, finding the nearest point of S i (u) and the obstacleInsert it into the key pointIn (a) and (b); the above process is repeated until the maximum iteration number it is reached, and an optimized parameter curve is obtainedI.e. the final global path.
3. The navigation path planning system based on parameter curve optimization is characterized by comprising a planning configuration generating module, an initial path acquisition module, a key point acquisition module, a parameter curve acquisition module and a path calculation module, wherein the navigation path planning system based on parameter curve optimization is used for realizing the navigation path planning method based on parameter curve optimization as set forth in claim 1 or 2;
the planning configuration generation module is used for generating planning configuration according to the positioning, the laser radar and the map information;
The initial path acquisition module is used for carrying out initial path search by using a Lazy Theta star algorithm according to planning configuration to obtain an initial path;
The key point acquisition module is used for performing geometric analysis on the initial path to obtain a part of key points, and amplifying the key points to obtain the rest key points;
The parameter curve acquisition module is used for carrying out cubic spline interpolation on all the key points to obtain a parameter curve;
The path calculation module defines an objective function, takes the parameter curve as the input of the objective function, takes a key point as a decision variable, and outputs the key point as a measured value of collision risk and smoothness of the parameter curve; and optimizing the objective function through geometric optimization and numerical optimization to obtain the navigation path.
4. A computer device comprising a processor and a memory, the memory storing a computer executable program, the processor reading the computer executable program from the memory and executing the computer executable program, the processor executing the computer executable program to implement the parameter curve-based optimized navigation path planning method of any one of claims 1-2.
5. A computer readable storage medium, wherein a computer program is stored in the computer readable storage medium, and when the computer program is executed by a processor, the computer program can implement the navigation path planning method based on parameter curve optimization as claimed in any one of claims 1-2.
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