CN113886764B - Intelligent vehicle multi-scene track planning method based on Frenet coordinate system - Google Patents
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Abstract
An intelligent vehicle multi-scene track planning method based on Frenet coordinate system belongs to the technical field of intelligent vehicle control and vehicle-road coordination. The invention solves the problems of limited applicable scene and low efficiency of the coordinate system used by the existing intelligent vehicle cooperative control algorithm. According to the actual track of the intelligent vehicle, track information of x and y reference directions of the current intelligent vehicle under a Cartesian coordinate system is obtained, and then transverse and longitudinal coordinates, transverse and longitudinal speed and acceleration information of the intelligent vehicle under a Frenet coordinate system are obtained; establishing a transverse and longitudinal track planning set model of the intelligent vehicle under a Frenet coordinate system, and deducing and obtaining a transverse and longitudinal movement track set of the intelligent vehicle; and combining track optimization functions of transverse and longitudinal motions of the intelligent vehicle, and optimizing the actual application scene track of the intelligent vehicle by using the total optimization function to obtain an optimal track in the application scene. The method is suitable for intelligent vehicle track planning.
Description
Technical Field
The invention belongs to the technical field of intelligent vehicle control and vehicle-road coordination.
Background
The vehicle-road cooperation realizes the information interaction and intelligent cooperation management and control between the human-vehicle-road-cloud-network through the fusion of technologies such as perception, communication and the like, and is an important development direction of technical innovation in the field of road transportation. Intelligent vehicle technology is an important component of vehicle-road coordination. Decision making is a key element of intelligent vehicle technology, and comprises behavior decision making and motion planning. The track planning in the motion planning is a direct factor for determining the running safety and comfort of the vehicle, and is also an important embodiment of the technical capability of the intelligent vehicle.
At present, when an intelligent vehicle finishes behavior decision, a coordinate system is usually a Cartesian coordinate system, an odometer coordinate system, a polar coordinate system and the like. However, in the implementation of intelligent vehicle decision algorithms, the use of these coordinate systems has certain drawbacks: (1) The track information is limited to the local map based on the algorithm of the global coordinate system, and the timeliness of sampling and fitting of the model are influenced by the track length. (2) Based on the algorithm of the Cartesian coordinate system, the efficiency restricts the bottleneck of the optimization of the decision-making system. (3) The calculation of the algorithm based on the odometer coordinate system has larger accumulated error.
Disclosure of Invention
The invention provides an intelligent vehicle multi-scene track planning method based on a Frenet coordinate system, which aims to solve the problems that a coordinate system used by the existing intelligent vehicle cooperative control algorithm is limited in applicable scene and low in efficiency.
The invention discloses an intelligent vehicle multi-scene track planning method based on a Frenet coordinate system, which comprises the following steps:
step one, acquiring speed, motion curvature, acceleration and azimuth angle information of a current intelligent vehicle in x and y reference directions under a Cartesian coordinate system according to an actual track of the intelligent vehicle;
Step two, acquiring horizontal and longitudinal coordinates of the intelligent vehicle in the Frenet coordinate system and horizontal and longitudinal speed and acceleration information by utilizing a conversion formula from the Cartesian coordinate system to the Frenet coordinate system and speed, motion curvature, acceleration and azimuth angle information in x and y reference directions in the Cartesian coordinate system;
Thirdly, respectively establishing a transverse track planning set model and a longitudinal track planning set model of the intelligent vehicle under the Frenet coordinate system according to transverse and longitudinal coordinates of the intelligent vehicle under the Frenet coordinate system and transverse and longitudinal speed and acceleration information;
Step four, utilizing the transverse and longitudinal track planning set model of the intelligent vehicle, the transverse and longitudinal coordinates, transverse and longitudinal speed and acceleration information of the intelligent vehicle, deducing for a plurality of times according to asynchronous long sampling, and obtaining a transverse and longitudinal movement track set of the intelligent vehicle;
Establishing a track optimization function of transverse movement and a track optimization function of longitudinal movement of the intelligent vehicle according to transverse and longitudinal application scenes of the intelligent vehicle, and combining the track optimization function of transverse movement and the track optimization function of longitudinal movement to obtain a total optimization function suitable for the total application scene;
And step six, optimizing the motion trail in the actual application scene of the intelligent vehicle by utilizing the total optimization function suitable for the total application scene and the transverse and longitudinal motion trail sets of the intelligent vehicle in the step four to obtain the optimal motion trail in the current application scene of the intelligent vehicle. Further, in the first step of the present invention, the conversion formula from the cartesian coordinate system to the Frenet coordinate system is as follows:
s=s p formula one
D' = (1-dk p)tan(θx-θp) equation four
Wherein S is the longitudinal coordinate of the trace point x under the Frenet coordinate system, S p is the longitudinal coordinate of a point p nearest to the trace point x in the Frenet coordinate system,The derivative of the longitudinal coordinate of the trace point x under the Frenet coordinate system with respect to time is expressed as the speed of the vehicle along the direction of the reference line,/>The second derivative of the longitudinal coordinate of the track point x in the Frenet coordinate system with respect to time is represented by the acceleration of the vehicle along the reference line direction, d is the transverse coordinate of the track point x in the Frenet coordinate system, d ' is the first derivative of the transverse coordinate of the track point x in the Frenet coordinate system with respect to the longitudinal coordinate, d ' is the second derivative of the transverse coordinate of the track point x in the Frenet coordinate system with respect to the longitudinal coordinate, θ x is the azimuth angle of the track point x in the Cartesian coordinate system, θ p is the azimuth angle of the point P in the Cartesian coordinate system, k x is the curvature of the track point x in the Cartesian coordinate system, k p is the curvature of the point P in the Cartesian coordinate system, v x is the speed of the track point x in the Cartesian coordinate system, a x is the acceleration of the point x in the Cartesian coordinate system, and k p ' is the derivative of the curvature k p of the point P in the Cartesian coordinate system.
In the second step, in the present invention, the building of the transverse track planning set model of the intelligent vehicle is:
The five-degree polynomial transverse trajectory planning model of the intelligent vehicle is determined according to the vehicle kinematic model under the Frenet coordinate system:
d(t)＝a0+a1t+a2t2+a3t3+a4t4+a5t5 Formula six
Wherein, a 0＝d(t0), D (t 0) is the transverse trajectory at the planned trajectory initial time t 0,For planning the lateral velocity of the trajectory initiation instant t 0,/>For the lateral acceleration at the initial time t 0 of the planned trajectory, let the final time of the planned trajectory be t f,T＝tf-t0, a 3,a4,a5 is obtained by:
Calculating to obtain;
The five-degree polynomial longitudinal trajectory planning model of the intelligent vehicle is determined according to the vehicle kinematic model under the Frenet coordinate system:
s(t)＝b0+b1t+b2t2+b3t3+b4t4+b5t5 Equation eight
Wherein, b 0＝s(t0), S (t 0) is the longitudinal offset of the planned trajectory initial instant t 0,For planning the lateral velocity of the trajectory initiation instant t 0,/>For the lateral acceleration at the planned trajectory initial time t 0, then b 3,b4,b5 passes:
And (5) calculating to obtain the product.
Further, in the fourth step of the present invention, the method for obtaining the transverse motion track set of the intelligent vehicle includes:
according to the transverse track planning set model of the intelligent vehicle, for time t epsilon [ t i,ti+1 ], acquiring a transverse sampling model of the start and end states of the intelligent vehicle:
Wherein d (t i) is the lateral offset of the vehicle at time t i, For the lateral speed of the vehicle at time t i,/>The lateral acceleration of the vehicle at time t i is the lateral velocity/>, due to the lateral offset d (t i+1) of the vehicle at time t i+1 AndLateral acceleration of vehicle/>Mutually independent, deriving the transverse motion track of the intelligent vehicle by utilizing equal time step sampling of a transverse track planning model of the intelligent vehicle, and selecting different time step sampling to derive for multiple times to obtain a transverse motion track set;
d set＝Ψ(t,d0,df),t＝{t0,t1…tN-1 formula eleven
Wherein d set represents the generated trajectory set of lateral motion; t represents N time points of sampling; d 0 represents the transverse coordinate of the intelligent vehicle in the initial state, d f represents the transverse coordinate of the final state sequentially deduced from the sampling model type of the initial and final states of the vehicle and the sampling time point; psi (t i,d0,df) represents a determined trajectory of lateral motion at t.epsilon.t 0,ti.
Further, in the fourth step of the present invention, the method for obtaining the longitudinal motion track set of the intelligent vehicle includes:
According to the longitudinal track planning set model of the intelligent vehicle, for time t epsilon [ t i,ti+1 ], the intelligent vehicle start and end state longitudinal sampling model is as follows:
s (t i) is the longitudinal offset of the vehicle at time t i, For the longitudinal speed of the vehicle at time t i,/>For the longitudinal acceleration of the vehicle at time t i, s (t i+1) is the longitudinal displacement of the vehicle at time t i+1,/>For the longitudinal speed of the vehicle at time t i+1,/>Longitudinal acceleration of the vehicle at time t i+1; the longitudinal movement of the intelligent vehicle has a desired destination s target, s target in different scenes are different, so that the track sets generated in different scenes are also different, and the end state is obtained by sampling and deducing the longitudinal track due to the existence of s target:
Wherein deltas (t i+1) is a sampling step length of longitudinal displacement, s target(ti+1) is a destination at the moment t i+1, and different numbers of sampling points are selected by changing the time step length to obtain a track set of longitudinal movement;
Thus, a set of trajectories of longitudinal motion is obtained:
s set＝Ω(t,s0,sf),t＝{t0,t1…tN-1 formula fourteen
Wherein s set represents the generated set of trajectories of longitudinal motion; t represents N time points of sampling; s 0 represents the longitudinal coordinates of the intelligent vehicle in the initial state, s f represents the longitudinal coordinates of the final state derived from the sampling model of the vehicle start-end state; omega (t i,s0,sf) represents a determined trajectory of longitudinal movement at t e [ t 0,ti ].
Further, in the present invention, the lateral application scenario of the intelligent vehicle includes: a high-speed scene and a low-speed scene, wherein the high-speed scene is when the vehicle speed is greater than or equal to 80km/h, and the low-speed scene is when the vehicle speed is less than 80 km/h.
In the fifth step, a track optimization function of the transverse motion of the intelligent vehicle is established according to the transverse application scene of the intelligent vehicle;
High-speed scene: the vehicle runs along the direction parallel to the reference line (the central line of the road), so that the transverse speed and acceleration are set to 0, the target configuration only relates to the transverse coordinate d i and the sampling time points t j,di∈(dmin,dmax) and t j∈(tmin,tmax), wherein d min is the transverse minimum displacement, d max is the transverse maximum displacement, t min is the minimum value of the sampling time points, t max is the maximum value of the sampling time points, and the transverse track set is obtained by controlling the sampling number:
An optimization function of the transverse track constructed according to the shape quality factor and the dynamic quality factor:
Wherein J t (d (T)), T is a dynamic quality factor, J t (d (T)) is a change rate of a lateral acceleration time domain, t=t f-t0 represents a time period of track planning, T 0 is a vehicle initial state time point, T f is a vehicle last state time point, C o、Cobs-s、Cobs-d is a shape quality factor, C o＝|di | represents a lateral distance of a track from a reference line, and track behavior is described; c obs-s、Cobs-d represents the straight line distance between the intelligent vehicle and the static and dynamic barriers respectively, and is used for describing the track safety; w j、wt、wd、wobs-s、wobs-d represents a weight coefficient of comfort level, a weight coefficient of track efficiency, a weight coefficient of transverse track behavior, a weight coefficient of linear distance between the intelligent vehicle and the dynamic obstacle, and a weight coefficient of linear distance between the intelligent vehicle and the static obstacle respectively;
In low speed scenarios, lateral motion is a function of longitudinal motion:
d(t)＝d(s(t))＝a0+a1s+a2s2+a3s3+a4s4+a5s5 Sixteen formulas
D (t) is the lateral offset of the vehicle at time t, and J t (d (S)) is the lateral acceleration rate of the S domain, so the optimization function of the lateral trajectory in the low-speed scenario is:
further, in the present invention, the longitudinal track optimization scenario includes: a following scene, a lane changing scene, a vehicle speed keeping scene and a parking scene.
In the fifth step, a track optimization function of the intelligent vehicle longitudinal motion is established according to the intelligent vehicle longitudinal application scene;
trajectory optimization function for intelligent vehicle longitudinal motion:
Wherein, For the longitudinal speed of the intelligent vehicle at time t,/>For the longitudinal speed of the tracked vehicle at time t, w s is a weight of the longitudinal trajectory behavior.
Further, in the sixth step of the present invention, the total track optimization function C total is:
Equation twenty of C total＝kdCd+ksCs
Wherein k d、ks is the weight coefficient of horizontal and vertical scene optimization.
The invention relates to an intelligent vehicle multi-scene track planning method based on a Frenet coordinate system, which uses a variable representing distance along a road and a variable representing left and right positions on the road to describe the position of a vehicle on the road or a reference path. The method is suitable for track planning and decision of various scenes, can improve the calculation efficiency and reduce the influence of road curvature, and ensures that the obtained track is safer and more comfortable.
Drawings
FIG. 1 is a schematic diagram of a method for planning a multi-scene track of an intelligent vehicle based on a Frenet coordinate system;
Fig. 2 is a graph of the transformation of the relationship between the vehicle trajectory in a cartesian coordinate system and a Frenet coordinate system, where O is the origin of the cartesian coordinate system, x is the actual trajectory point of the intelligent vehicle at a certain moment in the cartesian coordinate system, Is a unit vector perpendicular to the Ox direction under a Cartesian coordinate system,/>Is unit vector/>, which is Ox direction under Cartesian coordinate systemIs a unit vector perpendicular to the Op direction in a Cartesian coordinate system/>R(s) is a unit vector of an Op direction under a Cartesian coordinate system, and r(s) is an Op track of a point p under the Cartesian coordinate system when the longitudinal coordinate of the point x is s, s (t) is the longitudinal coordinate of the point x at the moment t under the Frenet coordinate system, and θ r is an azimuth angle of the point p under the Cartesian coordinate system when the Op track is r;
fig. 3 is a trajectory set acquisition flowchart.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The first embodiment is as follows: next, referring to fig. 1, a method for planning a multi-scene track of an intelligent vehicle according to the present embodiment is described, where the method includes:
step one, acquiring speed, motion curvature, acceleration and azimuth angle information of a current intelligent vehicle in x and y reference directions under a Cartesian coordinate system according to an actual track of the intelligent vehicle;
Step two, acquiring horizontal and longitudinal coordinates of the intelligent vehicle in the Frenet coordinate system and horizontal and longitudinal speed and acceleration information by utilizing a conversion formula from the Cartesian coordinate system to the Frenet coordinate system and speed, motion curvature, acceleration and azimuth angle information in x and y reference directions in the Cartesian coordinate system;
Thirdly, respectively establishing a transverse track planning set model and a longitudinal track planning set model of the intelligent vehicle under the Frenet coordinate system according to transverse and longitudinal coordinates of the intelligent vehicle under the Frenet coordinate system and transverse and longitudinal speed and acceleration information;
step four, utilizing the transverse and longitudinal track planning set model of the intelligent vehicle and transverse and longitudinal coordinates, transverse and longitudinal speed and acceleration information of the intelligent vehicle to deduce and obtain a transverse and longitudinal movement track set of the intelligent vehicle for a plurality of times according to asynchronous long sampling;
Establishing a track optimization function of transverse movement and a track optimization function of longitudinal movement of the intelligent vehicle according to transverse and longitudinal application scenes of the intelligent vehicle, and combining the track optimization function of transverse movement and the track optimization function of longitudinal movement to obtain a total optimization function suitable for the total application scene;
And step six, optimizing the motion trail in the actual application scene of the intelligent vehicle by utilizing the total optimization function suitable for the total application scene and the transverse and longitudinal motion trail sets of the intelligent vehicle in the step four to obtain the optimal motion trail in the current application scene of the intelligent vehicle. The actual application scene described in the present embodiment is generally a combination of a landscape application scene and a portrait application scene, for example, a high-speed or low-speed following scene, a high-speed or low-speed lane change scene, a high-speed or low-speed vehicle speed maintenance scene, and a low-speed or high-speed parking scene.
The invention provides an intelligent vehicle multi-scene track planning method based on a Frenet coordinate system, which can be used for vehicle-road coordination, and can accurately and efficiently solve the track planning problem of an intelligent vehicle in various traffic scenes, and help the intelligent vehicle automatically and safely complete driving tasks; the Frenet coordinate system adopted by the invention is obviously superior to other coordinate systems in the calculation of driving behaviors. The method reduces the influence of the curvature of the road on the track planning result, simplifies the calculation process of the track planning model, ensures that the calculated time cost is in direct proportion to the horizontal and vertical sampling granularity, improves the model efficiency, and ensures that the obtained planning result is safer, more comfortable and more efficient.
Further, in the first step of the present invention, the conversion formula from the cartesian coordinate system to the Frenet coordinate system is as follows:
s=s p formula one
D' = (1-dk p)tan(θx-θp) equation four
Wherein S is the longitudinal coordinate of the trace point x under the Frenet coordinate system, S p is the longitudinal coordinate of a point p nearest to the trace point x in the Frenet coordinate system,The derivative of the longitudinal coordinate of the trace point x under the Frenet coordinate system with respect to time is expressed as the speed of the vehicle along the direction of the reference line,/>The second derivative of the longitudinal coordinate of the track point x in the Frenet coordinate system with respect to time is represented by the acceleration of the vehicle along the reference line direction, d is the transverse coordinate of the track point x in the Frenet coordinate system, d ' is the first derivative of the transverse coordinate of the track point x in the Frenet coordinate system with respect to the longitudinal coordinate, d ' is the second derivative of the transverse coordinate of the track point x in the Frenet coordinate system with respect to the longitudinal coordinate, θ x is the azimuth angle of the track point x in the Cartesian coordinate system, θ p is the azimuth angle of the point P in the Cartesian coordinate system, k x is the curvature of the track point x in the Cartesian coordinate system, k p is the curvature of the point P in the Cartesian coordinate system, v x is the speed of the track point x in the Cartesian coordinate system, a x is the acceleration of the point x in the Cartesian coordinate system, and k p ' is the derivative of the curvature k p of the point P in the Cartesian coordinate system.
In this embodiment, the relationship between the trajectories of the intelligent vehicle in the Frenet coordinate system and the cartesian coordinate system is transformed as shown in fig. 2. Under the Cartesian coordinate system, let p (x p,yp) be the nearest point to the trajectory point x (x x,yy); then in the Frenet coordinate system the point p is equal to the ordinate of the point x.
In the second step, in the present invention, the building of the transverse track planning set model of the intelligent vehicle is:
Determining a five-degree polynomial transverse trajectory planning model of the intelligent vehicle according to the vehicle kinematic model under the Frenet coordinate system:
d(t)＝a0+a1t+a2t2+a3t3+a4t4+a5t5 Formula six
Wherein, a 0＝d(t0), D (t 0) is the transverse trajectory at the planned trajectory initial time t 0,For planning the lateral velocity of the trajectory initiation instant t 0,/>For the lateral acceleration at the initial time t 0 of the planned trajectory, let the final time of the planned trajectory be t f,T＝tf-t0, a 3,a4,a5 is obtained by:
Calculating to obtain;
determining a five-degree polynomial longitudinal track planning model of the intelligent vehicle according to the vehicle kinematic model under the Frenet coordinate system:
s(t)＝b0+b1t+b2t2+b3t3+b4t4+b5t5 Equation eight
Wherein, b 0＝s(t0), S (t 0) is the longitudinal offset of the planned trajectory initial instant t 0,For planning the lateral velocity of the trajectory initiation instant t 0,/>For the lateral acceleration at the planned trajectory initial time t 0, then b 3,b4,b5 passes:
And (5) calculating to obtain the product.
And determining a fifth-order polynomial curve as a track planning model of the intelligent vehicle by the vehicle kinematic model. On the basis of the Frenet coordinate system, the track planning is decoupled into independent problems in the longitudinal direction s and the transverse direction d. Let t be the lateral offset, lateral speed, lateral acceleration, longitudinal offset, longitudinal speed, longitudinal acceleration of the vehicle, respectively, d (t),s(t)，/>
Further, in the fourth step of the present invention, the method for obtaining the transverse motion track set of the intelligent vehicle includes:
according to the transverse track planning set model of the intelligent vehicle, for time t epsilon [ t i,ti+1 ], acquiring a transverse sampling model of the start and end states of the intelligent vehicle:
Wherein d (t i) is the lateral offset of the vehicle at time t i, For the lateral speed of the vehicle at time t i,/>The lateral acceleration of the vehicle at time t i is the lateral velocity/>, due to the lateral offset d (t i+1) of the vehicle at time t i+1 AndThe transverse acceleration of the vehicle is mutually independent, transverse motion tracks of the intelligent vehicle are deduced by utilizing equal time step sampling of a transverse track planning model of the intelligent vehicle, and different time step sampling is selected for multiple deductions, so that a transverse motion track set is obtained;
d set＝Ψ(t,d0,df),t＝{t0,t1…tN-1 formula eleven
Wherein d set represents the generated trajectory set of lateral motion; t represents N time points of sampling; d 0 represents the transverse coordinate of the intelligent vehicle in the initial state, d f represents the transverse coordinate of the final state sequentially deduced from the sampling model type of the initial and final states of the vehicle and the sampling time point; psi (t i,d0,df) represents a determined trajectory of lateral motion at t.epsilon.t 0,ti.
Further, in the present embodiment, in the fourth step, the method for obtaining the longitudinal movement track set of the intelligent vehicle includes:
According to the longitudinal track planning set model of the intelligent vehicle, for time t epsilon [ t i,ti+1 ], the intelligent vehicle start and end state longitudinal sampling model is as follows:
s (t i) is the longitudinal offset of the vehicle at time t i, For the longitudinal speed of the vehicle at time t i,/>For the longitudinal acceleration of the vehicle at time t i, s (t i+1) is the longitudinal displacement of the vehicle at time t i+1,/>For the longitudinal speed of the vehicle at time t i+1,/>Longitudinal acceleration of the vehicle at time t i+1; the longitudinal movement of the intelligent vehicle has a desired destination s target, s target in different scenes are different, so that the track sets generated in different scenes are also different, and the end state is obtained by sampling and deducing the longitudinal track due to the existence of s target:
Wherein deltas (t i+1) is the sampling step length of longitudinal displacement at the moment t i+1, s target(ti+1) is the destination at the moment t i+1, and different numbers of sampling points are selected by changing the time step length, so as to obtain a track set of longitudinal movement;
Thus, a set of trajectories of longitudinal motion is obtained:
s set＝Ω(t,s0,sf),t＝{t0,t1…tN-1 formula fourteen
Wherein s set represents the generated set of trajectories of longitudinal motion; t represents N time points of sampling; s 0 represents the longitudinal coordinates of the intelligent vehicle in the initial state, s f represents the longitudinal coordinates of the final state derived from the sampling model of the vehicle start-end state; omega (t i,s0,sf) represents a determined trajectory of longitudinal movement at t e [ t 0,ti ].
Further, in the present embodiment, in the fifth step, the lateral application scenario of the intelligent vehicle includes: a high-speed scene and a low-speed scene, wherein the high-speed scene is when the vehicle speed is greater than or equal to 80km/h, and the low-speed scene is when the vehicle speed is less than 80 km/h.
Further, in the fifth embodiment, a track optimization function of the lateral movement of the intelligent vehicle is established according to the lateral application scenario of the intelligent vehicle;
High-speed scene: the vehicle runs along the direction parallel to the reference line (the central line of the road), so that the transverse speed and acceleration are set to 0, the target configuration only relates to the transverse coordinate d i and the sampling time points t j,di∈(dmin,dmax) and t j∈(tmin,tmax), wherein d min is the transverse minimum displacement, d max is the transverse maximum displacement, t min is the minimum value of the sampling time points, t max is the maximum value of the sampling time points, and the transverse track set is obtained by controlling the sampling number:
An optimization function of the transverse track constructed according to the shape quality factor and the dynamic quality factor:
Wherein J t (d (T)), T is a dynamic quality factor, J t (d (T)) is a change rate of a lateral acceleration time domain, t=t f-t0 represents a time period of track planning, T 0 is a vehicle initial state time point, T f is a vehicle last state time point, C o、Cobs-s、Cobs-d is a shape quality factor, C o＝|di | represents a lateral distance of a track from a reference line, and track behavior is described; c obs-s、Cobs-d represents the straight line distance between the intelligent vehicle and the static and dynamic barriers respectively, and is used for describing the track safety; w j、wt、wd、wobs-s、wobs-d represents a weight coefficient of comfort level, a weight coefficient of track efficiency, a weight coefficient of transverse track behavior, a weight coefficient of linear distance between the intelligent vehicle and the dynamic obstacle, and a weight coefficient of linear distance between the intelligent vehicle and the static obstacle respectively;
In low speed scenarios, lateral motion is a function of longitudinal motion:
d(t)＝d(s(t))＝a0+a1s+a2s2+a3s3+a4s4+a5s5 Sixteen formulas
D (t) is the lateral offset of the vehicle at time t, and J t (d (S)) is the rate of change of the lateral acceleration in the S domain, so the optimization function of the lateral trajectory in the low speed scenario is:
In this embodiment, the sampling step means a time step: assuming that the track of the time interval [0,10] is to be obtained, the sampling step length is set to be 0.1, the track of the time 0.1 can be deduced from the track of the time 0 by the formula (5), the track of the time 0.2 can be deduced from the track of the time 0.1, the track of the time 0.3 can be deduced from the track of the time 0.2, the track of the time 10 can be obtained by analogy, a set of tracks of the time interval [0,10] can be obtained, the sampling step length is set to be 0.2, the track of the time 0.2 can be deduced from the track of the time 0 by the formula (5), the track of the time 0.4 can be deduced from the track of the time 0.2, the track of the time 0.6 can be deduced from the track of the time 0.4, the track of the time 10 can be deduced from the track of the time 0.6, the track of the time 10 can be deduced from the track of the time 0.2, the track of the time 0.3 can be deduced from the track of the time 0.3, the track of the time 10 can be obtained by analogy, the track of the time 10 can be obtained, the track of the sampling frame number of the frames of the time 0.3, the transverse frames can be set to be obtained, and the transverse frames of the transverse frames can be obtained. In one sampling, the sampling step length can be of different lengths and dynamically changed. As particularly shown in fig. 3.
Further, in the present invention, the acceleration change rate Jerk (J t) is:
wherein, the time period t f-t0 is the time period of track planning, t 0 is the initial state time point of the vehicle, t f is the final state time point of the vehicle, and J t(s(t))Jt (d (t)) is the lateral acceleration change rate and the longitudinal acceleration change rate respectively.
Further, in the present invention, the longitudinal application scenario includes: a following scene, a lane changing scene, a vehicle speed keeping scene and a parking scene.
In the fifth step, a track optimization function of the intelligent vehicle longitudinal motion is established according to the intelligent vehicle longitudinal application scene;
trajectory optimization function for intelligent vehicle longitudinal motion:
Wherein, For the longitudinal speed of the intelligent vehicle at time t,/>For the longitudinal speed of the tracked vehicle at time t, w s is a weight of the longitudinal trajectory behavior.
Further, in the sixth step of the present invention, the total track optimization function C total is:
Equation twenty of C total＝kdCd+ksCs
Wherein k d、ks is the weight coefficient of horizontal and vertical scene optimization.
In the invention, t=t f-t0 represents the time consumption of transverse movement and describes the track efficiency; c o＝|di is the horizontal distance between the track and the reference line, and describes track behavior; c obs-s、Cobs-d represents the straight line distance between the intelligent vehicle and the static and dynamic barriers respectively, and is used for describing the track safety; w j、wt、wd represents comfort, track efficiency, track behavior, respectively; w obs-s、wobs-d represents the weight coefficients of the intelligent vehicle and the dynamic obstacle straight-line distance, the intelligent vehicle and the static obstacle straight-line distance, respectively, the size of which determines which aspect of optimization the function is more focused on.
The optimization scenarios of the lateral trajectories fall into two categories: ① high speed; ② low speed.
(1) High speed
In this scenario, the vehicle is traveling in a direction parallel to the reference line (road center line), so the vehicle is caused to travelThe target configuration involves only two variables d i and T j, defining d i∈(dmin,dmax) and T j∈(tmin,tmax), the sampling density is controlled by Δd and Δt, optimizing the transverse trajectory set.
(2) Low speed
In this scenario, the lateral motion is a function of the longitudinal motion, namely:
d(t)＝d(s)＝a0+a1s+a2s2+a3s3+a4s4+a5s5
Therefore, the optimization function of the transverse track in the low-speed scene is as follows:
Longitudinal track planning set optimization method
The optimization scenarios of the longitudinal trajectory are broadly divided into four categories: ① follows; ② lane change; ③ Maintaining the vehicle speed; ④ parking.
(1) Heel relaxation
Under the following scene, only if certain speed and interval conditions are met between the intelligent vehicles in the motorcade and the followed vehicles, the intelligent vehicles can consider to maintain the following state. The following conditions may be designed as shown in table 1. Where s c is the longitudinal position of the tracked vehicle, s e is the longitudinal position of the intelligent vehicle, and v c is the longitudinal speed of the tracked vehicle.
Table 1 following conditions
The longitudinal desired position s target of the intelligent vehicle is:
Wherein s c (t) is the longitudinal displacement of the followed vehicle at time t; A longitudinal speed of the followed vehicle at time t; /(I) Is a safe distance kept from the front vehicle in the following state; d 0 and u are both constants. Then for a track planning period t e [ t 0,tf ], the start and end states of the vertical track set are:
s target(tf) is the desired position of the intelligent vehicle at time t f, For the longitudinal speed of the vehicle being tracked at time t f in the following scenario, Δs (t f) is the sampling step of the longitudinal displacement at time t f,/>For the longitudinal acceleration of the followed vehicle at time t f in the following scenario,/>The change rate of the longitudinal acceleration of the tracked vehicle at the time t f in the following scene is set;
The optimization function of the longitudinal track in the scene is as follows:
for the longitudinal speed of the intelligent vehicle at time t,/> For the longitudinal speed of the followed vehicle at time t, w s is the weight of the intelligent vehicle longitudinal trajectory behavior;
(2) Variable-track scene
In this scenario, the longitudinal desired position s target of the intelligent vehicle is:
Where s c1(t)、sc2 (t) represents the longitudinal positions of the front and rear two neighboring vehicles, respectively, at which the intelligent vehicle is to be inserted into the lane gap of the overtaking vehicle at time t.
Then for a track planning period t e [ t 0,tf ], the start and end states of the vertical track set are:
s c1(tf)sc2(tf) respectively represent the longitudinal positions of the front and rear two adjacent vehicles of the intelligent vehicle to be inserted into the passing lane gap at time t f
Respectively representing the longitudinal speeds of the front and rear adjacent vehicles of the intelligent vehicle to be inserted into the overtaking lane gap at the time t f
Longitudinal acceleration of front and rear adjacent vehicles respectively representing that intelligent vehicle is about to be inserted into overtaking lane gap at time t f
The optimization function of the longitudinal track in the scene is as follows:
(3) Vehicle speed maintenance
The scene does not need to consider the position information of the last state, does not directly sample the longitudinal position s, but rather samples the vehicle speedAs a sampling basis, for a track planning period t e [ t 0,tf ], the start and end states of the longitudinal track set are:
The rate of change of the longitudinal sampling step at time t f is shown.
The optimization function of the longitudinal track in the scene is as follows:
Where w s represents the weight coefficient of the longitudinal trajectory behavior.
(3) Parking scene
In this scenario, the last state speed and acceleration of the intelligent vehicle are both 0, and for a track planning period t e [ t 0,tf ], the start and end states of the longitudinal track set are:
The optimization function of the longitudinal track in the scene is as follows:
Total optimization function of trajectory:
Ctotal＝kdCd+ksCs
The invention provides a track planning model of 2 scenes (high speed and low speed) which are transversely applied after decoupling and 4 scenes (following, lane changing overtaking, parking and vehicle speed keeping) which longitudinally move, and provides a model optimization method based on different scenes;
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.
Claims (9)
1. An intelligent vehicle multi-scene track planning method based on a Frenet coordinate system is characterized by comprising the following steps:
step one, acquiring speed, motion curvature, acceleration and azimuth angle information of a current intelligent vehicle in x and y reference directions under a Cartesian coordinate system according to an actual track of the intelligent vehicle;
Step two, acquiring horizontal and longitudinal coordinates of the intelligent vehicle in the Frenet coordinate system and horizontal and longitudinal speed and acceleration information by utilizing a conversion formula from the Cartesian coordinate system to the Frenet coordinate system and speed, motion curvature, acceleration and azimuth angle information in x and y reference directions in the Cartesian coordinate system;
Thirdly, respectively establishing a transverse track planning set model and a longitudinal track planning set model of the intelligent vehicle under the Frenet coordinate system according to transverse and longitudinal coordinates of the intelligent vehicle under the Frenet coordinate system and transverse and longitudinal speed and acceleration information;
Step four, utilizing the transverse and longitudinal track planning set model of the intelligent vehicle, the transverse and longitudinal coordinates, transverse and longitudinal speed and acceleration information of the intelligent vehicle, deducing for a plurality of times according to asynchronous long sampling, and obtaining a transverse and longitudinal movement track set of the intelligent vehicle;
Establishing a track optimization function of transverse movement and a track optimization function of longitudinal movement of the intelligent vehicle according to transverse and longitudinal application scenes of the intelligent vehicle, and combining the track optimization function of transverse movement and the track optimization function of longitudinal movement to obtain a total optimization function suitable for the total application scene;
step six, optimizing the motion trail of the current intelligent vehicle in the actual application scene by utilizing the total optimization function suitable for the total application scene and the transverse and longitudinal motion trail sets of the intelligent vehicle in the step four to obtain the optimal motion trail of the intelligent vehicle in the current application scene;
in the third step, a transverse track planning set model of the intelligent vehicle is established as follows:
Determining a five-degree polynomial transverse trajectory planning model of the intelligent vehicle according to the vehicle kinematic model under the Frenet coordinate system:
d(t)＝a0+a1t+a2t2+a3t3+a4t4+a5t5 Formula six
Wherein, a 0＝d(t0),D (t 0) is the transverse trajectory at the planned trajectory initial time t 0,For planning the lateral velocity of the trajectory initiation instant t 0,/>For the lateral acceleration at the initial time t 0 of the planned trajectory, let the final time of the planned trajectory be t f,T＝tf-t0, a 3,a4,a5 is obtained by:
Calculating to obtain;
determining a five-degree polynomial longitudinal trajectory planning model of the intelligent vehicle according to the vehicle kinematic model under the Frenet coordinate system:
s(t)＝b0+b1t+b2t2+b3t3+b4t4+b5t5 Equation eight
Wherein, b 0＝s(t0),S (t 0) is the longitudinal offset of the planned trajectory initial time t 0,/>For planning the lateral velocity of the trajectory initiation instant t 0,/>For the lateral acceleration at the planned trajectory initial time t 0, then b 3,b4,b5 passes:
And (5) calculating to obtain the product.
2. The intelligent vehicle multi-scene track planning method based on the Frenet coordinate system according to claim 1, wherein in the second step, the conversion formula from the Cartesian coordinate system to the Frenet coordinate system is as follows:
s=s p formula one
D' = (1-dk p)tan(θx-θp) equation four
Wherein S is the longitudinal coordinate of the trace point x under the Frenet coordinate system, S p is the longitudinal coordinate of a point p nearest to the trace point x in the Frenet coordinate system,The derivative of the longitudinal coordinate of the trace point x under the Frenet coordinate system with respect to time is expressed as the speed of the vehicle along the direction of the reference line,/>The second derivative of the longitudinal coordinate of the track point x in the Frenet coordinate system with respect to time is represented by the acceleration of the vehicle along the reference line direction, d is the transverse coordinate of the track point x in the Frenet coordinate system, d ' is the first derivative of the transverse coordinate of the track point x in the Frenet coordinate system with respect to the longitudinal coordinate, d ' is the second derivative of the transverse coordinate of the track point x in the Frenet coordinate system with respect to the longitudinal coordinate, θ x is the azimuth angle of the track point x in the Cartesian coordinate system, θ p is the azimuth angle of the point P in the Cartesian coordinate system, k x is the curvature of the track point x in the Cartesian coordinate system, k p is the curvature of the point P in the Cartesian coordinate system, v x is the speed of the track point x in the Cartesian coordinate system, a x is the acceleration of the point x in the Cartesian coordinate system, and k p ' is the derivative of the curvature k p of the point P in the Cartesian coordinate system.
3. The method for planning multiple scenes trajectories of an intelligent vehicle based on a Frenet coordinate system according to claim 1 or 2, wherein in the fourth step, the method for obtaining a set of lateral motion trajectories of the intelligent vehicle is as follows:
according to the transverse track planning set model of the intelligent vehicle, for time t epsilon [ t i,ti+1 ], acquiring a transverse sampling model of the start and end states of the intelligent vehicle:
Wherein d (t i) is the lateral offset of the vehicle at time t i, For the lateral speed of the vehicle at time t i,/>The lateral acceleration of the vehicle at time t i is the lateral velocity/>, due to the lateral offset d (t i+1) of the vehicle at time t i+1 And lateral acceleration of the vehicle/>Independent of each other, selecting different time step samples for multiple deduction, and obtaining a transverse motion track set;
d set＝Ψ(t,d0,df),t＝{t0,t1…tN-1 formula eleven
Wherein d set represents the generated trajectory set of lateral motion; t represents N time points of sampling; d 0 represents the transverse coordinate of the intelligent vehicle in the initial state, d f represents the transverse coordinate of the final state sequentially deduced from the sampling model type of the initial and final states of the vehicle and the sampling time point; psi (t i,d0,df) represents a determined trajectory of lateral motion at t.epsilon.t 0,ti.
4. The method for planning multiple scenes trajectories of an intelligent vehicle based on a Frenet coordinate system according to claim 1 or 2, wherein in the fourth step, the method for obtaining a longitudinal motion trajectory set of the intelligent vehicle is as follows:
According to the longitudinal track planning set model of the intelligent vehicle, for time t epsilon [ t i,ti+1 ], the intelligent vehicle start and end state longitudinal sampling model is as follows:
s (t i) is the longitudinal offset of the vehicle at time t i, For the longitudinal speed of the vehicle at time t i,/>For the longitudinal acceleration of the vehicle at time t i, s (t i+1) is the longitudinal displacement of the vehicle at time t i+1,/>At the longitudinal speed of the vehicle at time t i+1,Longitudinal acceleration of the vehicle at time t i+1; the longitudinal movement of the intelligent vehicle has a desired destination s target, s target in different scenes are different, so that the track sets generated in different scenes are also different, and the end state is obtained by sampling and deducing the longitudinal track due to the existence of s target:
Wherein deltas (t i+1) is the sampling step length of longitudinal displacement at the moment t i+1, s target(ti+1) is the destination at the moment t i+1, and different numbers of sampling points are selected by changing the time step length, so as to obtain a track set of longitudinal movement;
Thus, a set of trajectories of longitudinal movement is obtained:
s set＝Ω(t,s0,sf),t＝{t0,t1…tN-1 formula fourteen
Wherein s set represents the generated set of trajectories of longitudinal motion; t represents N time points of sampling; s 0 represents the longitudinal coordinates of the intelligent vehicle in the initial state, s f represents the longitudinal coordinates of the final state derived from the sampling model of the vehicle start-end state; omega (t i,s0,sf) represents a determined trajectory of longitudinal movement at t e [ t 0,ti ].
5. The method for planning multi-scene trajectories of intelligent vehicles based on Frenet coordinate system according to claim 1 or 2, wherein in the fifth step, the lateral application scene of the intelligent vehicle comprises: a high-speed scene and a low-speed scene, wherein the high-speed scene is when the vehicle speed is greater than or equal to 80km/h, and the low-speed scene is when the vehicle speed is less than 80 km/h.
6. The intelligent vehicle multi-scene track planning method based on the Frenet coordinate system according to claim 1 or 2, wherein in the fifth step, a track optimization function of the intelligent vehicle transverse motion is established according to the transverse application scene of the intelligent vehicle;
High-speed scene: the vehicle runs along the direction parallel to the reference line, so that the transverse speed and acceleration are set to 0, the target configuration only relates to the transverse coordinate d i and the sampling time points t j,di∈(dmin,dmax) and t j∈(tmin,tmax), wherein d min is the transverse minimum displacement, d max is the transverse maximum displacement, r min is the minimum value of the sampling time points, t max is the maximum value of the sampling time points, and the transverse track set is obtained by controlling the sampling number:
An optimization function of the transverse track constructed according to the shape quality factor and the dynamic quality factor:
Wherein J t (d (T)), T is a dynamic quality factor, J t (d (T)) is a change rate of a lateral acceleration time domain, t=t f-t0 represents a time period of track planning, T 0 is a vehicle initial state time point, T f is a vehicle last state time point, C o、Cobs-s、Cobs-d is a shape quality factor, C o＝|di | represents a lateral distance of a track from a reference line, and track behavior is described; c obs-s represents the linear distance between the intelligent vehicle and the static obstacle, C obs-d represents the linear distance between the intelligent vehicle and the dynamic obstacle, w j represents the weight coefficient of comfort, w t represents the weight coefficient of track efficiency, w d represents the weight coefficient of lateral track behavior, w obs-s represents the weight coefficient of the linear distance between the intelligent vehicle and the dynamic obstacle, and w obs-d represents the weight coefficient of the linear distance between the intelligent vehicle and the static obstacle;
In low speed scenarios, lateral motion is a function of longitudinal motion:
d(t)＝d(s(t))＝a0+a1s+a2s2+a3s3+a4s4+a5s5 Sixteen formulas
D (t) is the lateral offset of the vehicle at time t, and J t (d (S)) is the rate of change of the lateral acceleration in the S domain, so the optimization function of the lateral trajectory in the low speed scenario is:
7. The intelligent vehicle multi-scene track planning method based on Frenet coordinate system according to claim 1 or 2, wherein the longitudinal application scene comprises: a following scene, a lane changing scene, a vehicle speed keeping scene and a parking scene.
8. The intelligent vehicle multi-scene track planning method based on the Frenet coordinate system according to claim 1 or 2, wherein in the fifth step, a track optimization function of the intelligent vehicle longitudinal motion is established according to the intelligent vehicle longitudinal application scene;
trajectory optimization function for intelligent vehicle longitudinal motion:
Wherein, For the longitudinal speed of the intelligent vehicle at time t,/>For the longitudinal speed of the tracked vehicle at time t, w s is a weight of the longitudinal trajectory behavior.
9. The intelligent vehicle multi-scene track planning method based on the Frenet coordinate system according to claim 1 or 2, wherein in the sixth step, the total track optimization function C total is:
Equation twenty of C total＝kdCd+ksCs
Wherein k d、ks is the weight coefficient of horizontal and vertical scene optimization.
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