CN115730756A - Staged automatic driving vehicle track planning method - Google Patents
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Abstract
The invention relates to the technical field of automatic driving, and particularly discloses a staged automatic driving vehicle trajectory planning method. In the searching stage, sampling under a Frenet coordinate system is carried out, a fifth-order polynomial is used for connecting sampling points, a reference track is obtained through dynamic planning and searching, and a travelable channel is constructed; in the optimization stage, a vehicle kinematics model is established, a cost function and boundary constraint are constructed, space-time linkage optimization is carried out by using an ILQR algorithm, and an optimal track is output. The advantages of the two methods based on sampling and optimization are combined, the advantages of a Frenet coordinate system and the advantages of a Cartesian coordinate system are taken into consideration, the problems that calculation is complex and real-time performance is difficult to meet in space-time joint trajectory planning are solved, the requirements of a dynamic scene are easily met, the problems that decoupling methods are prone to fall into local optimal solutions or even do not have solutions are solved, and the problem that a vehicle kinematics model cannot be established in the Frenet coordinate system is also solved.
Description
Technical Field
The invention belongs to the technical field of automatic driving, and particularly relates to a staged automatic driving vehicle trajectory planning method.
Background
The planning module is a key module for automatic driving, and needs to comprehensively consider perception, prediction, map information and vehicle states and output a safe and comfortable track. At present, there are many research works on trajectory planning of an autonomous vehicle, and different classification methods are available according to different emphasis points.
According to different track generation modes, track planning can be divided into a sampling-based method and an optimization-based method, the sampling-based method generates a large number of candidate tracks by sampling a state space, and then an optimal track is selected according to a pre-designed evaluation index. The sampling-based method is simple to implement and high in real-time performance, but the planning result is easily influenced by the sampling interval, the generated track is too rough if the sampling interval is too large, and the calculated amount is remarkably increased if the sampling interval is too small, so that the real-time performance requirement is not favorably met. Corresponding to this is an optimization-based method that obtains trajectories that satisfy constraints by building a minimum cost problem with the constraints and solving the problem. The optimization-based method is not limited by a sampling mode, the cost function and the constraint condition can be adjusted according to different scenes, and the method has higher flexibility and is more suitable for coping with complex scenes. However, the optimization-based method often needs to solve a complex nonlinear programming problem, and needs more computing resources to obtain an optimal solution, so that when the scale of the problem is large, it is difficult to ensure that the requirement of real-time performance is met.
Trajectory planning can be divided into methods based on the Frenet coordinate system and methods based on the cartesian coordinate system, depending on the coordinate system. The Frenet coordinate system is a curved coordinate system, and can well simplify the curvature of the road, so that the expression is more brief and visual. Since Frenet ignores the curvature of the road, the kinematic model of the vehicle cannot be accurately described in a scene with a large curvature. Although the kinematic model of the vehicle can be accurately described in the cartesian coordinate system to obtain a track more conforming to the vehicle and the kinematic model, the description of the lane boundary and the obstacle in the cartesian coordinate system is complex and not concise, so that the constraint solution of the planning is difficult, and the calculation amount is significantly increased.
Disclosure of Invention
The embodiment of the invention aims to provide a staged automatic driving vehicle track planning method, aiming at solving the problems in the background technology.
In order to achieve the above purpose, the embodiments of the present invention provide the following technical solutions:
a staged automatic driving vehicle trajectory planning method specifically comprises the following steps:
in the searching stage, sampling is carried out under a Frenet coordinate system, a quintic polynomial is used for connecting sampling points to form a directed acyclic graph, a reference track is obtained through dynamic planning and searching, and a travelable channel is constructed;
and in the optimization stage, a vehicle kinematics model is established, a cost function is established according to the travelable channel, boundary constraint is established, space-time linkage optimization is performed by using an ILQR algorithm, and an optimal track is output.
As a further limitation of the technical solution of the embodiment of the present invention, in the search stage, sampling is performed in a Frenet coordinate system, a quintic polynomial is used to connect sampling points to form a directed acyclic graph, a reference trajectory is obtained by dynamic planning and searching, and the construction of a travelable channel specifically includes the following steps:
obtaining map information of an automatic driving vehicle, constructing a Frenet coordinate system, obtaining obstacle information and automatic driving vehicle information, and projecting the obstacle information and the automatic driving vehicle information to the Frenet coordinate system;
sampling in the Frenet coordinate system to obtain sampling points, connecting the sampling points by using a fifth-order polynomial, and calculating corresponding cost according to a preset cost function;
and performing dynamic planning and searching to obtain an optimal path in a searching stage, performing expansion to obtain a travelable channel, and converting the travelable channel into a Cartesian coordinate system.
As a further limitation of the technical solution of the embodiment of the present invention, the formula using a fifth-order polynomial to connect sampling points is:
wherein the content of the first and second substances,
is a parameter of a fifth-order polynomial,
is an argument of a fifth order polynomial.
As a further limitation of the technical solution of the embodiment of the present invention, the cost function is:
c path ＝c ref +c smooth +c obs
wherein, c path As a path cost, c ref As a reference line offset cost, c smooth At the cost of smoothness, c obs At the expense of the obstacle.
As a further limitation of the technical solution of the embodiment of the present invention, the formula of the offset cost of the reference line is as follows:
wherein, w 0 As a weight coefficient, l(s) is a degree of offset.
As a further limitation of the technical solution of the embodiment of the present invention, the smoothness cost formula is:
wherein, w 1 ,w 2 ,w 3 All of which are weight coefficients, are obtained,
the first, second and third derivatives of l(s), respectively.
As a further limitation of the technical solution of the embodiment of the present invention, the formula of the barrier cost is as follows:
as a further limitation of the technical solution of the embodiment of the present invention, the motion state equation of the vehicle in the vehicle kinematics model is:
v i+1 ＝v i +a i δ t
θ i+1 ＝θ i +ω i δ t
wherein, the first and the second end of the pipe are connected with each other,
is t i The amount of state at the moment in time,
is a coordinate point in a Cartesian coordinate system, v i And theta i Respectively the vehicle speed and the course angle, a i Is the acceleration.
As a further limitation of the technical solution of the embodiment of the present invention, the cost function includes a control cost function and a state cost function, specifically:
the control cost function is:
wherein, J u To control the cost, ω acc ,ω ω Are all weight coefficients, a i ,ω i Acceleration and yaw rate, respectively;
the state cost function is:
wherein (r) i x ,r i y ) Is a point
Projected point on the reference path, v r Reference speed for autonomous driving of the vehicle, w ref ,w vel Are all weight coefficients, J x Is the state cost.
As a further limitation of the technical solution of the embodiment of the present invention, the expression of the boundary constraint is as follows:
compared with the prior art, the invention has the beneficial effects that:
1. a staged planning method is adopted and divided into a searching stage and an optimizing stage, the advantages of two methods based on sampling and optimizing are combined, and the advantages of a Frenet coordinate system and a Cartesian coordinate system are also considered;
2. the problems that the calculation is complex and the real-time performance is difficult to meet in the space-time joint trajectory planning are solved;
3. the optimization mode is space-time coupled, so that the requirements of a dynamic scene are more easily met, and the problem that a decoupling method is easily trapped into a local optimal solution or even has no solution is solved;
4. the optimization stage is carried out under a Cartesian coordinate system, and the problem that a vehicle kinematic model cannot be established under a Frenet coordinate system is solved.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention.
Fig. 1 shows a schematic flow chart of a method provided by an embodiment of the present invention.
Fig. 2 is a schematic diagram illustrating a vehicle kinematics model in a method provided by an embodiment of the invention.
Fig. 3 is a schematic diagram illustrating establishment of a boundary constraint in the method according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
It can be understood that the existing automatic driving vehicle trajectory planning technology has the following disadvantages: (1) Based on the sampling method, the planning result is easily influenced by the sampling interval, if the sampling interval is too large, the generated track is too rough, and if the sampling interval is too small, the calculated amount is obviously increased, which is not beneficial to meeting the real-time requirement; (2) Based on an optimization method, a complex nonlinear programming problem is often solved, and more computing resources are needed to obtain an optimal solution, so that when the problem scale is large, the requirement of real-time performance is difficult to meet; (3) The method comprises the following steps that (1) track planning based on a Frenet coordinate system ignores road curvature, and cannot accurately describe a vehicle kinematic model under a scene with large curvature; (4) The trajectory planning based on the Cartesian coordinate system has complex description of lane boundaries and obstacles, and is not concise enough, so that the planning constraint solving is difficult, and the calculation amount is obviously increased.
In order to solve the problems, in the searching stage, sampling under a Frenet coordinate system is carried out, a fifth-order polynomial is used for connecting sampling points, a reference track is obtained through dynamic planning and searching, and a travelable channel is constructed; in the optimization stage, a vehicle kinematics model is established, a cost function and boundary constraint are established, space-time linkage optimization is performed by using an ILQR algorithm, and an optimal track is output. The advantages of the two methods based on sampling and optimization are combined, the advantages of a Frenet coordinate system and the advantages of a Cartesian coordinate system are taken into consideration, the problems that calculation is complex and real-time performance is difficult to meet in space-time joint trajectory planning are solved, the requirements of a dynamic scene are easily met, the problems that decoupling methods are prone to falling into local optimal solutions or even do not have solutions are solved, and the problem that a vehicle kinematics model cannot be established in the Frenet coordinate system is solved.
Fig. 1 shows a schematic flow chart of a method provided by an embodiment of the present invention.
Specifically, in a preferred embodiment provided by the present invention, a staged automatic driving vehicle trajectory planning method specifically includes the following steps:
step one, a searching stage, namely sampling under a Frenet coordinate system, connecting sampling points by using a fifth-order polynomial to form a directed acyclic graph, dynamically planning and searching to obtain a reference track, and constructing a travelable channel;
and step two, in an optimization stage, a vehicle kinematic model is established, a cost function is established according to the travelable channel, boundary constraint is established, space-time linkage optimization is carried out by using an ILQR algorithm, and an optimal track is output.
In the embodiment of the invention, the process of planning the track of the automatic driving vehicle is divided into a searching stage and an optimizing stage, wherein the searching stage aims to obtain a drivable channel, a sampling method is used, the searching process is completed under the condition of extremely small calculation amount, and a reference basis is provided for the next optimizing stage; the purpose of the optimization stage is to obtain a more perfect track, the result obtained in the search stage is too coarse, a space-time joint plan is made in the optimization stage, and a space-time smooth track is calculated under the condition that various constraints are met. Specifically, the method comprises the following steps: in the searching stage, map information where the automatic driving vehicle is located is obtained firstly, a Frenet coordinate system is built according to a target lane, and obstacle information and automatic driving vehicle information are projected under the coordinate system (so that the obstacle information and the automatic driving vehicle information are projected to the Frenet, the purpose is to simplify geometrical information of a road structure and an obstacle track, simplify constraint and reduce calculated amount); then sampling is carried out under a Frenet coordinate system to obtain sampling points, and the sampling points are connected by a fifth-order polynomial. Calculating the cost according to a preset cost function to obtain the cost of each edge; finally, dynamic planning and searching are carried out to obtain the optimal path in the searching stage, the feasible driving channel is obtained through expansion, and the feasible driving channel is converted into a Cartesian coordinate system; in the optimization stage, a vehicle kinematics model is established, a track boundary establishing limiting condition is established according to a travelable channel obtained in the searching stage, then a barrier function is used for converting the constrained optimization problem into an unconstrained problem, and then an ILQR algorithm is used for solving the problem to obtain an optimized optimal track and outputting the optimized optimal track.
In the embodiment of the invention, sampling is carried out under a Frenet coordinate system, a fifth-order polynomial is used for connecting sampling points to form a Directed Acyclic Graph (DAG), a sampling path is obtained through Dynamic Programming (DP) search, a travelable channel is constructed, the fifth-order polynomial is a common curve for trajectory planning, and the formula is as follows:
wherein, the first and the second end of the pipe are connected with each other,
is a parameter of a fifth-order polynomial,
is independent variable of quintic polynomial, the sampling is to determine the expression form of these quintic polynomials, since the quintic polynomial needs six parameters, six equations, namely boundary conditions, can be obtained for the initial state and the end state, so that the parameters can be solved, and the optimal evaluation is performed by determining the standard, which is the path cost c path Offsetting the cost c from the reference line ref Smoothness cost c smooth And obstacle cost c obs And (3) the sum of the two, and the formed expression of the cost function is as follows:
c path ＝c ref +c smooth +c obs
the formula for the reference line offset cost is:
wherein, w 0 Is the weight coefficient, l(s) is the degree of offset;
the smoothness cost is formulated as:
wherein w 1 ,w 2 ,w 3 Are all the weight coefficients of the weight coefficient,
first, second, third derivatives of l(s), respectively;
the formula for the obstacle cost is:
it can be understood that the reference line offset cost c ref The method is used for evaluating the deviation of a curve and a lane central line, and the smaller the deviation is, the better the deviation is, the closer an automatically-driven vehicle is to the lane central line; cost of smoothness c smooth Is used to evaluate the smoothness of the curve, c smooth The smaller the value of (A), the smoother the curve, and the more comfortable the automobile is; cost of obstacle c obs Is used for evaluating the principle degree of the curve and the barrier, is beneficial to ensuring the safety of the vehicle when being far away from the barrier, c obs A smaller value of (c) indicates a greater distance from the obstacle.
In the embodiment of the invention, after the cost of all curves is calculated, because a clear target position does not exist, the heuristic search is difficult to obtain the most available path, so the exhaustive search can be used, the optimal path is searched by adopting a Dynamic Programming (DP) algorithm, the path with the minimum cost of relative smoothness and no collision is generated in a non-convex space, the optimal path obtained by the search is expanded, and thus the travelable channel is obtained, and then the travelable channel is converted from a Frenet coordinate system to a Cartesian coordinate system, thereby providing a basis for the boundary limit of the optimized stage.
In the embodiment of the invention, a travelable channel in a Frenet coordinate system is converted into a constraint limit in a Cartesian coordinate system, and space-time coupling trajectory optimization is carried out in the Cartesian coordinate system based on ILQR (CILQR) with the constraint limit, as shown in FIG. 2, a schematic diagram of a vehicle kinematics model in the method provided by the embodiment of the invention is shown, vehicle motion is described by using a vehicle-bicycle kinematics model,
is t i State quantity of time of day wherein
Is a coordinate point in a Cartesian coordinate system, v i And theta i Respectively the vehicle speed and course angle u i ＝[a i ,ω i ] T Is t i Control amount of time, a i As acceleration, ω i For the yaw rate, the control of the overall motion trajectory of the vehicle can be accomplished by controlling the acceleration and yaw rate of the vehicle, assuming that the controlled variable is [ t ] i ,t i+1 ]If the vehicle is kept constant, the equation of state of motion of the vehicle can be expressed approximately as:
v i+1 ＝v i +a i δ t
θ i+1 ＝θ i +ω i δ t
wherein the content of the first and second substances,
is t i The amount of state at the moment of time,
is a coordinate point in a Cartesian coordinate system, v i And theta i Respectively the vehicle speed and the course angle, a i Is the acceleration, δ t ＝t i+1 -t i Represents an extremely short time during which the control quantity is assumed to be constant, naturally represented by t i The state of the moment can be deduced to t i+1 State of (1)
In the embodiment of the invention, the cost of the optimization process is divided into control cost and state cost, and the control cost aims to facilitate control of the automatic driving vehicle. The control cost includes an acceleration cost and a yaw rate cost, as follows:
wherein, J u To control cost, ω acc ,ω ω Are all weight coefficients, a i ,ω i Acceleration and yaw rate, respectively;
the objective of the state cost is to make the trajectory obtained in the optimization stage not deviate too much from the path obtained in the search stage, and to satisfy the boundary constraint of the travelable path in the search stage as much as possible, and the state cost is defined as the deviation from the path in the search stage and the error from the reference speed as follows:
wherein (r) i x ,r i y ) Is a point
Projection point on the reference path, v r Reference speed for autonomous driving of the vehicle, w ref ,w vel Are all weight systemsNumber, J x Is the state cost;
boundary constraints of the trajectory can be established according to the travelable path obtained in the search stage, and as shown in fig. 3, a schematic diagram and points for establishing the boundary constraints in the method provided by the embodiment of the present invention
Is t i At the time of the day the vehicle position,
and the projected point of the vehicle position on the boundary of the travelable passage. Constraints are established at the projection points and the function g (x, y) describes a straight line passing through the projection points and making it possible to tangent the channel boundaries, establishing the following constraints.
The meaning of the constraint is to keep the vehicle away from the boundaries of the feasible access, and the purpose of using tangent lines is to simplify the form of the constraint.
It should be understood that, although the steps in the flowcharts of the embodiments of the present invention are shown in sequence as indicated by the arrows, the steps are not necessarily performed in sequence as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of steps in various embodiments may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed alternately or alternatingly with other steps or at least a portion of sub-steps or stages of other steps.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a non-volatile computer-readable storage medium, and can include the processes of the embodiments of the methods described above when the program is executed. Any reference to memory, storage, database or other medium used in the embodiments provided herein can include non-volatile and/or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), rambus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is specific and detailed, but not to be understood as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent should be subject to the appended claims.
The above description is intended to be illustrative of the preferred embodiment of the present invention and should not be taken as limiting the invention, but rather, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (10)
1. A staged automatic driving vehicle trajectory planning method is characterized by specifically comprising the following steps:
in the searching stage, sampling is carried out under a Frenet coordinate system, a quintic polynomial is used for connecting sampling points to form a directed acyclic graph, a reference track is obtained through dynamic planning and searching, and a travelable channel is constructed;
and in the optimization stage, a vehicle kinematic model is established, a cost function is established according to the travelable channel, boundary constraint is established, space-time joint optimization is carried out by using an ILQR algorithm, and an optimal track is output.
2. The phased method for planning the trajectory of an autonomous vehicle according to claim 1, characterized in that in the search phase, sampling is performed in a Frenet coordinate system, a quintic polynomial is used to connect sampling points to form a directed acyclic graph, a reference trajectory is obtained by dynamic planning and searching, and the construction of a travelable channel specifically comprises the following steps:
obtaining map information of an automatic driving vehicle, constructing a Frenet coordinate system, obtaining obstacle information and automatic driving vehicle information, and projecting the obstacle information and the automatic driving vehicle information to the Frenet coordinate system;
sampling in the Frenet coordinate system to obtain sampling points, connecting the sampling points by using a fifth-order polynomial, and calculating corresponding cost according to a preset cost function;
and performing dynamic planning and searching to obtain an optimal path in a searching stage, performing expansion to obtain a travelable channel, and converting the travelable channel into a Cartesian coordinate system.
3. The phased autonomous vehicle trajectory planning method of claim 2, wherein the formula using a fifth order polynomial to tie the sample points is:
wherein the content of the first and second substances,
is a parameter of a fifth-order polynomial,
is an argument of a fifth order polynomial.
4. The phased autonomous vehicle trajectory planning method of claim 2, wherein the cost function is:
c path ＝c ref +c smooth +c obs
wherein, c path As a path cost, c ref As a reference line offset cost, c smooth At the cost of smoothness, c obs At the expense of the obstacle.
5. The phased autonomous vehicle trajectory planning method of claim 4, wherein the reference line offset cost is formulated as:
wherein, w 0 As a weight coefficient, l(s) is a degree of offset.
6. The phased autonomous vehicle trajectory planning method of claim 5, wherein the smoothness cost is formulated as:
wherein, w 1 ,w 2 ,w 3 Are all the weight coefficients of the weight coefficient,
the first, second, and third derivatives of l(s), respectively.
7. The phased autonomous vehicle trajectory planning method of claim 6, characterized in that the formula of the obstacle cost is:
8. the phased autonomous vehicle trajectory planning method of claim 1, wherein the equations of motion states of the vehicles in the vehicle kinematics model are:
v i+1 ＝v i +a i δ t
θ i+1 ＝θ i +ω i δ t
wherein the content of the first and second substances,
is t i The amount of state at the moment of time,
is a coordinate point in a Cartesian coordinate system, v i And theta i Respectively the vehicle speed and the course angle, a i Is the acceleration.
9. The phased automated driven vehicle trajectory planning method of claim 8, in which the cost function comprises a control cost function and a state cost function, specifically:
the control cost function is:
wherein, J u To control cost, ω acc ,ω ω Are all weight coefficients, a i ,ω i Acceleration and yaw angular velocity, respectively;
the state cost function is:
wherein, the first and the second end of the pipe are connected with each other,
is a point
Projected point on the reference path, v r Reference speed for autonomous driving of the vehicle, w ref ,w vel Are all weight coefficients, J x Is a state cost.
10. The phased autonomous vehicle trajectory planning method of claim 9, wherein the boundary constraint is expressed as:
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