CN114454871A - Unmanned platform stable tracking control method for four-wheel independent drive - Google Patents

Unmanned platform stable tracking control method for four-wheel independent drive Download PDF

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CN114454871A
CN114454871A CN202210224502.7A CN202210224502A CN114454871A CN 114454871 A CN114454871 A CN 114454871A CN 202210224502 A CN202210224502 A CN 202210224502A CN 114454871 A CN114454871 A CN 114454871A
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unmanned platform
yaw
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李灏铧
马瀚森
陶立波
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W30/00—Purposes of road vehicle drive control systems not related to the control of a particular sub-unit, e.g. of systems using conjoint control of vehicle sub-units, or advanced driver assistance systems for ensuring comfort, stability and safety or drive control systems for propelling or retarding the vehicle
    • B60W30/02—Control of vehicle driving stability
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W10/00—Conjoint control of vehicle sub-units of different type or different function
    • B60W10/04—Conjoint control of vehicle sub-units of different type or different function including control of propulsion units
    • B60W10/08—Conjoint control of vehicle sub-units of different type or different function including control of propulsion units including control of electric propulsion units, e.g. motors or generators
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W10/00—Conjoint control of vehicle sub-units of different type or different function
    • B60W10/18—Conjoint control of vehicle sub-units of different type or different function including control of braking systems
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
    • B60W40/10—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to vehicle motion
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    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
    • B60W40/10—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to vehicle motion
    • B60W40/105—Speed
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    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
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    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
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    • B60W60/00—Drive control systems specially adapted for autonomous road vehicles
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    • B60W60/0018—Planning or execution of driving tasks specially adapted for safety by employing degraded modes, e.g. reducing speed, in response to suboptimal conditions
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    • B—PERFORMING OPERATIONS; TRANSPORTING
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    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W60/00—Drive control systems specially adapted for autonomous road vehicles
    • B60W60/001—Planning or execution of driving tasks
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    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0043—Signal treatments, identification of variables or parameters, parameter estimation or state estimation
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    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2520/00—Input parameters relating to overall vehicle dynamics
    • B60W2520/10—Longitudinal speed
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2520/00—Input parameters relating to overall vehicle dynamics
    • B60W2520/14—Yaw
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2710/00—Output or target parameters relating to a particular sub-units
    • B60W2710/08—Electric propulsion units
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2710/00—Output or target parameters relating to a particular sub-units
    • B60W2710/18—Braking system

Abstract

The invention discloses a stable tracking control method for an unmanned platform driven by four wheels independently, which is characterized in that when the longitudinal speed is constant, after the unmanned platform starts to track, the longitudinal speed continuously approaches to the expected longitudinal speed; in the process, the driving stability of the unmanned platform is judged by using the unmanned platform driving stability judging module, and when the unmanned platform is in a stable working condition, the track tracking is realized only by adopting a model prediction controller based on active front wheel steering; when the unmanned platform runs on a large-curvature road or at a high speed, the longitudinal torque controller based on hierarchical coordination intervenes to enable the brake control system to send out corresponding brake torque, so that the running stability of the unmanned platform is ensured, and the stable tracking of the unmanned platform driven by four wheels independently is realized. The invention can ensure the driving stability of the unmanned platform and realize the stable tracking of the unmanned platform track.

Description

Unmanned platform stable tracking control method for four-wheel independent drive
Technical Field
The invention relates to the technical field of automatic driving of automobiles, in particular to a stable tracking control method for an unmanned platform with four wheels driven independently.
Background
At present, the intelligent degree of the vehicle is higher and higher, and an automatic driving vehicle gradually appears. The automatic driving automobile becomes the focus of the modern automobile development, various advanced technologies are fused in the automatic driving automobile, so that the automobile can be safely driven in a non-driver state, the road safety is improved, the road efficiency is improved, and the traffic accident rate of the driver in dangerous behaviors is reduced. However, the advanced technology relates to a safety problem, and therefore, how to effectively ensure the driving stability of the unmanned platform to avoid traffic accidents caused by driving behaviors and reduce the harm brought by driving becomes a technical problem to be solved by the applicant.
Disclosure of Invention
The invention aims to provide a stable tracking control method for an unmanned platform with four wheels driven independently. The invention can ensure the driving stability of the unmanned platform and realize the stable tracking of the unmanned platform track.
The technical scheme of the invention is as follows: a stability tracking control method for an unmanned platform driven by four wheels independently comprises a model prediction controller based on active front wheel steering, a longitudinal moment controller based on hierarchical coordination and an unmanned platform driving stability judgment module;
when the longitudinal speed is constant, after the unmanned platform starts to track, the longitudinal speed of the unmanned platform continuously approaches to the expected longitudinal speed; in the process, the driving stability of the unmanned platform is judged by using the unmanned platform driving stability judging module, and when the unmanned platform is in a stable working condition, the track tracking is realized only by adopting a model prediction controller based on active front wheel steering; when the unmanned platform runs on a large-curvature road or at a high speed, the longitudinal torque controller based on hierarchical coordination intervenes to enable the brake control system to send out corresponding brake torque, so that the running stability of the unmanned platform is ensured, and the stable tracking of the unmanned platform driven by four wheels independently is realized.
According to the method for stably tracking and controlling the unmanned platform with four wheels driven independently, the driving stability judgment module of the unmanned platform comprises driving stability analysis and driving stability judgment;
the driving stability analysis is to obtain the beta-r phase tracks under the conditions of different vehicle speeds and road adhesion coefficients by setting the mass center slip angle and the yaw angular velocity of different initial values:
Figure BDA0003538729060000021
Figure BDA0003538729060000022
Figure BDA0003538729060000023
FY＝D sin(C arctan(Bη-E(Bη-arctanBη)+SV；
η＝α+Sh；
in the formula, beta is a centroid slip angle; r is a yaw angular velocity; fYFor lateral forces of the tire, FyfIs a front wheel lateral force, FyrIs the side force of the rear wheel; deltafIs a front wheel corner; v. ofxIs the vehicle longitudinal speed; v. ofyThe vehicle lateral speed; m is the vehicle mass; i isZIs the rotational inertia of the vehicle around the z-axis of the mass center, B is a rigidity factor, E is a curvature factor, C is a shape factor, eta is a lateral force combination variable, and SVIs the vertical offset of the curve, ShIs the horizontal offset of the curve; a is the distance of the centroid from the front axis;
drawing a beta-r phase trajectory stable domain based on a diamond method, wherein the stable domain is in a stable state when beta and r are in the stable domain, and the unstable state is shown when the beta and r are outside the stable domain;
and the driving stability judgment is to compare the obtained steady-state mass center slip angle and yaw rate with the actual mass center slip angle and yaw rate, if the actual value is higher than the steady-state value, the vehicle is in a destabilization state, and if the actual value is lower than the steady-state value, the vehicle is in a stable state.
In the method for controlling the stable tracking of the unmanned platform for four-wheel independent drive, the longitudinal moment controller based on hierarchical coordination obtains the difference between the yaw rate of the ideal two-degree-of-freedom vehicle model and the output yaw rate of the whole vehicle model, calculates the additional yaw moment required by adjusting the driving posture of the vehicle and improving the stability through a control algorithm, distributes the generated additional yaw moment and the driving moment of the motor to each wheel through a reasonable torque distribution algorithm, and realizes the instability trend of the direct yaw moment balancing vehicle through the driving moment difference between the wheels so that the vehicle tends to the ideal path to drive;
in an ideal two-degree-of-freedom vehicle model:
Figure BDA0003538729060000031
Figure BDA0003538729060000032
wherein a is the distance between the centroid and the front axis; b is the distance of the centroid from the rear axis; k is a radical offAnd krFront wheel and rear wheel cornering stiffness, respectively; mzIs a yaw moment; beta is the centroid slip angle, m is the vehicle mass, vxIs the vehicle longitudinal speed; v. ofyFor vehicle lateral speed, r yaw rate, deltafFor the angle of rotation of the front wheel, IZThe moment of inertia of the vehicle around the z-axis of the center of mass;
when the vehicle is in a steady state, the yaw angular velocity and the centroid slip angle are both constant values, so that
Figure BDA0003538729060000041
The desired yaw rate is calculated at this time as:
Figure BDA0003538729060000042
wherein L is the vehicle wheel base; k represents a stability factor;
defining the tracking error as er＝r-rdThen the handover function is defined as:
Figure BDA0003538729060000043
in the formula: c. CrRelative weight coefficient being error and error change rate
And (5) obtaining a derivative:
Figure BDA0003538729060000044
comparing the expected yaw velocity with the actual yaw velocity of the unmanned platform, designing a sliding mode surface of the unmanned platform, and further solving an additional yaw moment which ensures the stability:
Figure BDA0003538729060000045
distributing the obtained additional yaw moment to 4 wheels to ensure the stable running of the vehicle;
and proving the stability of the longitudinal torque controller based on hierarchical coordination, and defining a Lyapunov function:
Figure BDA0003538729060000046
the first derivative is obtained by calculating:
Figure BDA0003538729060000051
will be Δ MzSubstitution formula (8):
Figure BDA0003538729060000052
wherein: krControlling the approaching speed to the sliding mode surface;
because of Kr＞0，krIs greater than 0, so
Figure BDA0003538729060000057
The longitudinal torque controller based on hierarchical coordination is therefore stable.
According to the stable tracking control method for the four-wheel independent driving unmanned platform, according to the tire adhesion ellipse, the resultant force of the vehicle tires is far away from the adhesion edge, one tire force among the four wheels is close to the road adhesion limit, the tire force of the tire is controlled, and the target resultant force required by the whole vehicle is compensated by increasing the tire forces of the other three tires;
establishing an objective function:
Figure BDA0003538729060000053
in the formula: i is a front wheel or a rear wheel, and j is a left wheel or a right wheel; μ is the coefficient of adhesion;
because the wheel hub motor can only control the longitudinal force, then simplify to:
Figure BDA0003538729060000054
due to the fact that
Figure BDA0003538729060000055
r is the tire rolling radius, so the final objective function is:
Figure BDA0003538729060000056
the constraint conditions are as follows:
Tfl+Tfr+Trl+Trrt; formula (13)
Figure BDA0003538729060000061
In the formula, Tfl、Tfr、Trl、TrrRespectively representing the drive torque distributed to the front left, front right, rear left and rear right wheels, T representing the total drive torque required to maintain the desired speed, Δ MzThe system represents the additional yaw moment generated by the independent driving of four wheels due to different driving forces; d is the wheel track;
modifying formulae (8) and (9) to obtain:
Figure BDA0003538729060000062
Figure BDA0003538729060000063
formula (12):
Figure BDA0003538729060000064
t in pair formula (17)rl，TrrCalculating a partial derivative:
Figure BDA0003538729060000065
Figure BDA0003538729060000066
equation (18) and equation (19) equal zero, the minimum is found, i.e.:
Figure BDA0003538729060000071
Figure BDA0003538729060000072
substituting the formula (20) and the formula (21) for the formula (20) and the formula (16) to obtain TfrAnd Tfl(ii) a Meanwhile, the driving torque is limited by the output torque of the motor, and the following requirements are met:
Tij≤Tmax(ii) a And (4) formula (22).
In the stable tracking control method for the unmanned platform driven by four wheels independently, the track tracking realized by the model predictive controller based on active front wheel steering specifically comprises the following steps:
step 1, vehicle model establishment:
neglecting the influence of a suspension system and air resistance, neglecting transverse load transfer, assuming that the vehicle moves on a horizontal plane and has only two degrees of freedom of lateral direction and transverse swing, establishing a vehicle kinematic model,
Figure BDA0003538729060000073
Figure BDA0003538729060000074
in the formula (I), the compound is shown in the specification,
Figure BDA0003538729060000075
for the purpose of lateral vehicle speed,
Figure BDA0003538729060000076
is the longitudinal vehicle speed, u is the vehicle speed,
Figure BDA0003538729060000077
is the yaw angle, beta is the centroid slip angle;
from newton's second law, the vehicle dynamics model is:
Figure BDA0003538729060000078
Figure BDA0003538729060000079
Fyf＝-kfαf；
Fyr＝-krαr；
Figure BDA0003538729060000081
Figure BDA0003538729060000082
in the formula: m is vehicle mass, r is yaw rate, FyfIs a front wheel lateral force, FyrFor rear wheel lateral force, IZIs the moment of inertia of the vehicle around the z-axis of the center of mass, a is the distance of the center of mass from the front axis, b is the distance of the center of mass from the rear axis, kfAnd krSide cornering stiffness, δ, of the front and rear wheels, respectivelyfIs a front wheel corner; alpha is alphafIs a front wheel side slip angle, αrIs a rear wheel side slip angle;
the cornering stiffness of a tyre is related to the vertical load by:
Figure BDA0003538729060000083
Figure BDA0003538729060000084
in the formula: fzfFor vertical loading of the front wheels, FzrVertical loading for the rear wheels;
order to
Figure BDA0003538729060000085
Is a state variable of the vehicle, mu-deltaf(t) is a control variable which is,
Figure BDA0003538729060000086
for output quantity, a small angle hypothesis is adopted to obtain a state equation:
Figure BDA0003538729060000087
η(t)＝Ctx(t)；
in the formula: y (t) is the lateral displacement,
Figure BDA0003538729060000088
is a variable for yaw angle, r (t) is a variable for yaw rate, β (t) is a variable for centroid yaw; deltaf(t) is a variable of the front wheel turning angle,
Figure BDA0003538729060000089
is the derivative of the state quantity;
Figure BDA0003538729060000091
Figure BDA0003538729060000092
Ct＝[1 0 0 0；0 1 0 0]T；
step 2: model prediction control:
the method comprises the following steps of setting longitudinal vehicle speed to be constant, and establishing an unmanned platform trajectory tracking control system based on MPC model predictive control, wherein the method comprises the following steps:
s2.1: discretizing a continuous equation shown by the state equation to obtain:
x(k+1|t)＝Ak，tx(k|t)+Bk，tμ(k|t)；
η(k|t)＝Ck，tx(k|t)；
setting the prediction time domain of the MPC controller to be NpControl time domain as NcObtaining the output quantity eta (k | t) of the system in the prediction time domain, and continuously iterating the state equation to obtain the output quantity Y (k +1| t) in the prediction time domain:
Y(k+1|t)＝Ψk，tx(k|t)+Θk，tΔ(t)；
in the formula:
Figure BDA0003538729060000093
Figure BDA0003538729060000094
Figure BDA0003538729060000101
s2.2: establishing an objective optimization function:
the controlled system is in the control time domain NcThe objective optimization function in (1) is:
Figure BDA0003538729060000102
in the formula: j is an optimization function, epsilon is a relaxation factor, and rho means a relaxation factor weight coefficient;
the objective optimization function is transformed into a standard quadratic form:
Figure BDA0003538729060000103
due to the limitation of an actuating mechanism of the unmanned platform, parameters such as a front wheel deflection angle and a front wheel deflection angle increment need to be restrained:
Figure BDA0003538729060000104
in the formula: delta U is the variation of the front wheel turning angle; u is a front wheel corner; y iscIs soft constraint; y issIs a hard constraint; m is a state matrix of a constraint state equation;
converting the constraint expression into a constraint expression form which can be identified by quadratic programming:
Figure BDA0003538729060000105
solving the above formula to obtain a control input increment sequence in each control time domain:
Figure BDA0003538729060000111
and applying the solved first control increment to a vehicle control system to obtain the control quantity which needs to be applied to the system at the current moment.
Compared with the prior art, the unmanned platform driving stability judging module is used for judging the driving stability of the unmanned platform, and when the unmanned platform is in a stable working condition, the track tracking is realized only by adopting a model prediction controller based on active front wheel steering; when the unmanned platform runs on a large-curvature road or at a high speed, the longitudinal torque controller based on hierarchical coordination intervenes to enable the brake control system to send out corresponding brake torque, so that the running stability of the unmanned platform is ensured, and the stable tracking of the unmanned platform driven by four wheels independently is realized. The invention can ensure the driving stability of the unmanned platform and realize the stable tracking of the unmanned platform track.
Drawings
FIG. 1 is a schematic diagram of a communication network for an unmanned platform;
FIG. 2 is a schematic diagram of a trajectory tracking control algorithm framework of the present invention;
FIG. 3 is a schematic diagram of an envelope-based ride stability analysis module;
FIG. 4 is a schematic diagram of a stability determination module;
FIG. 5 is a schematic illustration of a vehicle dynamics model;
FIG. 6 is a schematic diagram of an MPC trajectory tracking control system;
FIG. 7 is a schematic diagram of a comparison of a driving trajectory of an unmanned platform with a reference trajectory;
FIG. 8 is a schematic diagram of the actual yaw angle of the unmanned platform compared to a reference yaw angle;
FIG. 9 is a schematic diagram of the actual yaw-rate versus the reference yaw-rate of the unmanned platform;
FIG. 10 is a schematic illustration of yaw rate versus lateral vehicle speed;
FIG. 11 is a graphical illustration of centroid slip angle velocity versus centroid slip angle.
Detailed Description
The invention is further illustrated by the following figures and examples, which are not to be construed as limiting the invention.
Example (b): a stable tracking control method for an unmanned platform driven by four wheels independently comprises the unmanned platform, as shown in figure 1, a hub motor control system, a brake system, a battery box, a whole VCU, an industrial personal computer and a 2.4G wireless remote controller are arranged in the unmanned platform, wherein the 2.4G wireless remote controller adopts a serial port communication mode to send/receive instructions, and other components send/receive the instructions through a CAN communication network. The industrial personal computer receives the state information of roads and vehicles obtained from the perception decision layer, receives other state information representing the real-time of the unmanned platform on the CAN network, calculates according to the information to finally obtain the corner and the longitudinal moment of the vehicles expected at the current moment, and sends the 2 instructions to the VCU of the whole vehicle through CAN communication; the VCU of the whole vehicle receives the corner and longitudinal moment commands of the vehicle expected at the current moment, sends the corresponding commands to the hub motor and the brake control system through the CAN network, and simultaneously receives the real-time state of the motor collected by the control system of the bottom actuating mechanism and sends the real-time state of the motor to the CAN network of the whole vehicle; the wheel hub motor control system, the brake system and the C-EPS-based steer-by-wire control system receive and follow the commands of the horizontal and longitudinal moments expected by the unmanned platform and sent by the VCU of the whole vehicle, so that the track tracking of the unmanned platform is realized, and meanwhile, the real-time motor state is sent to the VCU of the whole vehicle through the CAN network; the battery box sends the state of the battery in real time through the CAN network; the 2.4G wireless remote controller adopts a serial port communication mode, real-time control signals are sent to a complete vehicle VCU, the complete vehicle VCU judges and processes the control signals and sends the control signals to the MCU motor controller and the brake mechanism through the CAN bus, and the MCU motor controller and the brake mechanism execute corresponding actions after receiving corresponding control instructions, so that the functions of moving, steering, emergency stop and the like of the vehicle are realized.
In this embodiment, the calculation and decision of the unmanned platform stability tracking control method are performed in the vehicle VCU, as shown in fig. 2, the unmanned platform stability tracking control method includes a model prediction controller based on active front wheel steering, a longitudinal moment controller based on hierarchical coordination, and an unmanned platform driving stability determination module;
when the longitudinal speed is constant, after the unmanned platform starts to track, the longitudinal speed of the unmanned platform continuously approaches to the expected longitudinal speed; in the process, the driving stability of the unmanned platform is judged by using the unmanned platform driving stability judging module, and when the unmanned platform is in a stable working condition, the track tracking is realized only by adopting a model prediction controller based on active front wheel steering; when the unmanned platform runs on a large-curvature road or at a high speed, the longitudinal torque controller based on hierarchical coordination intervenes to enable the brake control system to send out corresponding brake torque, so that the running stability of the unmanned platform is ensured, and the stable tracking of the unmanned platform driven by four wheels independently is realized.
Specifically, the unmanned platform driving stability judging module comprises driving stability analysis and driving stability judgment;
under the influence of nonlinear external force, the vehicle is easy to be instable when running on a high-speed or low-adhesion road surface, and in order to ensure the running stability of the vehicle in the track tracking process, a stable limit envelope surface of the vehicle is determined firstly. The phase plane method is a common method for analyzing the stability of the vehicle, and the stability limit boundary of the vehicle can be determined by drawing a phase trajectory stability domain.
The centroid slip angle and the yaw rate are important parameters for studying the stability of the vehicle. The vehicle is easy to be unstable when running under a high-speed or low-attachment road surface, and the mass center slip angle can obviously reflect the stable state of the vehicle; with the gradual increase of the vehicle speed, the yaw rate also gradually increases, and the yaw rate can better reflect the control capability of the vehicle. And analyzing a beta-r phase trajectory stability region and a stability boundary of the vehicle by adopting a phase plane method, and providing a basis for the lateral stability constraint of the vehicle by the finally obtained value ranges of the front wheel side deflection angle and the rear wheel side deflection angle.
The vehicle speed and the road surface adhesion coefficient have important influence on the phase track stability boundary, the tire pressure of the tire is assumed to be kept constant in the simulation process, and the simulation control system shown in figure 3 is established by combining a vehicle model and a Pacejka magic tire model under a pure cornering condition. The driving stability analysis is to obtain the beta-r phase tracks under the conditions of different vehicle speeds and road adhesion coefficients by setting the mass center slip angle and the yaw angular velocity of different initial values:
Figure BDA0003538729060000141
Figure BDA0003538729060000142
Figure BDA0003538729060000143
FY＝D sin(C arctan(Bη-E(Bη-arctanBη)+SV；
η＝α+Sh；
in the formula, beta is a centroid slip angle; r is a yaw angular velocity; fYAs lateral force of the tire, FyfIs a front wheel lateral force, FyrIs the side force of the rear wheel; deltafIs a front wheel corner; v. ofxIs the vehicle longitudinal speed; v. ofyThe vehicle lateral speed; m is the vehicle mass; i isZIs a vehicleThe moment of inertia of the vehicle around the z-axis of the center of mass, B is a stiffness factor, E is a curvature factor, C is a shape factor, eta is a lateral force combination variable, and SVIs the vertical offset of the curve, ShIs the horizontal offset of the curve; a is the distance of the centroid from the front axis;
drawing a beta-r phase trajectory stable domain based on a diamond method, wherein the stable domain is in a stable state when beta and r are in the stable domain, and the unstable state is when the beta and r are outside the stable domain;
as shown in fig. 4, the steady-state centroid slip angle limit and yaw rate limit are determined by looking up a three-dimensional MAP according to the road adhesion coefficient, vehicle speed and 3 variables of front wheel steering angle. The actual mass center slip angle of the vehicle needs to be estimated through state to obtain a specific value, and the actual yaw rate can be obtained through yaw angle obtained by a sensor and calculated and estimated. And comparing the obtained steady-state mass center slip angle and yaw velocity with the actual mass center slip angle and yaw velocity, wherein if the actual value is higher than the steady-state value, the vehicle is in a destabilization state, and if the actual value is lower than the steady-state value, the vehicle is in a stable state.
The longitudinal moment controller based on hierarchical coordination obtains a difference value between the yaw velocity of an ideal two-degree-of-freedom vehicle model and the output yaw velocity of the whole vehicle model by comparing the yaw velocity with the output yaw velocity of the ideal two-degree-of-freedom vehicle model, calculates an additional yaw moment required for adjusting the driving posture of the vehicle and improving the stability by a control algorithm, distributes the generated additional yaw moment and the driving moment of a motor to each wheel by a reasonable torque distribution algorithm, and realizes the instability trend of a direct yaw moment balancing vehicle by the driving moment difference value among the wheels so that the vehicle tends to an ideal path to drive;
theoretically, system parameters or internal and external disturbances do not affect sliding mode movement, but under actual working conditions, due to the fact that time and space lag exists between inertia and state detection errors of the system or discontinuous switch characteristics, the sliding mode movement is accompanied by a buffeting phenomenon. The buffeting not only affects the stability of the system, but also consumes the energy of the system, but the buffeting is inevitable, and although the buffeting cannot be completely eliminated fundamentally, the amplitude of the buffeting can be reduced by thinking. And (3) weakening buffeting amplitude by adopting a constant-speed approach law, and calculating additional torque for ensuring stable running of the vehicle by establishing a sliding mode controller.
In an ideal two-degree-of-freedom vehicle model:
Figure BDA0003538729060000161
Figure BDA0003538729060000162
wherein a is the distance between the centroid and the front axis; b is the distance of the centroid from the rear axis; k is a radical offAnd krFront wheel and rear wheel cornering stiffness, respectively; mzIs a yaw moment; beta is the centroid slip angle, m is the vehicle mass, vxIs the vehicle longitudinal speed; v. ofyFor vehicle lateral speed, r yaw rate, deltafFor the angle of rotation of the front wheel, IZThe moment of inertia of the vehicle around the z-axis of the center of mass;
when the vehicle is in a steady state, the yaw angular velocity and the centroid slip angle are both constant values, so that
Figure BDA0003538729060000163
The desired yaw rate is calculated at this time as:
Figure BDA0003538729060000164
wherein L is the vehicle wheel base; k represents a stability factor;
defining the tracking error as er＝r-rdThen the handover function is defined as:
Figure BDA0003538729060000165
in the formula: c. CrThe relative weight coefficient of the error and the error change rate;
obtaining a derivative:
Figure BDA0003538729060000166
comparing the expected yaw velocity with the actual yaw velocity of the unmanned platform, designing a sliding mode surface of the unmanned platform, and further solving an additional yaw moment which ensures the stability:
Figure BDA0003538729060000167
distributing the obtained additional yaw moment to 4 wheels to ensure the stable running of the vehicle;
and proving the stability of the longitudinal torque controller based on hierarchical coordination, and defining a Lyapunov function:
Figure BDA0003538729060000171
the first derivative is obtained by calculating:
Figure BDA0003538729060000172
will be Δ MzSubstitution formula (8):
Figure BDA0003538729060000173
wherein: krControlling the approaching speed to the sliding mode surface;
because of Kr＞0，krIs greater than 0, so
Figure BDA0003538729060000174
The longitudinal torque controller based on hierarchical coordination is therefore stable.
The tire adhesion ellipse shows that the resultant force of the vehicle tires needs to be far away from the adhesion edge, one tire force among four wheels is close to the road adhesion limit, the tire force of the tire is controlled, and the target resultant force required by the whole vehicle is compensated by increasing the tire forces of other three tires;
establishing an objective function:
Figure BDA0003538729060000175
in the formula: i is a front wheel or a rear wheel, and j is a left wheel or a right wheel; μ is the coefficient of adhesion;
because the wheel hub motor can only control the longitudinal force, then simplify to:
Figure BDA0003538729060000181
due to the fact that
Figure BDA0003538729060000182
r is the tire rolling radius, so the final objective function is:
Figure BDA0003538729060000183
the constraint conditions are as follows:
Tfl+Tfr+Trl+Trr-T; formula (13)
Figure BDA0003538729060000184
In the formula, Tfl、Tfr、Trl、TrrRespectively representing the drive torque distributed to the front left, front right, rear left and rear right wheels, T representing the total drive torque required to maintain the desired speed, Δ MzThe system represents the additional yaw moment generated by the independent driving of four wheels due to different driving forces; d is the wheel track;
modifying formulae (8) and (9) to obtain:
Figure BDA0003538729060000185
Figure BDA0003538729060000186
formula (12):
Figure BDA0003538729060000187
t in pair formula (17)rl，TrrCalculating a partial derivative:
Figure BDA0003538729060000188
Figure BDA0003538729060000191
equation (18) and equation (19) equal zero, the minimum is found, i.e.:
Figure BDA0003538729060000192
Figure BDA0003538729060000193
substituting the formula (20) and the formula (21) for the formula (20) and the formula (16) to obtain TfrAnd Tfl(ii) a Meanwhile, the driving torque is limited by the output torque of the motor, and the following requirements are met:
Tij≤Tmax(ii) a And (4) formula (22).
The track tracking realized by the model predictive controller based on active front wheel steering specifically comprises the following steps:
step 1, vehicle model establishment:
as shown in fig. 5, to better reflect the vehicle kinematics and dynamics, the vehicle dynamics model is constructed assuming the effects of suspension system and air resistance are ignored, lateral load transfer is ignored, the vehicle is assumed to move in the horizontal plane and have only two degrees of freedom, lateral and yaw,
Figure BDA0003538729060000194
Figure BDA0003538729060000195
in the formula (I), the compound is shown in the specification,
Figure BDA0003538729060000196
for the purpose of lateral vehicle speed,
Figure BDA0003538729060000197
is the longitudinal vehicle speed, u is the vehicle speed,
Figure BDA0003538729060000198
is the yaw angle, beta is the centroid slip angle;
from newton's second law, the vehicle dynamics model is:
Figure BDA0003538729060000201
Figure BDA0003538729060000202
Fyf＝-kfαf；
Fyr＝-krαr；
Figure BDA0003538729060000203
Figure BDA0003538729060000204
in the formula: m is vehicle mass, r is yaw rate, FyfIs a front wheel lateral force, FyrFor rear wheel lateral force, IZIs the moment of inertia of the vehicle around the z-axis of the center of mass, a is the distance of the center of mass from the front axis, b is the distance of the center of mass from the rear axis, kfAnd krSide cornering stiffness, δ, of the front and rear wheels, respectivelyfIs a front wheel corner; alpha is alphafIs a front wheel side slip angle, αrIs a rear wheel side slip angle;
the cornering stiffness of a tyre is related to the vertical load by:
Figure BDA0003538729060000205
Figure BDA0003538729060000206
in the formula: fzfFor vertical loading of the front wheels, FZrVertical loading for the rear wheels;
order to
Figure BDA0003538729060000207
Is a state variable of the vehicle, mu-deltaf(t) is a control variable which is,
Figure BDA0003538729060000208
for output quantity, a small angle hypothesis is adopted to obtain a state equation:
Figure BDA0003538729060000209
η(t)＝Ctx(t)；
in the formula: y (t) is the lateral displacement,
Figure BDA00035387290600002010
is a variable of yaw angle, r (t) isA variable of yaw rate, β (t) being a variable of centroid yaw; deltaf(t) is a variable of the front wheel turning angle,
Figure BDA0003538729060000214
is the derivative of the state quantity;
Figure BDA0003538729060000211
Figure BDA0003538729060000212
Ct＝[1 0 0 0；0 1 0 0]T；
and 2, step: model prediction control:
setting the longitudinal vehicle speed to be constant, as shown in fig. 6, establishing an unmanned platform trajectory tracking control system based on MPC model predictive control, wherein the diagram comprises an automatic driving vehicle equivalent dynamic model, a vehicle transverse stability constraint and an MPC trajectory tracking controller, and the method comprises the following steps:
s2.1: discretizing a continuous equation shown by the state equation to obtain:
x(k+1|t)＝Ak，tx(k|t)+Bk，tμ(k|t)；
η(k|t)＝Ck，tx(k|t)；
setting the prediction time domain of the MPC controller to be NpControl time domain as NcObtaining the output quantity eta (k | t) of the system in the prediction time domain, and continuously iterating the state equation to obtain the output quantity Y (k +1| t) in the prediction time domain:
Y(k+1|t)＝Ψk，ix(k|t)+Θk，tΔU(t)；
in the formula:
Figure BDA0003538729060000213
Figure BDA0003538729060000221
Figure BDA0003538729060000222
s2.2: establishing an objective optimization function:
the controlled system is in the control time domain NcThe objective optimization function in (1) is:
Figure BDA0003538729060000223
in the formula: j is an optimization function, epsilon is a relaxation factor, and rho means a relaxation factor weight coefficient;
the objective optimization function is transformed into a standard quadratic form:
Figure BDA0003538729060000224
due to the limitation of an actuating mechanism of the unmanned platform, parameters such as a front wheel deflection angle and a front wheel deflection angle increment need to be restrained:
Figure BDA0003538729060000225
in the formula: delta U is the variation of the front wheel turning angle; u is a front wheel corner; y iscIs soft constraint; y issIs a hard constraint; m is a state matrix of a constraint state equation;
converting the constraint expression into a constraint expression form which can be identified by quadratic programming:
Figure BDA0003538729060000231
solving the above formula to obtain a control input increment sequence in each control time domain:
Figure BDA0003538729060000232
and applying the solved first control increment to the system to obtain the control quantity which needs to be applied to the system at the current moment.
Further, to verify the effectiveness of the present invention, the applicant performed track following on a double-traverse track on a dry asphalt pavement at a vehicle speed of 54km/h with an average adhesion coefficient of 0.5 on a wet dirt pavement.
Fig. 7 is a designed control lateral displacement following simulation result diagram, and it can be seen from the diagram that the designed controller has high lateral displacement trajectory tracking accuracy at a vehicle speed of 54km/h, when the vehicle follows to 75-79m, the maximum lateral displacement deviation is 0.23m, and for analysis reasons, the vehicle is on a low-adhesion road surface, and the reference trajectory curvature changes rapidly, however, the generated deviations are all within 0.25m, and the designed controller has certain robustness for the vehicle speed and the road surface adhesion coefficient and good lateral displacement tracking accuracy by combining the high-adhesion road surface simulation result.
8-9 are diagrams of track following and yaw rate simulation results of the designed controller at a vehicle speed of 54km/h, and it can be known from the diagrams that the designed controller has a relatively low real-time following performance of the yaw angle and the yaw rate at the vehicle speed of 54km/h, and in the following process, the output curve of the yaw angle and the yaw rate is very smooth, and has no surge or irregular buffeting phenomenon, and can rapidly converge to 0 along with the reference value when tracking to 100m, which indicates that the vehicle yaw output is very stable in the track following process, the yaw stability is relatively good, the maximum value of the yaw output is 0.315rad, and the maximum value of the yaw output is 0.377 rad/s.
FIG. 10 is a side vehicle speed v at the controlled vehicle centroid at a vehicle speed of 54km/hyAnd a plane diagram of a track corresponding to the yaw angular velocity omega, wherein the lower the vehicle speed is, the more stable the vehicle runs, which accords with the same actual rule, and the ranges of the vehicle and the stable area are all within the range of the stable area, and finally all the vehicle can be converged to the stable origin. FIG. 11 shows the centroid of the controlled vehicle at 54km/hSlip angle beta and centroid slip angular velocity
Figure BDA0003538729060000241
And as can be seen from the phase locus plan, as the vehicle speed increases, the phase locus range is gradually reduced, and the phase loci are all in the stable region and can finally converge to the stable origin.
In conclusion, the driving stability of the unmanned platform is judged by the unmanned platform driving stability judging module, and when the unmanned platform is in a stable working condition, the track tracking is realized only by adopting a model prediction controller based on active front wheel steering; when the unmanned platform runs on a large-curvature road or at a high speed, the longitudinal torque controller based on hierarchical coordination intervenes to enable the brake control system to send out corresponding brake torque, so that the running stability of the unmanned platform is ensured, and the stable tracking of the unmanned platform driven by four wheels independently is realized. The invention can ensure the driving stability of the unmanned platform and realize the stable tracking of the unmanned platform track.

Claims (5)

1. A stable tracking control method for an unmanned platform driven by four wheels independently is characterized by comprising the following steps: the system comprises a model prediction controller based on active front wheel steering, a longitudinal torque controller based on hierarchical coordination and an unmanned platform driving stability judgment module;
when the longitudinal speed is constant, after the unmanned platform starts to track, the longitudinal speed of the unmanned platform continuously approaches to the expected longitudinal speed; in the process, the driving stability of the unmanned platform is judged by using the unmanned platform driving stability judging module, and when the unmanned platform is in a stable working condition, the track tracking is realized only by adopting a model prediction controller based on active front wheel steering; when the unmanned platform runs on a large-curvature road or at a high speed, the longitudinal torque controller based on hierarchical coordination intervenes to enable the brake control system to send out corresponding brake torque, so that the running stability of the unmanned platform is ensured, and the stable tracking of the unmanned platform driven by four wheels independently is realized.
2. The unmanned aerial vehicle platform stable tracking control method for four-wheel independent drive according to claim 1, characterized in that: the unmanned platform driving stability judging module comprises driving stability analysis and driving stability judgment;
the driving stability analysis is to obtain the beta-r phase tracks under the conditions of different vehicle speeds and road adhesion coefficients by setting the mass center slip angle and the yaw angular velocity of different initial values:
Figure FDA0003538729050000011
Figure FDA0003538729050000012
Figure FDA0003538729050000021
FY＝Dsin(Carctan(Bη-E(Bη-arctanBη)+SV；
η＝α+Sh；
in the formula, beta is a centroid slip angle; r is a yaw angular velocity; fYFor lateral forces of the tire, FyfIs a front wheel lateral force, FyrIs the side force of the rear wheel; deltafIs a front wheel corner; v. ofxIs the vehicle longitudinal speed; v. ofyThe vehicle lateral speed; m is the vehicle mass; i isZIs the rotational inertia of the vehicle around the z-axis of the mass center, B is a rigidity factor, E is a curvature factor, C is a shape factor, eta is a lateral force combination variable, and SVIs the vertical offset of the curve, ShIs the horizontal offset of the curve; a is the distance of the centroid from the front axis;
drawing a beta-r phase trajectory stable domain based on a diamond method, wherein the stable domain is in a stable state when beta and r are in the stable domain, and the unstable state is shown when the beta and r are outside the stable domain;
and the driving stability judgment is to compare the obtained steady-state mass center slip angle and yaw rate with the actual mass center slip angle and yaw rate, if the actual value is higher than the steady-state value, the vehicle is in a destabilization state, and if the actual value is lower than the steady-state value, the vehicle is in a stable state.
3. The unmanned aerial vehicle platform stable tracking control method for four-wheel independent drive according to claim 1, characterized in that: the longitudinal moment controller based on hierarchical coordination obtains a difference value between the yaw velocity of an ideal two-degree-of-freedom vehicle model and the output yaw velocity of the whole vehicle model by comparing the yaw velocity with the output yaw velocity of the ideal two-degree-of-freedom vehicle model, calculates an additional yaw moment required for adjusting the driving posture of the vehicle and improving the stability by a control algorithm, distributes the generated additional yaw moment and the driving moment of a motor to each wheel by a reasonable torque distribution algorithm, and realizes the instability trend of a direct yaw moment balancing vehicle by the driving moment difference value among the wheels so that the vehicle tends to an ideal path to drive;
in an ideal two-degree-of-freedom vehicle model:
Figure FDA0003538729050000035
Figure FDA0003538729050000031
wherein a is the distance between the centroid and the front axis; b is the distance of the centroid from the rear axis; k is a radical offAnd krFront wheel and rear wheel cornering stiffness, respectively; mzA yaw moment; beta is the centroid slip angle, m is the vehicle mass, vxIs the vehicle longitudinal speed; v. ofyFor vehicle lateral speed, r yaw rate, deltafFor the angle of rotation of the front wheel, IZThe moment of inertia of the vehicle around the z-axis of the center of mass;
when the vehicle is in a steady state, the yaw angular velocity and the centroid slip angle are both constant values, so that
Figure FDA0003538729050000032
The desired yaw rate is calculated at this time as:
Figure FDA0003538729050000033
wherein L is the vehicle wheel base; k represents a stability factor;
defining a tracking error as er＝r-rdThen the handover function is defined as:
Figure FDA0003538729050000034
in the formula: c. CrThe relative weight coefficient of the error and the error change rate;
and (5) obtaining a derivative:
Figure FDA0003538729050000041
comparing the expected yaw velocity with the actual yaw velocity of the unmanned platform, designing a sliding mode surface of the unmanned platform, and further solving an additional yaw moment which ensures the stability:
Figure FDA0003538729050000042
distributing the obtained additional yaw moment to 4 wheels to ensure the stable running of the vehicle;
and proving the stability of the longitudinal torque controller based on hierarchical coordination, and defining a Lyapunov function:
Figure FDA0003538729050000043
the first derivative is obtained by calculating:
Figure FDA0003538729050000044
will be Δ MzSubstitution formula (8):
Figure FDA0003538729050000045
Figure FDA0003538729050000051
wherein: krControlling the approaching speed to the sliding mode surface;
because k isr＞0，krIs greater than 0, so
Figure FDA0003538729050000052
The longitudinal torque controller is therefore stabilized based on hierarchical coordination.
4. The unmanned aerial vehicle platform stable tracking control method for four-wheel independent drive according to claim 3, characterized in that: according to the tire adhesion ellipse, the resultant force of the vehicle tires is far away from the adhesion edge, one tire force among four wheels is close to the road adhesion limit, the tire force of the tire is controlled, and the target resultant force required by the whole vehicle is compensated by increasing the tire forces of other three tires;
establishing an objective function:
Figure FDA0003538729050000053
in the formula: i is the front wheel or the rear wheel, j is the left wheel or the right wheel, and mu is the adhesion coefficient;
because the wheel hub motor can only control the longitudinal force, then simplify to:
Figure FDA0003538729050000054
due to the fact that
Figure FDA0003538729050000055
r is the tire rolling radius, so the final objective function is:
Figure FDA0003538729050000056
the constraint conditions are as follows:
Figure FDA0003538729050000061
Figure FDA0003538729050000062
in the formula, Tfl、Tfr、Trl、TrrRespectively representing the drive torque distributed to the front left, front right, rear left and rear right wheels, T representing the total drive torque required to maintain the desired speed, Δ MzThe system represents the additional yaw moment generated by the independent driving of four wheels due to different driving forces; d is the wheel track;
modifying the formula (8) and the formula (9) to obtain:
Figure FDA0003538729050000063
Figure FDA0003538729050000064
formula (12):
Figure FDA0003538729050000065
t in pair formula (17)rl，TrrCalculating a partial derivative:
Figure FDA0003538729050000066
Figure FDA0003538729050000067
equation (18) and equation (19) equal zero, the minimum is found, i.e.:
Figure FDA0003538729050000071
Figure FDA0003538729050000072
by substituting formula (20) and formula (21) for formula (20) and formula (16), T is obtainedfrAnd Tfl(ii) a Meanwhile, the driving torque is limited by the output torque of the motor, and the following requirements are met:
Tij≤Tmax(ii) a And (4) formula (22).
5. The unmanned aerial vehicle platform stable tracking control method for four-wheel independent drive according to claim 1, characterized in that: the track tracking realized by the model predictive controller based on active front wheel steering specifically comprises the following steps:
step 1, vehicle model establishment:
neglecting the influence of a suspension system and air resistance, neglecting transverse load transfer, assuming that the vehicle moves on a horizontal plane and has only two degrees of freedom of lateral direction and transverse swing, establishing a vehicle kinematic model:
Figure FDA0003538729050000073
Figure FDA0003538729050000074
in the formula (I), the compound is shown in the specification,
Figure FDA0003538729050000075
for the purpose of lateral vehicle speed,
Figure FDA0003538729050000076
is the longitudinal vehicle speed, u is the vehicle speed,
Figure FDA0003538729050000077
is the yaw angle, beta is the centroid slip angle;
from newton's second law, the vehicle dynamics model is:
Figure FDA0003538729050000081
Figure FDA0003538729050000082
Fyf＝-kfαf；
Fyr＝-krαr；
Figure FDA0003538729050000083
Figure FDA0003538729050000084
in the formula: m is vehicle mass, r is yaw rate, FyfIs a front wheel lateral force, FyrFor rear wheel lateral force, IZIs the moment of inertia of the vehicle around the z-axis of the center of mass, a is the distance of the center of mass from the front axis, b is the distance of the center of mass from the rear axis, kfAnd krSide cornering stiffness, δ, of the front and rear wheels, respectivelyfIs a front wheel corner; alpha is alphafIs a front wheel side slip angle, αrIs a rear wheel side slip angle;
the cornering stiffness of a tyre is related to the vertical load by:
Figure FDA0003538729050000085
Figure FDA0003538729050000086
in the formula: fzfFor vertical loading of the front wheels, FzrVertical loading for the rear wheels;
order to
Figure FDA0003538729050000091
Is a state variable of the vehicle,
μ＝δf(t) is a control variable which is,
Figure FDA0003538729050000092
for output quantity, a small angle hypothesis is adopted to obtain a state equation:
Figure FDA0003538729050000093
η(t)＝Ctx(t)；
in the formula: y (t) is the lateral displacement,
Figure FDA0003538729050000094
is a variable for yaw angle, r (t) is a variable for yaw rate, β (t) is a variable for centroid yaw; deltaf(t) at the angle of rotation of the front wheelThe variables are the variables of the process,
Figure FDA0003538729050000095
is the derivative of the state quantity;
Figure FDA0003538729050000096
Figure FDA0003538729050000097
Ct＝[1 0 0 0；0 1 0 0]T；
step 2: model prediction control:
the method comprises the following steps of setting longitudinal vehicle speed to be constant, and establishing an unmanned platform trajectory tracking control system based on MPC model predictive control, wherein the method comprises the following steps:
s2.1, discretizing a continuous equation shown by a state equation to obtain:
x(k+1|t)＝Ak，tx(k|t)+Bk，tμ(k|t)；
η(k|t)＝Ck，tx(k|t)；
setting the prediction time domain of the MPC controller to be NpControl time domain as NcObtaining the output quantity eta (k + t) of the system in the prediction time domain, and continuously iterating the state equation to obtain the output quantity Y (k +1| t) in the prediction time domain:
Y(k+1|t)＝Ψk，tx(k|t)+Θk，tΔU(t)；
in the formula:
Figure FDA0003538729050000101
Figure FDA0003538729050000102
Figure FDA0003538729050000103
s2.2, establishing an objective optimization function:
the controlled system is in the control time domain NcThe objective optimization function in (1) is:
Figure FDA0003538729050000111
in the formula: j is an optimization function, epsilon is a relaxation factor, and rho means a relaxation factor weight coefficient;
the objective optimization function is transformed into a standard quadratic form:
Figure FDA0003538729050000112
due to the limitation of an actuating mechanism of the unmanned platform, parameters such as a front wheel deflection angle and a front wheel deflection angle increment need to be restrained:
Figure FDA0003538729050000113
in the formula: delta U is the variation of the front wheel turning angle; u is a front wheel corner; y iscIs soft constraint; y issIs a hard constraint; m is a state matrix of a constraint state equation;
converting the constraint expression into a constraint expression form which can be identified by quadratic programming:
Figure FDA0003538729050000115
solving the above formula to obtain a control input increment sequence in each control time domain:
Figure FDA0003538729050000114
and applying the solved first control increment to a vehicle control system to obtain the control quantity which needs to be applied to the system at the current moment.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115195860A (en) * 2022-07-29 2022-10-18 中国第一汽车股份有限公司 Vehicle steering control method and device, storage medium, processor and vehicle
CN115635485A (en) * 2022-11-09 2023-01-24 苏州智康机器人有限公司 Real-time human-computer interaction force control method of mobile rehabilitation robot

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115195860A (en) * 2022-07-29 2022-10-18 中国第一汽车股份有限公司 Vehicle steering control method and device, storage medium, processor and vehicle
CN115635485A (en) * 2022-11-09 2023-01-24 苏州智康机器人有限公司 Real-time human-computer interaction force control method of mobile rehabilitation robot
CN115635485B (en) * 2022-11-09 2024-03-15 嘉兴智康机器人有限公司 Real-time human-computer interaction force control method of mobile rehabilitation robot

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