CN114879698A - Robot-driven vehicle obstacle avoidance method based on improved artificial potential field and MPC - Google Patents

Robot-driven vehicle obstacle avoidance method based on improved artificial potential field and MPC Download PDF

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CN114879698A
CN114879698A CN202210660051.1A CN202210660051A CN114879698A CN 114879698 A CN114879698 A CN 114879698A CN 202210660051 A CN202210660051 A CN 202210660051A CN 114879698 A CN114879698 A CN 114879698A
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赵磊
牛文铁
王韬
郭永豪
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Tianjin University
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    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0231—Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means
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    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
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    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
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Abstract

The invention discloses a robot-driven vehicle obstacle avoidance method based on an improved artificial potential field and MPC.A control system of a driving robot is divided into an upper control system and a lower control system, wherein the upper control system is combined with a repulsion function in the artificial potential field method and is used for constructing an obstacle avoidance function model and a road boundary magnetic field model based on a driving speed and a road boundary, and the next-step running track of a vehicle is obtained based on a model prediction control algorithm of a vehicle dynamic model; the upper control system comprises an MPC controller, and the MPC controller inputs the next operation track of the vehicle and the current state of the vehicle and outputs an 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 the automatic driving to a greater extent.

Description

Robot-driven vehicle obstacle avoidance method based on improved artificial potential field and MPC
Technical Field
The invention relates to a control method for automatically completing a road test by driving a robot-driven vehicle, in particular to a robot-driven vehicle obstacle avoidance method based on an improved artificial potential field and a MPC (MPC).
Background
At present, an automobile driving robot is another important embodiment of automatic driving development, has the characteristic of a human-simulated mechanical structure, the mechanical structure mainly comprises an accelerator/brake mechanical leg, a steering manipulator and a gear shifting manipulator, and the automobile driving robot can be simply installed on an automobile to realize the driving control of the automobile while the existing automobile internal mechanism is not damaged. The system has the advantages of high control precision, good repeatability, strong durability, high safety and the like, and can be widely used for replacing human beings in various automobile test projects, so that more accurate test data can be obtained. The driving robot is widely applied to high-risk testing and ADAS testing of automobiles and the like, the ADAS testing mainly focuses on testing of an automatic emergency braking system (AEB), a lane keeping system and the like, and therefore the driving robot is required to be capable of completing accurate vehicle speed tracking control and steering control according to corresponding testing conditions, namely coordinated control. On the other hand, the corresponding road condition test is mainly embodied in that the automobile is tested according to a given path, namely the driving robot is used for driving the automobile to realize path tracking, when an obstacle or an emergency situation appears suddenly in the test process, the safety of the automobile test is difficult to guarantee, the realization of obstacle avoidance and risk relief by local path planning of the automobile in the driving process has important significance for improving the safety of the automobile test, and meanwhile, the reference value is provided for the automatic driving of the existing automobile by combining an automobile ADAS system on the basis of a driving robot control system added with the local planning.
The model prediction control algorithm is an advanced control algorithm, is widely applied to the field of automatic driving at present, is an optimization algorithm based on an automobile model, predicts the condition of a future automobile in real time, can efficiently and stably realize the tracking of a track, and determines the real-time property and the stability of the algorithm according to the complexity of the automobile model and a multi-constraint optimization solution method; the path planning aims at providing an optimal fastest path which can reach a destination for an automobile, and the manual potential field method is applied to local path planning, establishes attraction and repulsion magnetic fields around an obstacle and a target object, and guides the automobile to search for an obstacle avoidance path through the resultant force of the repulsion and the attraction. In order to enable a driving robot to drive a vehicle to complete a task of avoiding an obstacle under a fixed path test, a method based on an improved artificial potential field and model prediction is used for driving the robot to control the vehicle.
Disclosure of Invention
The invention provides a robot-driven vehicle obstacle avoidance method based on an improved artificial potential field and MPC (dynamic host control) for solving the technical problems in the prior art, aiming at overcoming the problem of lower safety of a driving robot-driven vehicle for road testing, realizing that the driving robot controls the vehicle to complete an automatic obstacle avoidance task when encountering an obstacle during running in a fixed track, and simultaneously, under the condition of no human intervention, the driving robot can automatically drive the vehicle to come to the test initial place again after completing the test.
The technical scheme adopted by the invention for solving the technical problems in the prior art is as follows: a robot driving vehicle obstacle avoidance method based on 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 is combined with a repulsion function in the artificial potential field method and establishes an obstacle avoidance function model and a road boundary magnetic field model based on the driving speed and the road boundary, and the next step of the vehicle running track is obtained based on a model prediction control algorithm of a vehicle dynamic model; the upper control system comprises an MPC controller, and the MPC controller inputs the next operation track of the vehicle and the current state of the vehicle and outputs an 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 the road environment condition and a positioning system for positioning the real-time position of a vehicle on the vehicle; leading the upper control system into 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 obstacle avoidance function model, the road boundary magnetic field model and the constraint of the control quantity, generating optimal track discrete points from the imported preset path through a QP optimization algorithm, and transmitting the track discrete points into the MPC controller;
step 4, establishing a vehicle dynamic 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 sequential quadratic programming problem; and based on the fast dual neural network, converting the sequence quadratic programming problem into a dual problem to optimize and solve, and calculating to obtain the expected course angle.
Further, in step 2, regarding the vehicle as a mass point and regarding the obstacle as a quadrilateral, constructing an obstacle avoidance function as follows:
Figure BDA0003690333710000021
in the formula:
F obs,vehicle (X) represents a total repulsive force of an obstacle to which the vehicle is subjected;
eta is a direct proportionality coefficient;
d(x i ,x 0 ) Respectively Euclidean distances from the vehicle to four points of the quadrangle;
ρ is the maximum distance that the obstacle has an effect on the vehicle.
Further, in step 2, the road is divided into two areas, and the following road boundary magnetic field function is established:
Figure BDA0003690333710000031
in the formula:
F rep,edge repulsion forces on both sides of the road;
w edge is the weight coefficient of the repulsive force potential field;
d is the width of one area of the road;
y is the transverse position of the vehicle;
w is the general width of the vehicle body;
v x is the vehicle speed.
Further, in step 3, transmitting position signals of the obstacles and the vehicles to an MPC (personal computer) planner, and establishing a vehicle model by adopting a point mass model method; setting: x is the longitudinal position of the vehicle in the body coordinate system; y is the transverse position of the vehicle in the body coordinate system; x is the longitudinal position of the vehicle in the inertial coordinate system; y is the transverse position of the vehicle in the inertial coordinate system;
Figure BDA0003690333710000032
is the yaw angle of the vehicle;
Figure BDA0003690333710000033
selecting a state quantity of
Figure BDA0003690333710000034
Setting the control quantity u as a front wheel deflection angle delta; then there are:
Figure BDA0003690333710000035
in the formula:
Figure BDA0003690333710000036
the change rate of the longitudinal position of the vehicle under the self coordinate system is obtained;
Figure BDA0003690333710000037
the change rate of the transverse position of the vehicle under the self coordinate system is obtained;
Figure BDA0003690333710000038
for the transverse position of the vehicle in the inertial frameThe rate of change of position;
Figure BDA0003690333710000039
is the rate of change of the longitudinal position of the vehicle in the inertial frame;
xi is the newly built state quantity;
ξ i a change vector matrix in the ith rolling time domain;
Figure BDA00036903337100000310
is xi i The transposed matrix of (2);
H i a weight matrix for the ith reduced rolling time domain;
U i is the sum of all potential fields;
N p a prediction time domain in a rolling time domain;
J min is the minimum value of the cost function;
solving by QP optimization algorithm
Figure BDA0003690333710000041
And generating the optimal discrete point meeting the corresponding condition, performing curve fitting on the discrete point by adopting a Bezier curve, defining the fitted curve as a local path curve required by the MPC and transmitting the local path curve into the MPC controller.
Further, in step 4, a vehicle dynamics model based on tire slip and road curvature is established as follows:
Figure BDA0003690333710000042
Figure BDA0003690333710000043
Figure BDA0003690333710000044
Figure BDA0003690333710000045
Figure BDA0003690333710000046
in the formula:
I z the moment of inertia of the vehicle in the z-axis direction;
m is the mass of the vehicle;
k ref road curvature obtained for the reference path;
v x the longitudinal speed of the vehicle mass center under the vehicle body coordinate system;
v y the transverse speed of the mass center of the vehicle under the vehicle body coordinate system;
l f the distance from the center of mass of the vehicle to the front axle;
l r the distance from the center of mass of the vehicle to the rear axle;
Figure BDA0003690333710000047
tracking course error;
e d is the tracking distance error;
F xf is the vehicle front wheel longitudinal force;
F xr is the vehicle rear wheel longitudinal force;
F yf is a front wheel side biasing force;
F yr is a rear wheel side biasing force;
Figure BDA0003690333710000048
is the vehicle yaw rate.
Further, let C f Is vehicle front wheel cornering stiffness; c r Is vehicle rear wheel cornering stiffness; alpha is alpha f Is the slip angle of the front wheel; alpha is alpha r Is the slip angle of the rear wheel;
suppose F yf ＝C f α f ,F yr ＝-C r α r ；
Estimating the cornering stiffness of the tire based on a nonlinear Kalman filter, wherein the uncertain cornering stiffness of the tire has the following expression:
Figure BDA0003690333710000051
in the formula:
C f,0 a linear standard value of the cornering stiffness of the front wheel side of the vehicle;
γ f is a time-based variable for the front wheel;
Figure BDA0003690333710000052
is a front wheel yaw stiffness variable;
C r is rear wheel cornering stiffness;
C r,0 a linear standard value of the cornering stiffness of the rear wheel side of the vehicle;
γ r is a time-based variable for the rear wheel;
Figure BDA0003690333710000053
is a rear wheel cornering stiffness variable.
Further, in step 4, the state quantity is set
Figure BDA0003690333710000054
Discretizing and linearizing a nonlinear equation in the vehicle dynamics model through a Taylor-level expansion method and a forward Euler method to obtain:
Figure BDA0003690333710000055
constructing a new state space equation:
Figure BDA0003690333710000056
predicting future N based on state trajectories p Time of dayEpsilon (k + N) p ) While error e (k) is equal to x 0 (k+1)-A k x 0 (k)-B k u 0 (k) Updating in real time;
in the formula:
a is a state quantity Jacobian matrix;
b is a control quantity Jacobian matrix;
Figure BDA0003690333710000057
the difference value of the vehicle state quantity conversion rate at the moment k +1 and the moment k is obtained;
Figure BDA0003690333710000058
the difference value of the vehicle state quantity at the moment k +1 and the moment k is obtained;
Figure BDA0003690333710000059
the difference value of the vehicle control quantity at the moment k +1 and the moment k is obtained;
N p a prediction time domain in a rolling time domain;
epsilon (k) is a new state space expression;
e (k) is an error expression;
u (k-1) is a control quantity at the time of k-1;
x 0 developing state quantities of the selected points for the Taylor stage;
A k a state quantity Jacobian matrix newly constructed at the moment k;
B k a control quantity Jacobian matrix newly constructed at the moment k;
k is the number of sampling steps;
ε(k+N p ) For future N p A state quantity and a control quantity at a time;
u 0 (k) the control quantity of the selected point is developed for the taylor stage at the time k.
Further, in step 4, the following objective functions and constraint conditions are established based on the model prediction optimization algorithm: the objective function is:
Figure BDA0003690333710000061
the constraint conditions are as follows:
e max -w d ≤e d (k+i|k)≤-e min +w d ；
δ f,min ≤δ f (k+i|k)≤δ f,max ；
Δδ f,min ≤δ f (k+i|k)-δ f (k+i-1|k)≤Δδ f,max ；
Figure BDA0003690333710000062
in the formula:
J min tracking a minimum value of the objective function for the trajectory;
i is a sampling step length; 1,2, …, N p ；
N p Predicting a time domain for a model prediction algorithm;
N c to control the time domain;
Figure BDA0003690333710000063
is an output course error weight matrix;
Q d outputting a distance error weight matrix;
w d defining a safety distance for the vehicle body in the driving process;
W f a control increment weight matrix;
ε is the relaxation factor weight;
s is a relaxation factor;
k is the number of sampling steps;
δ f turning a front wheel of the vehicle;
e max tracking a maximum value of the lateral position deviation for the vehicle;
e min tracking a minimum value of lateral position deviation for the vehicle;
δ f,min the minimum value of the rotation angle of the front wheel of the vehicle;
δ f,max the maximum value of the rotation angle of the front wheel of the vehicle;
Δδ f,min is the minimum value of the vehicle front wheel steering angle increment;
Δδ f,max the maximum value of the increment of the front wheel steering angle of the vehicle;
Figure BDA0003690333710000071
is the minimum value of the vehicle yaw angle change rate;
Figure BDA0003690333710000072
is the maximum value of the vehicle yaw rate.
The invention has the advantages and positive effects that: the invention effectively combines the improved artificial potential field method with model prediction planning and control together to be applied to the driving robot to test the vehicle, and has the characteristics of high control speed, high safety, high stability and the like. In the process of controlling the vehicle to carry out road test under a fixed track by driving the robot, the sudden risk can be effectively avoided; meanwhile, the model predictive control objective function is solved based on the rapid dual neural network, 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 can be effectively and stably completed
Drawings
Fig. 1 is a design block diagram of a driving robot-vehicle obstacle avoidance control system.
Fig. 2 is a schematic diagram of an automobile dynamic model considering road curvature and slippage.
Fig. 3 is a simplified robot-vehicle (steering robot) mechanical structure.
In the figure:
y new the lateral position of the new reference trajectory is planned for the local path.
Figure BDA0003690333710000073
And planning the yaw angle of the new reference track for the local path.
δ f Is the front wheel angle of the vehicle.
x is; the x-axis of the body coordinate system.
y is; and a y-axis of a body coordinate system.
z is; the z-axis of the body coordinate system.
X is; global coordinate system X-axis.
Y is; global coordinate system Y-axis.
Figure BDA0003690333710000074
Is the included angle between the tangent line of the road reference point and the global coordinate system.
Figure BDA0003690333710000075
The lateral speed change rate of the vehicle under the self coordinate system.
Figure BDA0003690333710000076
Is the yaw angle of the vehicle.
θ vf Is as follows; the included angle between the speed direction of the front wheel of the vehicle and the axial direction of the vehicle body.
v f Is as follows; vehicle front wheel speed direction.
l f Is the distance from the center of mass of the vehicle to the front axle.
l r Is the distance from the center of mass of the vehicle to the rear axle.
Figure BDA0003690333710000081
To track heading errors.
F xf Is the vehicle front wheel longitudinal force.
F xr Is the vehicle rear wheel longitudinal force.
F yf Is a front wheel side biasing force.
F yr Is a rear wheel side biasing force.
Figure BDA0003690333710000082
Is the vehicle yaw rate.
α f Is the slip angle of the front wheel.
α r Is the slip angle of the rear wheel.
i m Is the gear reduction ratio of the motor.
i g 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 resisting moment of vehicle rotation.
i s Is the pinion-to-tire axle pin gear ratio.
J r Is the moment of inertia of the tire.
Detailed Description
For further understanding of the contents, features and effects of the present invention, the following embodiments are enumerated in conjunction with the accompanying drawings, and the following detailed description is given:
the following English words and English abbreviation Chinese explanations in the present application are as follows:
the GPS is a global navigation positioning system.
Ref point is a road reference point.
Tangent is the Tangent to the road.
The SQP is solved for the sequence quadratic programming.
MPC is model predictive control.
QP is solved for quadratic programming.
Referring to fig. 1 to 3, a robot-driven 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 is combined with a repulsion 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 next-step running track of a vehicle based on a model prediction control algorithm of a vehicle dynamic model; the upper control system comprises an MPC controller, and the MPC controller inputs the next operation track of the vehicle and the current state of the vehicle and outputs an 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 arranged on the vehicle; the upper control system can import the 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 from the imported preset path through a QP optimization algorithm, and transmitting the track discrete points into the MPC controller.
Step 4, a vehicle dynamic 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, converting the objective function and the constraint condition into a sequential quadratic programming problem; and based on the fast dual neural network, converting the sequence quadratic programming problem into a dual problem to optimize and solve, and calculating to obtain the expected course angle.
Preferably, in step 2, the vehicle may be regarded as a mass point, and the obstacle may be regarded as a quadrilateral, and the following obstacle avoidance function is constructed:
Figure BDA0003690333710000091
in the formula:
F obs,vehicle (X) represents the total repulsive force of the obstacle to which the vehicle is subjected.
Eta is a direct proportionality coefficient.
d(x i ,x 0 ) The euclidean distances of the vehicle to four points of the quadrangle, respectively.
ρ is the maximum distance that the obstacle has an effect on the vehicle.
Preferably, in step 2, the road may be divided into two regions, and the following road boundary magnetic field function is established:
Figure BDA0003690333710000101
in the formula:
F rep,edge the repulsive force of both sides of the road.
w edge Is the weight coefficient of the repulsive potential field.
d is the width of one of the zones of the road.
And y is the transverse position of the vehicle.
w is the general width of the vehicle body.
v x Is the vehicle speed.
Preferably, in step 3, the position signals of the obstacle and the vehicle can be transmitted to the MPC planner, and a vehicle model is established by using a point-mass model method; can be provided with: x is the longitudinal position of the vehicle in the body coordinate system; y is the transverse position of the vehicle in the body coordinate system; x is the longitudinal position of the vehicle in the inertial coordinate system; y is the transverse position of the vehicle in the inertial coordinate system;
Figure BDA0003690333710000102
is the yaw angle of the vehicle.
Figure BDA0003690333710000103
Optionally wherein the state quantity is
Figure BDA0003690333710000104
The control amount u can be set to the front wheel slip angle δ. Then there are:
Figure BDA0003690333710000105
in the formula:
Figure BDA0003690333710000106
is the change rate of the longitudinal position of the vehicle under the self coordinate system.
Figure BDA0003690333710000107
The change rate of the transverse position of the vehicle under the self coordinate system.
Figure BDA0003690333710000108
Is the rate of change of the lateral position of the vehicle in the inertial frame.
Figure BDA0003690333710000109
Is the rate of change of the longitudinal position of the vehicle in the inertial frame.
And xi is the newly-built state quantity.
ξ i Is the change vector matrix in the ith scroll time domain.
Figure BDA00036903337100001010
Is xi i The transposed matrix of (2).
H i The weight matrix of the rolling time domain is reduced for the ith.
U i Is the sum of all potential fields.
N p Is a prediction time domain in the rolling time domain.
J min Is the minimum value of the cost function.
Can be solved by QP optimization algorithm
Figure BDA0003690333710000111
And generating the optimal discrete point meeting the corresponding condition, performing curve fitting on the discrete point by adopting a Bezier curve, defining the fitted curve as a local path curve required by the MPC and transmitting the local path curve into the MPC controller.
Preferably, in step 4, a vehicle dynamics model based on tire slip and road curvature may be established as follows:
Figure BDA0003690333710000112
Figure BDA0003690333710000113
Figure BDA0003690333710000114
Figure BDA0003690333710000115
Figure BDA0003690333710000116
in the formula:
I z is the moment of inertia of the vehicle in the z-axis direction.
And m is the mass of the vehicle.
k ref The road curvature obtained for the reference path.
v x Is the longitudinal velocity of the vehicle's center of mass in the vehicle's body coordinate system.
v y Is the lateral velocity of the vehicle's center of mass in the vehicle body coordinate system.
l f Is the distance from the center of mass of the vehicle to the front axle.
l r Is the distance from the center of mass of the vehicle to the rear axle.
Figure BDA0003690333710000117
To track heading errors.
e d To track the range error.
F xf Is the vehicle front wheel longitudinal force.
F xr Is the vehicle rear wheel longitudinal force.
F yf Is a front wheel side biasing force.
F yr Is a rear wheel side biasing force.
Figure BDA0003690333710000118
Is the vehicle yaw rate.
Preferably, C may be provided f Is vehicle front wheel cornering stiffness; c r Is vehicle rear wheel cornering stiffness; alpha is alpha f Is the slip angle of the front wheel; alpha is alpha r Is the slip angle of the rear wheel.
Can assume F yf ＝C f α f ,F yr ＝-C r α r 。
Tire cornering stiffness can be estimated based on a non-linear kalman filter, and the expression for uncertain tire cornering stiffness is as follows:
Figure BDA0003690333710000121
in the formula:
C f,0 is a linear standard value of the cornering power of the front wheel side of the vehicle.
γ f Time-based variables for the front wheels.
Figure BDA0003690333710000122
Is a front wheel cornering stiffness variable.
C r Is rear wheel cornering stiffness.
C r,0 Is a linear standard value of the cornering power of the rear wheel side of the vehicle.
γ r Time-based variables for the rear wheels.
Figure BDA0003690333710000123
Is a rear wheel cornering stiffness variable.
Preferably, in step 4, the state quantity can be set
Figure BDA0003690333710000124
The non-linear equation in the vehicle dynamics model can be discretized and linearized through Taylor-level expansion and a forward Euler method to obtain:
Figure BDA0003690333710000125
a new state space equation can be constructed:
Figure BDA0003690333710000126
predicting future N based on state trajectories p Time epsilon (k + N) p ) While error e (k) is equal to x 0 (k+1)-A k x 0 (k)-B k u 0 (k) And performing real-time updating.
In the formula:
a is a state quantity Jacobian matrix.
And B is a control quantity Jacobian matrix.
Figure BDA0003690333710000127
The difference between the vehicle state quantity conversion rate at the time k +1 and the time k.
Figure BDA0003690333710000128
The difference between the vehicle state quantity at the time k +1 and the time k.
Figure BDA0003690333710000129
The difference between the vehicle control quantity at the time k +1 and the time k.
N p Is a prediction time domain in the rolling time domain.
ε (k) is a new state space expression.
e (k) is an error expression.
u (k-1) is the control quantity at the time of k-1.
x 0 The state quantities of the selected points are developed for the taylor stage.
A k Is a newly constructed state quantity jacobian matrix at time k.
B k Is a newly constructed control quantity jacobian matrix at the time k.
k is the number of steps of sampling.
ε(k+N p ) For future N p The state quantity at the time and the control quantity.
u 0 (k) The control quantity of the selected point is developed for the taylor stage at time k.
Preferably, in step 4, the following objective function and constraint condition may be established based on the model prediction optimization algorithm:
the objective function is:
Figure BDA0003690333710000131
the constraint conditions are as follows:
e max -w d ≤e d (k+i|k)≤-e min +w d 。
δ f,min ≤δ f (k+i|k)≤δ f,max 。
Δδ f,min ≤δ f (k+i|k)-δ f (k+i-1|k)≤Δδ f,max 。
Figure BDA0003690333710000132
in the formula:
J min the minimum of the objective function is tracked for the trajectory.
i is the sampling step size. 1,2, …, N p 。
N p The prediction time domain in the model prediction algorithm.
N c To control the time domain.
Figure BDA0003690333710000133
Is an output heading error weight matrix.
Q d Is an output distance error weight matrix.
w d A safety distance defined during the travel of the vehicle body.
W f To control the incremental weight matrix.
ε is the relaxation factor weight.
s is a relaxation factor.
k is the number of steps of sampling.
δ f The vehicle front wheel turning angle.
e max The maximum value of the lateral position deviation is tracked for the vehicle.
e min The minimum value of the lateral position deviation is tracked for the vehicle.
δ f,min Is the minimum value of the rotation angle of the front wheels of the vehicle.
δ f,max The maximum value of the vehicle front wheel turning angle.
Δδ f,min The minimum value of the vehicle front wheel steering angle increment.
Δδ f,max The maximum value of the vehicle front wheel steering angle increment.
Figure BDA0003690333710000141
Is the minimum value of the vehicle yaw rate of change.
Figure BDA0003690333710000142
Is the maximum value of the vehicle yaw rate.
The working process and working principle of the present invention are further explained by a preferred embodiment of the present invention as follows:
a robot-driven vehicle obstacle avoidance method based on an improved artificial potential field and MPC is used for road testing of a robot-driven vehicle, can ensure that the robot-driven vehicle controls the vehicle to complete obstacle avoidance in the testing process, and can also realize that the robot-driven vehicle completes the task of automatic driving to a greater extent, so that the automatic-driven vehicle returns to the original testing field after the testing is completed, and the specific method is as follows:
step one, presetting a test reference path to enable an automobile to run according to a preset track, 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 in advance, and providing the real-time position of the automobile for recording by adopting a GPS (x) i,t ,y i.t ) And the position (x) of the obstacle p,t ,y p.t )。
And step two, designing an upper controller to obtain an expected front wheel steering angle to complete track tracking and obstacle avoidance tasks, and embedding an improved artificial potential field method into the optimized 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 the following function is constructed by combining an improved artificial potential field method. The method simultaneously considers the speed and the limit value of the road boundary to the track planning, and the obstacle avoidance function is as follows:
Figure BDA0003690333710000143
where eta is a direct proportionality coefficient, d (x) i ,x 0 ) Respectively Euclidean distances from two points at the front end of the automobile to four points of the quadrangle, wherein rho is an obstacleThe maximum distance an object has an effect on the car.
The road is divided into two regions, and the road boundary magnetic field is as follows:
Figure BDA0003690333710000144
here, w is a general width of the vehicle body and is a direct proportional coefficient, and v is a vehicle speed.
The position signals of the obstacles and the automobile are transmitted to the MPC planner, and a point quality model is still adopted for the automobile model, so that the dynamic characteristics of the automobile are reflected, and the real-time performance of planning is also ensured.
Figure BDA0003690333710000151
Selecting a state quantity of
Figure BDA0003690333710000152
The control amount u is the front wheel slip angle δ.
Solving through a QP optimization algorithm based on the repulsion field limit and the control quantity limit:
Figure BDA0003690333710000153
and generating optimal discrete points meeting corresponding conditions, carrying out curve fitting on the discrete points by adopting a Bezier curve in order to be smoothly butted with the control layer, and transmitting the discrete points into the MPC controller.
Step three, improved model predictive control
In order to simplify and rationalize the control system, the control system is divided into upper control and lower control, the expected front wheel rotation angle is calculated based on a model predictive control algorithm of an automobile power model, and the required steering motor torque is obtained through a driving robot (steering robot) and a vehicle body model.
A common two-degree-of-freedom automotive dynamics model of a vehicle model assumes a small angle assumption for tire slip angle. For better tracking of the route, a vehicle dynamics model is established that takes into account the curvature of the road, the influence of which is directly related to the steering behavior and driving stability, and the model schematic is shown in fig. 2.
The mathematical model of the vehicle taking into account tire slip, road curvature is as follows:
Figure BDA0003690333710000154
Figure BDA0003690333710000155
Figure BDA0003690333710000156
Figure BDA0003690333710000157
Figure BDA0003690333710000158
wherein k ref Road curvature, v, obtained for the reference path x And v y Respectively the longitudinal speed and the transverse speed of the vehicle mass center under a vehicle body coordinate system, l f And l r Respectively the distance from the vehicle's center of mass to the front and rear axes,
Figure BDA0003690333710000159
and e d Defined as tracking heading bias and tracking distance bias. F yf And F yr Front and rear wheel yaw forces, respectively, the small yaw angle being assumed such that F yf ＝C f α f ,F yr ＝-C r α r ；
Figure BDA00036903337100001510
Yaw rate of vehicle f And alpha r Respectively the slip angles of the front and rear wheels.
During the process of high-speed running or turning of the automobile, because the model of the tire presents strong nonlinear characteristics, the tire cornering stiffness is estimated based on a nonlinear Kalman filter, and the uncertain tire cornering stiffness is as follows:
Figure BDA0003690333710000161
gamma is used for designing and representing the nonlinear characteristic of the cornering stiffness, and the value range is between 0 and 1.
Quantity of state
Figure BDA0003690333710000162
Discretizing and linearizing the nonlinear equation by a Taylor-level expansion method and a forward Euler method to obtain:
Figure BDA0003690333710000163
constructing a new state space equation:
Figure BDA0003690333710000164
predicting future N based on state trajectories p Time epsilon (k + N) p ) While error e (k) is equal to x 0 (K+1)-A k x 0 (k)-B k u 0 (k) And performing real-time updating.
And (3) solving an objective function and optimization:
Figure BDA0003690333710000165
constraint conditions are as follows:
e max -w d ≤e d (k+i|k)≤-e min +w d 。
δ f,min ≤δ f (k+i|k)≤δ f,max 。
Δδ f,min ≤δ f (k+i|k)-δ f (k+i-1|k)≤Δδ f,max 。
Figure BDA0003690333710000166
in which i is taken from 1 to N p ，N p Is the prediction time domain in a model prediction algorithm, N c Is a control time domain in which the control signal is,
Figure BDA0003690333710000168
and Q d Respectively represent the output transverse error weight matrix, W f To control the incremental weight matrix, ε is the relaxation factor weight and s is the relaxation factor.
The traditional model prediction control adopts an SQP method to solve an inequality multi-constraint optimization problem, in order to better achieve a convergence effect and a quick calculation speed, the SQP is solved based on quick dual neural network optimization, and a sequence quadratic programming form is converted into a dual problem:
Figure BDA0003690333710000167
at this time, the expected front wheel turning angle delta is calculated and obtained through the model prediction optimization algorithm f 。
In the formula: Δ U is the control increment of the system. H is a weight matrix. min is the minimum value for solving the objective function. l min Is the minimum value of the constraint variable. l max Is the maximum value of the constraint variable. v and w are optimization variables of the dual problem.
Fifthly, turning a front wheel by a delta based on a driving robot-vehicle body dynamic model f And converting the torque into the torque required by a steering motor of the steering robot. The driving robot used in the invention is a fourth generation steering robot of a steam data center in Tianjin, the steering robot is fixed on a steering wheel through a three-claw transmission mode, an internal gear drives the steering wheel to rotate, and the simplified structural diagram of the driving robot and the automobile steering system is shown in figure 3. Calculating the torque required by the steering motor of the steering robot according to the following formula:
Figure BDA0003690333710000171
wherein i m Is the gear reduction ratio of the motor, i g For the transmission ratio between steering mechanism and steering wheel, T s Actual torque of steering shaft, T m To steer the output torque of the motor, J S 、B S 、K S The moment of inertia, the damping coefficient and the stiffness coefficient, theta, of the steering shaft S Is the angle the steering wheel is turned.
Assuming that the vehicle is a column type electric power steering system, the rotational inertia J of a power-assisted motor m Assuming measurable, the model of the gear tire module is as follows:
Figure BDA0003690333710000172
wherein T is a To assist the torque of the system, M W Moment of resistance to vehicle rotation, i s For pinion-to-tire axle pin ratio, J r Is the moment of inertia of the tire, B r Is the damping coefficient. B is m Is the damping coefficient of the booster motor.
Figure BDA0003690333710000173
Is the rate of change of the front wheel turning angle.
Figure BDA0003690333710000174
Is the rate of change of the front wheel steering speed.
From the above equation, the relationship T between the torque required for the steering mechanism and the front wheel steering angle can be obtained m ＝f(δ f ). Based on experience, in order to be quickly applied to the engineering field, a complex vehicle body model is simplified, a suspension and a complex transmission process are omitted, and the following relation is established between the front wheel steering angle and the steering mechanism output angle of the vehicle: delta f ＝f(u x )θ s And the method is used for comparing and verifying the accuracy of the mathematical model of the formula.
The required torque of the steering robot is output, the steering motor of the steering mechanism obtains a signal from an upper-layer controller, and then the steering wheel is controlled to complete the control of the vehicle, and a lower-layer control system is not taken as the discussion scope of the invention.
And step six, after the test is finished, the automobile obtains an initial position through a GPS and a camera and obtains a returned path through the path planning algorithm, and the automatic return work of the test site is realized based on improved model prediction control and lower control of the driving robot.
The above-mentioned embodiments are only for illustrating the technical ideas and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and to carry out the same, and the present invention shall not be limited to the embodiments, i.e. the equivalent changes or modifications made within the spirit of the present invention shall fall within the scope of the present invention.

Claims (9)

1. A robot driving vehicle obstacle avoidance method based on an 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 is combined with a repulsion function in the artificial potential field method and establishes an obstacle avoidance function model and a road boundary magnetic field model based on a driving speed and a road boundary, and the next-step operation track of a vehicle is obtained based on a model prediction control algorithm of a vehicle dynamic model; the upper control system comprises an MPC controller, and the MPC controller inputs the next operation track of the vehicle and the current state of the vehicle and outputs an 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.
2. A method of robotic vehicle obstacle avoidance based on modified artificial potential field and MPC as claimed in claim 1, wherein the method comprises the steps of:
step 1, installing a laser radar and a camera for monitoring the road environment condition and a positioning system for positioning the real-time position of a vehicle on the vehicle; leading the upper control system into 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 obstacle avoidance function model, the road boundary magnetic field model and the constraint of the control quantity, generating optimal track discrete points from the imported preset path through a QP optimization algorithm, and transmitting the track discrete points into the MPC controller;
step 4, establishing a vehicle dynamic 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 sequential quadratic programming problem; and based on the fast dual neural network, converting the sequence quadratic programming problem into a dual problem to optimize and solve, and calculating to obtain the expected course angle.
3. The method as claimed in claim 2, wherein in step 2, the vehicle is regarded as a mass point, and the obstacle is regarded as a quadrilateral, and the following obstacle avoidance function is constructed:
Figure FDA0003690333700000011
in the formula:
F obs,vehicle (X) represents a total repulsive force of an obstacle to which the vehicle is subjected;
eta is a direct proportionality coefficient;
d(x i ,x 0 ) Respectively Euclidean distances from the vehicle to four points of the quadrangle;
ρ is the maximum distance that the obstacle has an effect on the vehicle.
4. The method of claim 2, wherein in step 2, the road is divided into two regions, and the following road boundary magnetic field function is established:
Figure FDA0003690333700000021
in the formula:
F rep,edge repulsion forces on both sides of the road;
w edge is the weight coefficient of the repulsive force potential field;
d is the width of one area of the road;
y is the transverse position of the vehicle;
w is the general width of the vehicle body;
v x is the vehicle speed.
5. The robot-driven vehicle obstacle avoidance method based on the improved artificial potential field and the MPC as claimed in claim 2, wherein in step 3, the position signals of the obstacle and the vehicle are transmitted to the MPC planner, and a vehicle model is established by adopting a point mass model method; setting: x is the longitudinal position of the vehicle in the body coordinate system; y is the transverse position of the vehicle in the body coordinate system; x is the longitudinal position of the vehicle in the inertial coordinate system; y is the transverse position of the vehicle in the inertial coordinate system;
Figure FDA0003690333700000022
is the yaw angle of the vehicle;
Figure FDA0003690333700000023
selecting a state quantity of
Figure FDA0003690333700000024
Setting the control quantity u as a front wheel deflection angle delta; then there are:
Figure FDA0003690333700000025
in the formula:
Figure FDA0003690333700000026
the change rate of the longitudinal position of the vehicle under the self coordinate system is obtained;
Figure FDA0003690333700000027
the change rate of the transverse position of the vehicle under the self coordinate system is obtained;
Figure FDA0003690333700000028
the change rate of the transverse position of the vehicle under the inertial coordinate system is shown;
Figure FDA0003690333700000029
is the rate of change of the longitudinal position of the vehicle in the inertial frame;
xi is the newly built state quantity;
ξ i a change vector matrix in the ith rolling time domain;
Figure FDA00036903337000000210
is xi i The transposed matrix of (2);
H i a weight matrix for the ith reduced rolling time domain;
U i is the sum of all potential fields;
N p a prediction time domain in a rolling time domain;
J min is the minimum value of the cost function;
solving by QP optimization algorithm
Figure FDA0003690333700000031
Generating the optimal discrete points meeting the corresponding conditions, adopting a Bezier curve to perform curve fitting on the discrete points, and fitting the discrete pointsIs defined as the local path curve that the MPC needs to track and is passed into the MPC controller.
6. A method as claimed in claim 2, wherein in step 4, a vehicle dynamics model based on tire slip and road curvature is established as follows:
Figure FDA0003690333700000032
Figure FDA0003690333700000033
Figure FDA0003690333700000034
Figure FDA0003690333700000035
Figure FDA0003690333700000036
in the formula:
I z the moment of inertia of the vehicle in the z-axis direction;
m is the mass of the vehicle;
k ref road curvature obtained for the reference path;
v x the longitudinal speed of the mass center of the vehicle under the vehicle body coordinate system;
v y the transverse speed of the mass center of the vehicle under the vehicle body coordinate system;
l f the distance from the center of mass of the vehicle to the front axle;
l r from the centre of mass of the vehicle to the rear axleThe distance of (d);
Figure FDA0003690333700000037
tracking course error;
e d is the tracking distance error;
F xf is the vehicle front wheel longitudinal force;
F xr is the vehicle rear wheel longitudinal force;
F yf is a front wheel side biasing force;
F yr is a rear wheel side biasing force;
Figure FDA0003690333700000041
is the vehicle yaw rate.
7. A method as claimed in claim 6, wherein C is provided f Is vehicle front wheel cornering stiffness; c r Is vehicle rear wheel cornering stiffness; alpha is alpha f Is the slip angle of the front wheel; alpha is alpha r Is the slip angle of the rear wheel;
suppose F yf ＝C f α f ，F yr ＝-C r α r ；
Estimating the cornering stiffness of the tire based on a nonlinear Kalman filter, wherein the uncertain cornering stiffness of the tire has the following expression:
Figure FDA0003690333700000042
in the formula:
C f，0 a linear standard value of the cornering stiffness of the front wheel side of the vehicle;
γ f time-based variables for the front wheels;
Figure FDA0003690333700000043
is a front wheel yaw stiffness variable;
C r is rear wheel cornering stiffness;
C r，0 a linear standard value of the cornering stiffness of the rear wheel side of the vehicle;
γ r is a time-based variable for the rear wheel;
Figure FDA0003690333700000044
is a rear wheel cornering stiffness variable.
8. A method as claimed in claim 6, wherein in step 4, the state quantities are set
Figure FDA0003690333700000045
Discretizing and linearizing a nonlinear equation in the vehicle dynamics model through a Taylor-level expansion and a forward Euler method to obtain:
Figure FDA0003690333700000046
constructing a new state space equation:
Figure FDA0003690333700000047
predicting future N based on state trajectories p Time epsilon (k + N) p ) While error e (k) is equal to x 0 (k+1)-A k x 0 (k)-B k u 0 (k) Updating in real time;
in the formula:
a is a state quantity Jacobian matrix;
b is a control quantity Jacobian matrix;
Figure FDA0003690333700000048
the difference value of the vehicle state quantity conversion rate at the moment k +1 and the moment k;
Figure FDA0003690333700000049
the difference value of the vehicle state quantity at the moment k +1 and the moment k is obtained;
Figure FDA00036903337000000410
the difference value of the vehicle control quantity at the moment k +1 and the moment k is obtained;
N p a prediction time domain in a rolling time domain;
epsilon (k) is a new state space expression;
e (k) is an error expression;
u (k-1) is a control quantity at the time of k-1;
x 0 developing state quantities of the selected points for the Taylor stage;
A k a state quantity Jacobian matrix newly constructed at the moment k;
B k a control quantity Jacobian matrix newly constructed at the moment k;
k is the number of sampling steps;
ε(k+N p ) For future N p A state quantity and a control quantity at a time;
u 0 (k) the control quantity of the selected point is developed for the taylor stage at time k.
9. The method for avoiding the obstacle by the robot-driven vehicle based on the improved artificial potential field and the MPC as claimed in claim 8, wherein in step 4, the following objective function and constraint condition are established based on a model prediction optimization algorithm:
the objective function is:
Figure FDA0003690333700000051
the constraint conditions are as follows:
e max -w d ≤e d (k+i|k)≤-e min +w d ；
δ f，min ≤δ f (k+i|k)≤δ f，max ；
Δδ f，min ≤δ f (k+i|k)-δ f (k+i-1|k)≤Δδ f，max ；
Figure FDA0003690333700000052
in the formula:
J min tracking the minimum value of the objective function for the trajectory;
i is a sampling step length; 1,2, …, N p ；
N p Predicting a time domain for a model prediction algorithm;
N c is a control time domain;
Figure FDA0003690333700000053
is an output course error weight matrix;
Q d is an output distance error weight matrix;
w d defining a safety distance for the vehicle body in the driving process;
W f a control increment weight matrix;
ε is the relaxation factor weight;
s is a relaxation factor;
k is the number of sampling steps;
δ f is the vehicle front wheel corner;
e max tracking a maximum value of the lateral position deviation for the vehicle;
e min tracking a minimum value of lateral position deviation for the vehicle;
δ f，min the minimum value of the rotation angle of the front wheel of the vehicle;
δ f，max the maximum value of the rotation angle of the front wheel of the vehicle;
Δδ f，min is the minimum value of the vehicle front wheel steering angle increment;
Δδ f，max the maximum value of the increment of the front wheel steering angle of the vehicle;
Figure FDA0003690333700000061
is the minimum value of the vehicle yaw angle change rate;
Figure FDA0003690333700000062
is the maximum value of the vehicle yaw rate.
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CN115320709B (en) * 2022-08-29 2023-04-18 东风悦享科技有限公司 Automatic driving hybrid control method based on four-wheel steering

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