CN114879698B - Robot driving vehicle obstacle avoidance method based on improved artificial potential field and MPC - Google Patents
Robot driving vehicle obstacle avoidance method based on improved artificial potential field and MPC Download PDFInfo
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Abstract
The invention discloses a robot driving vehicle obstacle avoidance method based on an improved artificial potential field and MPC, wherein a control system of a driving robot is divided into an upper control system and a lower control system, the upper control system is combined with a repulsive force function in the artificial potential field method, a obstacle avoidance function model and a road boundary magnetic field model are constructed based on a driving speed and a road boundary, and a running track of a next step of a vehicle is obtained based on a model prediction control algorithm of a vehicle power model; the upper control system comprises an MPC controller, wherein the MPC controller inputs the running track of the next step of the vehicle and the current state of the vehicle, and outputs the expected course angle and acceleration to the lower control system; the lower control system converts the desired course angle into a torque control signal of a steering motor of the steering robot based on the steering robot and the vehicle body motion model. The invention can avoid the obstacle and realize the task of driving the robot to complete automatic driving to a larger extent.
Description
Technical Field
The invention relates to a control method for automatically completing road test of a driving robot driving vehicle, in particular to a robot driving vehicle obstacle avoidance method based on an improved artificial potential field and MPC.
Background
At present, an automobile driving robot is another important embodiment of automatic driving development, has the mechanical structure characteristic of a humanoid body, and the mechanical structure mainly comprises an accelerator/brake mechanical leg, a steering mechanical arm and a gear shifting mechanical arm, and can be simply installed on an automobile to realize driving control of the automobile while the internal mechanism of the existing automobile is not damaged. Because the advantages of high control precision, good repeatability, strong durability, high safety and the like are widely used for replacing human beings to be applied to various automobile test projects, more accurate test data are obtained. The driving robot has been widely used in high-risk tests of automobiles, ADAS tests, etc., and the ADAS tests are mainly focused on tests of Automatic Emergency Brake Systems (AEBs), lane keeping systems, etc., which require that the driving robot can complete accurate vehicle speed tracking control and steering control, i.e., coordination control, according to corresponding test conditions. On the other hand, the method mainly aims at the corresponding road condition test, namely the automobile is tested according to a given path, namely the driving robot is used for driving the automobile to realize path tracking, and when an obstacle or an emergency appears suddenly in the test process, the safety of the automobile test is difficult to ensure, the realization of the local path planning of the automobile in the driving process for realizing obstacle avoidance and risk alleviation has important significance for improving the safety of the automobile test, and meanwhile, the method provides reference value for the automatic driving of the existing automobile by combining the automobile ADAS system on the basis of the driving robot control system added with the local planning.
The model predictive control algorithm is an advanced control algorithm, is widely applied to the field of automatic driving, is an optimization algorithm based on an automobile model, predicts the condition of a future automobile in real time, can efficiently and stably track the track, and determines the instantaneity and the stability of the algorithm by the complexity of the automobile model and a multi-constraint optimization solution method; the path planning aims at providing an optimal fastest path for the automobile to reach a destination, and the artificial potential field method is correspondingly applied to the local path planning, and the artificial potential field method guides the automobile to search for an obstacle avoidance path through the resultant force of repulsive force and attractive force by establishing attractive force and repulsive force magnetic fields around the obstacle and the target. In order to enable the driving robot to drive the vehicle under the fixed path test and to complete the task of avoiding the obstacle, a method based on improving the artificial potential field and model prediction is used on the driving robot control vehicle.
Disclosure of Invention
In order to solve the problem of lower safety of road test of a driving vehicle driven by a driving robot, realize that the driving robot controls the vehicle to run on a fixed track and meet an obstacle to complete an automatic avoidance task, and meanwhile, the driving vehicle can automatically drive the vehicle to come to a test initial place again after the test is completed without human intervention, the invention provides a robot driving vehicle obstacle avoidance method based on an improved artificial potential field and MPC (maximum likelihood controller) for solving the technical problems in the prior art.
The invention adopts the technical proposal for solving the technical problems in the prior art that: a robot driving vehicle obstacle avoidance method based on an improved artificial potential field and MPC divides a control system of a driving robot into an upper control system and a lower control system, wherein the upper control system combines a repulsive force function in the artificial potential field method and constructs an obstacle avoidance function model and a road boundary magnetic field model based on a driving speed and a road boundary, and obtains a running track of a vehicle in the next step based on a model prediction control algorithm of a vehicle power model; the upper control system comprises an MPC controller, wherein the MPC controller inputs the running track of the next step of the vehicle and the current state of the vehicle, and outputs the expected course angle and acceleration to the lower control system; the lower control system converts the desired course angle into a torque control signal of a steering motor of the steering robot based on the steering robot and the vehicle body motion model.
Further, the method comprises the following steps:
step 1, installing a laser radar and a camera for monitoring road environment conditions and a positioning system for positioning the real-time position of a vehicle on the vehicle; the upper control system imports a preset path;
Step 2, constructing an obstacle avoidance function model and a road boundary magnetic field model in an upper control system;
Step 3, constructing a vehicle motion track model based on the constraints of the obstacle avoidance function model, the road boundary magnetic field model and the control quantity, generating optimal track discrete points by the imported preset path through a QP optimization algorithm, and transmitting the track discrete points into the MPC controller;
Step4, establishing a vehicle dynamics model based on tire slip and road curvature in the MPC controller; establishing an objective function and constraint conditions based on a model prediction optimization algorithm;
Step 5, converting the objective function and the constraint condition into a sequence quadratic programming problem; based on the rapid dual neural network, the sequence quadratic programming problem is converted into the dual problem to be optimally solved, and the expected course angle is calculated.
Further, in step 2, the vehicle is regarded as a particle, the obstacle is regarded as a quadrilateral, and the following obstacle avoidance function is constructed:
Wherein:
f obs,vehicle (X) represents the total repulsive force of the obstacle to which the vehicle is subjected;
η is a positive scaling factor;
d (x i,x0) is the Euclidean distance of the vehicle to the four points of the quadrilateral respectively;
ρ is the maximum distance the obstacle will have on the vehicle.
Further, in step 2, the road is divided into two areas, and the following road boundary magnetic field function is established:
Wherein:
f rep,edge is the repulsive force of two sides of the road;
w edge is the weight coefficient of the repulsive potential field;
d is the width of one area of the road;
y is the lateral position of the vehicle;
w is the general width of the vehicle body;
v x is the vehicle speed.
Further, in step 3, position signals of the obstacle and the vehicle are transmitted to an MPC (MPC planning machine), and a vehicle model is built by adopting a point quality model method; setting: x is the longitudinal position of the vehicle in the body coordinate system; y is the lateral position of the vehicle in the body coordinate system; x is the longitudinal position of the vehicle in an inertial coordinate system; y is the lateral position of the vehicle in the inertial coordinate system; is the yaw angle of the vehicle;
Selecting the state quantity as
Setting the control quantity u as a front wheel deflection delta; then there are:
Wherein:
The change rate of the longitudinal position of the vehicle under the self coordinate system is given;
the change rate of the transverse position of the vehicle under the self coordinate system is given;
The change rate of the transverse position of the vehicle under an inertial coordinate system is given;
Is the rate of change of the longitudinal position of the vehicle in the inertial coordinate system;
ζ is the newly built state quantity;
Xi i is the change vector matrix in the ith scroll time domain;
is the transposed matrix of xi i;
H i is the ith reduced-roll time-domain weight matrix;
U i is the sum of all potential fields;
n p is the prediction horizon in the rolling horizon;
j min is the cost function minimum;
solving by QP optimization algorithm Generating optimal discrete points meeting corresponding conditions, performing curve fitting on the discrete points by adopting a Bezier curve, defining the fitted curve as a local path curve required by MPC to be tracked, and transmitting the curve into an MPC controller.
Further, in step4, a vehicle dynamics model based on the tire slip and the road curvature is established as follows:
Wherein:
I z is the moment of inertia of the vehicle in the z-axis direction;
m is the mass of the vehicle;
k ref is the road curvature obtained by the reference path;
v x is the longitudinal speed of the vehicle centroid in the vehicle body coordinate system;
v y is the lateral velocity of the vehicle centroid in the vehicle body coordinate system;
l f is the distance from the vehicle centroid to the front axle;
l r is the distance from the vehicle centroid to the rear axle;
tracking heading errors;
e d is tracking distance error;
F xf is the longitudinal force of the front wheels of the vehicle;
F xr is the longitudinal force of the rear wheels of the vehicle;
f yf is the front wheel side bias;
F yr is the rear wheel side bias;
is the vehicle yaw rate.
Further, let C f be the vehicle front wheel cornering stiffness; c r is the cornering stiffness of the rear wheels of the vehicle; alpha f is the slip angle of the front wheel; alpha r is the slip angle of the rear wheel;
Assume F yf＝Cfαf,Fyr＝-Crαr;
Estimating the tire cornering stiffness based on a nonlinear kalman filter, wherein the uncertain tire cornering stiffness expression is as follows:
Wherein:
c f,0 is a linear standard value of the cornering stiffness of the front wheels of the vehicle;
Gamma f is the front wheel time-based variable;
Is the lateral deflection rigidity variable of the front wheel;
C r is the cornering stiffness of the rear wheel;
c r,0 is a linear standard value of the cornering stiffness of the rear wheels of the vehicle;
Gamma r is a time-based variable for the rear wheel;
is the variation of the cornering stiffness of the rear wheel.
Further, in step 4, a state quantity is setDiscretizing and linearizing a nonlinear equation in a vehicle dynamics model by a Taylor-level expansion and forward Euler method to obtain the vehicle dynamics model: Constructing a new state space equation: Predicting epsilon (k+n p) at a future time N p based on the state trace, and simultaneously updating the error e (k) =x 0(k+1)-Akx0(k)-Bku0 (k) in real time;
Wherein:
a is a state quantity jacobian matrix;
B is a control quantity Jacobian matrix;
The vehicle state quantity conversion rate is the difference value between k+1 and k time;
the difference value between the vehicle state quantity at the time k+1 and the time k is obtained;
the difference between the control quantity of the vehicle and the moment k+1 is given;
n p is the prediction horizon in the rolling horizon;
epsilon (k) is a new state space expression;
e (k) is an error expression;
u (k-1) is the control amount at time k-1;
x 0 is the state quantity of the Taylor expansion selection point;
a k is a state quantity jacobian matrix newly constructed at the moment k;
B k is a control quantity jacobian matrix newly constructed at the moment k;
k is the number of steps of sampling;
Epsilon (k+N p) is the state quantity and control quantity of the future N p moment;
u 0 (k) is the control quantity of the taylor-stage expansion selection point at the moment k.
Further, in step 4, the following objective function and constraint conditions are established based on the model predictive optimization algorithm: the objective function is:
The constraint conditions are as follows:
emax-wd≤ed(k+i|k)≤-emin+wd；
δf,min≤δf(k+i|k)≤δf,max；
Δδf,min≤δf(k+i|k)-δf(k+i-1|k)≤Δδf,max；
Wherein:
J min is the minimum of the trajectory tracking objective function;
i is the sampling step length; i=1, 2, …, N p;
N p is a prediction time domain in a model prediction algorithm;
n c is the control time domain;
the method comprises the steps of outputting a heading error weight matrix;
Q d is an output distance error weight matrix;
w d is a safety distance defined in the driving process of the vehicle body;
w f is a control increment weight matrix;
epsilon is the relaxation factor weight;
s is a relaxation factor;
k is the number of steps of sampling;
Delta f is the front wheel corner of the vehicle;
e max is the maximum value of the vehicle tracking lateral position deviation;
e min is the minimum value of the vehicle tracking lateral position deviation;
δ f,min is the minimum value of the front wheel rotation angle of the vehicle;
delta f,max is the maximum value of the front wheel rotation angle of the vehicle;
Delta f,min is the minimum value of the vehicle front wheel steering angle increment;
Delta f,max is the maximum value of the vehicle front wheel steering angle increment;
Is the minimum value of the yaw rate change of the vehicle;
is the maximum value of the yaw rate change rate of the vehicle.
The invention has the advantages and positive effects that: the invention effectively combines the improved artificial potential field method with model predictive planning and control to be applied to the driving robot test vehicle, and has the characteristics of high control speed, high safety, high stability and the like. In the process that the driving robot controls the vehicle to perform road test under a fixed track, the risk of sudden accident can be effectively avoided; meanwhile, the model predictive control objective function is solved based on the rapid dual neural network, so that the solving difficulty of the multi-constraint objective function is reduced, the driving robot can rapidly complete the control of the vehicle according to the instruction, and the test work is effectively and stably completed
Drawings
FIG. 1 is a block diagram of a driving robot-vehicle obstacle avoidance control system.
Fig. 2 is a schematic diagram of an automobile dynamics model considering road curvature and slip.
Fig. 3 is a simplified steering robot-vehicle (steering robot) mechanical structure.
In the figure:
y new plans the lateral position of the new reference trajectory for the local path.
And planning the yaw angle of the new reference track for the local path.
Δ f is the front wheel steering angle of the vehicle.
X is; the x-axis of the vehicle body coordinate system.
Y is; and the y axis of the vehicle body coordinate system.
Z is; and a vehicle body coordinate system z-axis.
X is; global coordinate system X-axis.
Y is; and a global coordinate system Y-axis.
Is the included angle between the tangent line where the road reference point is located and the global coordinate system.
Is the rate of change of the lateral velocity of the vehicle in its own coordinate system.
Is the yaw angle of the vehicle.
Θ vf is; and an included angle between the front wheel speed direction of the vehicle and the axial direction of the vehicle body.
V f is; the front wheel speed direction of the vehicle.
And l f is the distance from the vehicle centroid to the front axle.
And l r is the distance from the vehicle center of mass to the rear axle.
Is tracking heading error.
F xf is the vehicle front wheel longitudinal force.
And F xr is the longitudinal force of the rear wheels of the vehicle.
And F yf is the front wheel side bias force.
And F yr is the rear wheel side bias.
Is the vehicle yaw rate.
Alpha f is the slip angle of the front wheel.
Alpha r is the slip angle of the rear wheel.
I m is the gear reduction ratio of the motor.
I g is the transmission ratio between the steering mechanism and the steering wheel.
T s is the actual torque of the steering shaft.
T m is the output torque of the steering motor.
T d is the input torque of the steering wheel.
Θ s is the steering wheel angle.
B s is the damping coefficient of the steering shaft.
J m is the moment of inertia of the steering motor.
M W is the drag torque of the vehicle rotation.
I s is the pinion to tire pin ratio.
J r is the moment of inertia of the tire.
Detailed Description
For a further understanding of the invention, its features and advantages, reference is now made to the following examples, which are illustrated in the accompanying drawings in which:
the following English words and English abbreviations in the application are defined as follows:
GPS is a Global navigation positioning System.
RefPoint is a road reference point.
Tangent is a road tangent.
SQP is a sequence quadratic programming solution.
The MPC is model predictive control.
QP is a quadratic programming solution.
Referring to fig. 1 to 3, a robot driving vehicle obstacle avoidance method based on an improved artificial potential field and MPC divides a control system of a driving robot into an upper control system and a lower control system, wherein the upper control system combines a repulsive force function in the artificial potential field method and constructs an obstacle avoidance function model and a road boundary magnetic field model based on a driving speed and a road boundary, and obtains a running track of a next step of a vehicle based on a model prediction control algorithm of a vehicle power model; the upper control system comprises an MPC controller, wherein the MPC controller inputs the running track of the next step of the vehicle and the current state of the vehicle, and outputs the expected course angle and acceleration to the lower control system; the lower control system converts the desired course angle into a torque control signal of a steering motor of the steering robot based on the steering robot and the vehicle body motion model.
Preferably, the method may comprise the steps of:
Step 1, a laser radar and a camera for monitoring road environment conditions and a positioning system for positioning the real-time position of a vehicle can be installed on the vehicle; the upper control system may introduce a predetermined path.
And 2, constructing an obstacle avoidance function model and a road boundary magnetic field model in the upper control system.
And 3, constructing a vehicle motion track model based on the obstacle avoidance function model, the road boundary magnetic field model and the constraint of the control quantity, generating optimal track discrete points by the imported preset path through a QP optimization algorithm, and transmitting the track discrete points into the MPC controller.
Step 4, a vehicle dynamics model based on tire slip and road curvature can be established in the MPC controller; and establishing an objective function and constraint conditions based on a model prediction optimization algorithm.
Step 5, the objective function and the constraint condition can be converted into a sequence quadratic programming problem; based on the rapid dual neural network, the sequence quadratic programming problem is converted into the dual problem to be optimally solved, and the expected course angle is calculated.
Preferably, in step 2, the vehicle may be regarded as a particle, the obstacle as a quadrilateral, and the following obstacle avoidance function is constructed:
Wherein:
f obs,vehicle (X) represents the total repulsive force of the obstacle to which the vehicle is subjected.
Η is a positive scaling factor.
D (x i,x0) is the Euclidean distance of the vehicle to the four points of the quadrilateral respectively.
Ρ is the maximum distance the obstacle will have on the vehicle.
Preferably, in step 2, the road is divided into two areas, and the following road boundary magnetic field functions are established:
Wherein:
F rep,edge is the repulsive force of two sides of the road.
W edge is the weight coefficient of the repulsive potential field.
D is the width of one area of the road.
Y is the lateral position where the vehicle is located.
W is the general width of the vehicle body.
V x is the vehicle speed.
Preferably, in step 3, position signals of the obstacle and the vehicle can be transmitted to an MPC (MPC planning) device, and a vehicle model is built by adopting a point quality model method; the method can be provided with: x is the longitudinal position of the vehicle in the body coordinate system; y is the lateral position of the vehicle in the body coordinate system; x is the longitudinal position of the vehicle in an inertial coordinate system; y is the lateral position of the vehicle in the inertial coordinate system; is the yaw angle of the vehicle.
The state quantity is selected as
The control amount u may be set as the front wheel slip angle δ. Then there are:
Wherein:
Is the rate of change of the longitudinal position of the vehicle in its own coordinate system.
Is the rate of change of the lateral position of the vehicle in its own coordinate system.
Is the rate of change of the lateral position of the vehicle in the inertial coordinate system.
Is the rate of change of the longitudinal position of the vehicle in the inertial coordinate system.
And xi is the newly built state quantity.
Ζ i is the change vector matrix in the ith scroll time domain.
Is the transposed matrix of ζ i.
H i is the ith reduced-roll time-domain weight matrix.
U i is the sum of all potential fields.
N p is the predicted time domain in the rolling time domain.
J min is the cost function minimum.
Can be solved by QP optimization algorithmGenerating optimal discrete points meeting corresponding conditions, performing curve fitting on the discrete points by adopting a Bezier curve, defining the fitted curve as a local path curve required by MPC to be tracked, and transmitting the curve into an MPC controller.
Preferably, in step 4, a vehicle dynamics model based on tire slip and road curvature can be established as follows:
Wherein:
I z is the moment of inertia of the vehicle in the z-axis direction.
M is the mass of the vehicle.
K ref is the road curvature obtained for the reference path.
V x is the longitudinal speed of the vehicle centroid in the body coordinate system.
V y is the lateral velocity of the vehicle centroid in the body coordinate system.
And l f is the distance from the vehicle centroid to the front axle.
And l r is the distance from the vehicle center of mass to the rear axle.
Is tracking heading error.
E d is the tracking distance error.
F xf is the vehicle front wheel longitudinal force.
And F xr is the longitudinal force of the rear wheels of the vehicle.
And F yf is the front wheel side bias force.
And F yr is the rear wheel side bias.
Is the vehicle yaw rate.
Preferably, C f may be set as the vehicle front wheel cornering stiffness; c r is the cornering stiffness of the rear wheels of the vehicle; alpha f is the slip angle of the front wheel; alpha r is the slip angle of the rear wheel.
F yf＝Cfαf,Fyr＝-Crαr can be assumed.
The tire cornering stiffness can be estimated based on a nonlinear kalman filter, and the uncertain tire cornering stiffness expression is as follows:
Wherein:
C f,0 is a linear standard value of the cornering stiffness of the front wheels of the vehicle.
Gamma f is a time-based variable for the front wheel.
Is the lateral deflection rigidity variable of the front wheel.
And C r is the cornering stiffness of the rear wheel.
And C r,0 is a linear standard value of the cornering stiffness of the rear wheels of the vehicle.
Gamma r is a time-based variable for the rear wheel.
Is the variation of the cornering stiffness of the rear wheel.
Preferably, in step 4, a state quantity may be setThe method can be obtained by discretizing and linearizing a nonlinear equation in a vehicle dynamics model through a Taylor-level expansion method and a forward Euler method: a new state space equation can be constructed: Epsilon (k+n p) at time N p in the future can be predicted based on the state trace, while the error e (k) =x 0(k+1)-Akx0(k)-Bku0 (k) is updated in real time.
Wherein:
a is a state quantity jacobian matrix.
B is a control quantity jacobian matrix.
The difference between the vehicle state quantity conversion rate and the time k is k+1.
Is the difference between the vehicle state quantity at the time k+1 and the time k.
Is the difference between the vehicle control amount at the time k+1 and the time k.
N p is the predicted time domain in the rolling time domain.
Epsilon (k) is a new state space expression.
E (k) is an error expression.
U (k-1) is the control amount at time k-1.
X 0 is the state quantity of the taylor-stage expansion selection point.
A k is the state quantity jacobian matrix newly constructed at time k.
And B k is a control quantity jacobian matrix newly constructed at the time k.
K is the number of steps of sampling.
Epsilon (k+N p) is the state quantity and control quantity of the future N p moment.
U 0 (k) is the control quantity of the taylor-stage expansion selection point at the moment k.
Preferably, in step 4, the following objective functions and constraints may be established based on the model predictive optimization algorithm:
The objective function is:
The constraint conditions are as follows:
emax-wd≤ed(k+i|k)≤-emin+wd。
δf,min≤δf(k+i|k)≤δf,max。
Δδf,min≤δf(k+i|k)-δf(k+i-1|k)≤Δδf,max。
Wherein:
j min is the minimum of the trajectory tracking objective function.
I is the sampling step size. i=1, 2, …, N p.
N p is the prediction time domain in the model prediction algorithm.
N c is the control time domain.
And outputting a heading error weight matrix.
Q d is the output distance error weight matrix.
W d is a safety distance defined during the running of the vehicle body.
W f is a control delta weight matrix.
Epsilon is the relaxation factor weight.
S is a relaxation factor.
K is the number of steps of sampling.
Delta f is the front wheel angle of the vehicle.
E max is the maximum value of the vehicle tracking lateral position deviation.
E min is the minimum value of the vehicle tracking lateral position deviation.
Δ f,min is the minimum value of the front wheel rotation angle of the vehicle.
Δ f,max is the maximum value of the front wheel rotation angle of the vehicle.
Delta f,min is the minimum value of the vehicle front wheel steering angle increment.
Delta f,max is the maximum value of the vehicle front wheel steering angle increment.
Is the minimum value of the yaw rate change of the vehicle.
Is the maximum value of the yaw rate change rate of the vehicle.
The workflow and working principle of the invention are further described in the following with a preferred embodiment of the invention:
The robot driving vehicle obstacle avoidance method based on the improved artificial potential field and MPC is used for driving a robot vehicle road test, can ensure that the driving robot controls the vehicle to complete the avoidance of obstacles in the test process, can realize the task of driving the robot to complete automatic driving to a greater extent, and enables the automatic driving vehicle to return to the original test site after the test is completed, and comprises the following steps:
The method comprises the steps of firstly, presetting a test reference path to enable an automobile to run according to a preset track, and meanwhile, installing a laser radar and a camera on the test automobile to monitor the environment state of a test site in real time while leading in the preset test path, and providing real-time positions of the automobile as (x i,t,yi.t) and the positions of obstacles (x p,t,yp.t) by adopting a GPS.
Step two, designing an upper controller to obtain a desired front wheel steering angle to complete track tracking and obstacle avoidance tasks, wherein the improved artificial potential field method is embedded into the optimal design control of the MPC planner to realize the application of tracking and obstacle avoidance.
The selection of the obstacle avoidance function comprehensively considers the speed and the influence of the relative distance between the vehicle and the obstacle on the obstacle avoidance effect, and combines the improved artificial potential field method to construct the following function, when the vehicle approaches the obstacle, the repulsive force of the obstacle is larger, and only the repulsive force function is introduced. The method simultaneously considers the speed and the limit value of the road boundary on the track planning, and the obstacle avoidance function is as follows:
Wherein eta is a positive proportionality coefficient, d (x i,x0) is Euclidean distance from two points at the front end of the automobile to four points of the quadrangle, and ρ is the maximum distance of influence of the obstacle on the automobile.
The road is divided into two areas, and the road boundary magnetic field is as follows:
where w is the general width of the vehicle body, is a positive scaling factor, and v is the vehicle speed.
The position signals of the obstacle and the automobile are transmitted to the MPC planner, and a point quality model is still adopted for the automobile model, so that the dynamics characteristic of the automobile is reflected, and the real-time performance of planning is ensured.
Selecting the state quantity asThe control amount u is the front wheel slip angle delta.
Based on the repulsive force field limitation and the control quantity limitation, solving by a QP optimization algorithm:
To generate optimal discrete points meeting corresponding conditions, and to smoothly interface with the control layer, performing curve fitting on the discrete points by adopting a Bezier curve, and transmitting the discrete points into the MPC controller.
Step three, improved model predictive control
In order to simplify and rationalize a control system, the control system is divided into upper control and lower control, a model prediction control algorithm based on an automobile power model is used for calculating to obtain the expected front wheel rotation angle, and then a driving robot (steering robot) and an automobile body are used for obtaining a model to obtain the required steering motor torque.
A two-degree-of-freedom automobile dynamics model common to vehicle models assumes a small angle assumption of tire slip angle. In order to better track the route, a vehicle dynamics model is built, which considers the curvature of the road, the influence of the curvature of the road directly relates to steering characteristics and driving stability, and a schematic diagram of the model is shown in fig. 2.
The mathematical model of the vehicle taking into account the tire slip, road curvature, is as follows:
Where k ref is the road curvature obtained by the reference path, v x and v y are the longitudinal and lateral speeds of the vehicle centroid in the body coordinate system, respectively, l f and l r are the distances of the vehicle centroid to the front-rear axis, And e d is defined as tracking heading bias and tracking distance bias. F yf and F yr are respectively front and rear wheel cornering forces, and the small angle cornering angle is assumed to be F yf＝Cfαf,Fyr＝-Crαr; alpha f and alpha r are the slip angles of the front and rear wheels, respectively.
During high-speed running or cornering of an automobile, since a tire model presents strong nonlinear characteristics, tire cornering stiffness is estimated based on a nonlinear Kalman filter, and the uncertain tire cornering stiffness is as follows: gamma is used for designing nonlinear characteristics for representing cornering stiffness, and the value range is between 0 and 1.
State quantityDiscretizing and linearizing a nonlinear equation by a Taylor-level expansion and forward Euler method to obtain the nonlinear equation: Constructing a new state space equation: Epsilon (k+n p) at time N p in the future is predicted based on the state trajectory, while the error e (k) =x 0(K+1)-Akx0(k)-Bku0 (k) is updated in real time.
Objective function and optimization solution:
Constraint conditions:
emax-wd≤ed(k+i|k)≤-emin+wd。
δf,min≤δf(k+i|k)≤δf,max。
Δδf,min≤δf(k+i|k)-δf(k+i-1|k)≤Δδf,max。
Where i is taken from 1 to N p,Np is the prediction horizon in the model prediction algorithm, N c is the control horizon, And Q d represent the output transverse error weight matrix, W f is the control increment weight matrix, ε is the relaxation factor weight, and s is the relaxation factor, respectively.
The traditional model prediction control adopts an SQP method to solve the inequality multi-constraint optimization problem, and in order to better achieve a convergence effect and a rapid calculation speed, the method is designed to solve the SQP based on the rapid dual neural network optimization, and a sequential quadratic programming form is converted into a dual problem: at this time, the expected front wheel rotation angle δ f is calculated by a model-based predictive optimization algorithm.
Wherein: ΔU is the control increment of the system. H is a weight matrix. min is the minimum of the solution objective function. And l min is the minimum value of the constraint variable. And l max is the maximum value of the constraint variable. v and w are both optimization variables for the dual problem.
And fifthly, converting the front wheel turning angle delta f into the torque required by the steering motor of the steering robot based on the driving robot-vehicle body dynamics model. The driving robot used in the invention is a fourth-generation steering robot of the Tianjin middle steam data center, the steering robot is fixed on the steering wheel through three grippers, the driving mode is that an internal gear drives the steering wheel to rotate, and a simplified structure diagram of the driving robot and an automobile steering system is shown in fig. 3. The torque required for the steering motor of the steering robot is calculated as follows:
Wherein i m is the gear reduction ratio of the motor, i g is the transmission ratio between the steering mechanism and the steering wheel, T s is the actual torque of the steering shaft, T m is the output torque of the steering motor, J S、BS、KS is the rotational inertia, damping coefficient and rigidity coefficient of the steering shaft, and θ S is the angle rotated by the steering wheel.
Assuming that the vehicle is a column-type electric power steering system, the power motor moment of inertia J m is assumed to be measurable, and the gear tire module model is as follows:
Wherein T a is torque of a power assisting system, M W is resistance moment of vehicle rotation, i s is transmission ratio of a pinion to a tire axle pin, J r is rotational inertia of a tire, and B r is damping coefficient. And B m is the damping coefficient of the power-assisted motor. Is the rate of change of the front wheel rotation angle.Is the rate of change of the front wheel rotational speed.
The relation T m＝f(δf between the steering mechanism required torque and the front wheel steering angle is obtained from the above equation). Based on experience, in order to be applied to the engineering field rapidly simultaneously, simplify complicated car body models, neglect suspension and complicated transmission process, establish the following relation between the front wheel steering angle of the vehicle and the steering mechanism output angle: delta f＝f(ux)θs for comparative verification of the accuracy of the mathematical model of the above formula.
The required torque of the steering robot is output, the steering motor of the steering mechanism obtains signals from an upper controller, the steering wheel is further controlled to control the vehicle, and the lower control system is not used as the discussion scope of the invention.
And step six, after the test is completed, the automobile obtains an initial position through a GPS and a camera and obtains a return path through the path planning algorithm, and the automatic return work of the test site is realized based on improved model predictive control and driving robot lower control.
The above-described embodiments are only for illustrating the technical spirit and features of the present invention, and it is intended to enable those skilled in the art to understand the content of the present invention and to implement it accordingly, and the scope of the present invention is not limited to the embodiments, i.e. equivalent changes or modifications to the spirit of the present invention are still within the scope of the present invention.
Claims (6)
1. The robot driving vehicle obstacle avoidance method based on the improved artificial potential field and MPC is characterized in that a control system of a driving robot is divided into an upper control system and a lower control system, the upper control system combines a repulsive force function in the artificial potential field method, constructs an obstacle avoidance function model and a road boundary magnetic field model based on a driving speed and a road boundary, and obtains a running track of a next step of a vehicle based on a model predictive control algorithm of a vehicle power model; the upper control system comprises an MPC controller, wherein the MPC controller inputs the running track of the next step of the vehicle and the current state of the vehicle, and outputs the expected course angle and acceleration to the lower control system; the lower control system converts the expected course angle into a torque control signal of a steering motor of the steering robot based on the steering robot and the vehicle body motion model;
the method comprises the following steps:
step 1, installing a laser radar and a camera for monitoring road environment conditions and a positioning system for positioning the real-time position of a vehicle on the vehicle; the upper control system imports a preset path;
Step 2, constructing an obstacle avoidance function model and a road boundary magnetic field model in an upper control system;
Step 3, constructing a vehicle motion track model based on the constraints of the obstacle avoidance function model, the road boundary magnetic field model and the control quantity, generating optimal track discrete points by the imported preset path through a QP optimization algorithm, and transmitting the track discrete points into the MPC controller;
Step4, establishing a vehicle dynamics model based on tire slip and road curvature in the MPC controller; establishing an objective function and constraint conditions based on a model prediction optimization algorithm;
step 5, converting the objective function and the constraint condition into a sequence quadratic programming problem; based on a rapid dual neural network, converting a sequence quadratic programming problem into a dual problem to optimize and solve, and calculating to obtain an expected course angle;
In step 2, the vehicle is regarded as a particle, the obstacle is regarded as a quadrilateral, and the following obstacle avoidance function is constructed:
Wherein:
f obs,vehicle (X) represents the total repulsive force of the obstacle to which the vehicle is subjected;
η is a positive scaling factor;
d (x i,x0) is the Euclidean distance of the vehicle to the four points of the quadrilateral respectively;
ρ is the maximum distance the obstacle will have on the vehicle;
in step 2, the road is divided into two areas, and the following road boundary magnetic field function is established:
Wherein:
f rep,edge is the repulsive force of two sides of the road;
w edge is the weight coefficient of the repulsive potential field;
d is the width of one area of the road;
y is the lateral position of the vehicle;
w is the general width of the vehicle body;
v x is the vehicle speed.
2. The robot-driven vehicle obstacle avoidance method based on improved artificial potential field and MPC of claim 1 wherein in step 3, position signals of the obstacle and vehicle are transmitted to the MPC planner, and a vehicle model is built using a point mass model method; setting: x is the longitudinal position of the vehicle in the body coordinate system; y is the lateral position of the vehicle in the body coordinate system; x is the longitudinal position of the vehicle in an inertial coordinate system; y is the lateral position of the vehicle in the inertial coordinate system; is the yaw angle of the vehicle;
Selecting the state quantity as
Setting the control quantity u as a front wheel deflection delta; then there are:
Wherein:
The change rate of the longitudinal position of the vehicle under the self coordinate system is given;
the change rate of the transverse position of the vehicle under the self coordinate system is given;
The change rate of the transverse position of the vehicle under an inertial coordinate system is given;
Is the rate of change of the longitudinal position of the vehicle in the inertial coordinate system;
ζ is the newly built state quantity;
Xi i is the change vector matrix in the ith scroll time domain;
is the transposed matrix of xi i;
H i is the ith reduced-roll time-domain weight matrix;
U i is the sum of all potential fields;
n p is the prediction horizon in the rolling horizon;
j min is the cost function minimum;
solving by QP optimization algorithm Generating optimal discrete points meeting corresponding conditions, performing curve fitting on the discrete points by adopting a Bezier curve, defining the fitted curve as a local path curve required by MPC to be tracked, and transmitting the curve into an MPC controller.
3. The robot-driven vehicle obstacle avoidance method based on improved artificial potential field and MPC of claim 1 wherein, in step 4, a vehicle dynamics model based on tire slip and road curvature is established as follows:
Wherein:
I z is the moment of inertia of the vehicle in the z-axis direction;
m is the mass of the vehicle;
k ref is the road curvature obtained by the reference path;
v x is the longitudinal speed of the vehicle centroid in the vehicle body coordinate system;
v y is the lateral velocity of the vehicle centroid in the vehicle body coordinate system;
l f is the distance from the vehicle centroid to the front axle;
l r is the distance from the vehicle centroid to the rear axle;
tracking heading errors;
e d is tracking distance error;
F xf is the longitudinal force of the front wheels of the vehicle;
F xr is the longitudinal force of the rear wheels of the vehicle;
F yr is the front wheel side bias;
F yr is the rear wheel side bias;
is the vehicle yaw rate.
4. The robot-driven vehicle obstacle avoidance method based on improved artificial potential field and MPC of claim 3 wherein C f is set as the vehicle front wheel cornering stiffness; c r is the cornering stiffness of the rear wheels of the vehicle; alpha f is the slip angle of the front wheel; alpha r is the slip angle of the rear wheel;
Assume F yf＝Cfαf,Fyr＝-Crαr;
Estimating the tire cornering stiffness based on a nonlinear kalman filter, wherein the uncertain tire cornering stiffness expression is as follows:
Wherein:
c f,0 is a linear standard value of the cornering stiffness of the front wheels of the vehicle;
Gamma f is the front wheel time-based variable;
Is the lateral deflection rigidity variable of the front wheel;
C r is the cornering stiffness of the rear wheel;
c r,0 is a linear standard value of the cornering stiffness of the rear wheels of the vehicle;
Gamma r is a time-based variable for the rear wheel;
is the variation of the cornering stiffness of the rear wheel.
5. The robot-driven vehicle obstacle avoidance method based on improved artificial potential field and MPC of claim 3 wherein, in step 4, the state quantity is setDiscretizing and linearizing a nonlinear equation in a vehicle dynamics model by a Taylor-level expansion and forward Euler method to obtain the vehicle dynamics model: Constructing a new state space equation: Predicting epsilon (k+n p) at a future time N p based on the state trace, and simultaneously updating the error e (k) =x 0(k+1)-Akx0(k)-Bku0 (k) in real time;
Wherein:
a is a state quantity jacobian matrix;
B is a control quantity Jacobian matrix;
The vehicle state quantity conversion rate is the difference value between k+1 and k time;
the difference value between the vehicle state quantity at the time k+1 and the time k is obtained;
the difference between the control quantity of the vehicle and the moment k+1 is given;
n p is the prediction horizon in the rolling horizon;
epsilon (k) is a new state space expression;
e (k) is an error expression;
u (k-1) is the control amount at time k-1;
x 0 is the state quantity of the Taylor expansion selection point;
a k is a state quantity jacobian matrix newly constructed at the moment k;
B k is a control quantity jacobian matrix newly constructed at the moment k;
k is the number of steps of sampling;
Epsilon (k+N p) is the state quantity and control quantity of the future N p moment;
u 0 (k) is the control quantity of the taylor-stage expansion selection point at the moment k.
6. The robot-driven vehicle obstacle avoidance method based on improved artificial potential field and MPC of claim 5 wherein, in step 4, the following objective function and constraints are established based on a model predictive optimization algorithm:
The objective function is:
The constraint conditions are as follows:
emax-wd≤ed(k+i|k)≤-emin+wd；
δf,min≤δf(k+i|k)≤δf,max；
Δδf,min≤δf(k+i|k)-δf(k+i-1|k)≤Δδf,max；
Wherein:
J min is the minimum of the trajectory tracking objective function;
i is the sampling step length; i=1, 2, …, N p;
N p is a prediction time domain in a model prediction algorithm;
n c is the control time domain;
the method comprises the steps of outputting a heading error weight matrix;
Q d is an output distance error weight matrix;
w d is a safety distance defined in the driving process of the vehicle body;
w f is a control increment weight matrix;
epsilon is the relaxation factor weight;
s is a relaxation factor;
k is the number of steps of sampling;
Delta f is the front wheel corner of the vehicle;
e max is the maximum value of the vehicle tracking lateral position deviation;
e min is the minimum value of the vehicle tracking lateral position deviation;
δ f,min is the minimum value of the front wheel rotation angle of the vehicle;
delta f,max is the maximum value of the front wheel rotation angle of the vehicle;
Delta f,min is the minimum value of the vehicle front wheel steering angle increment;
Delta f,max is the maximum value of the vehicle front wheel steering angle increment;
Is the minimum value of the yaw rate change of the vehicle;
is the maximum value of the yaw rate change rate of the vehicle.
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