CN115563694B - Vehicle dynamics model precision evaluation method based on prediction time domain error - Google Patents
Vehicle dynamics model precision evaluation method based on prediction time domain error Download PDFInfo
- Publication number
- CN115563694B CN115563694B CN202211051623.2A CN202211051623A CN115563694B CN 115563694 B CN115563694 B CN 115563694B CN 202211051623 A CN202211051623 A CN 202211051623A CN 115563694 B CN115563694 B CN 115563694B
- Authority
- CN
- China
- Prior art keywords
- vehicle
- time domain
- prediction
- model
- state
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000011156 evaluation Methods 0.000 title claims abstract description 33
- 238000005070 sampling Methods 0.000 claims abstract description 23
- 238000012360 testing method Methods 0.000 claims description 19
- 238000004088 simulation Methods 0.000 claims description 16
- 238000000034 method Methods 0.000 claims description 12
- 238000013210 evaluation model Methods 0.000 abstract 1
- 230000033001 locomotion Effects 0.000 description 11
- 238000004364 calculation method Methods 0.000 description 5
- 238000007796 conventional method Methods 0.000 description 3
- 238000005457 optimization Methods 0.000 description 3
- 239000000725 suspension Substances 0.000 description 3
- 238000013461 design Methods 0.000 description 2
- 238000005096 rolling process Methods 0.000 description 2
- 230000001133 acceleration Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004422 calculation algorithm Methods 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000011217 control strategy Methods 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 238000013016 damping Methods 0.000 description 1
- 238000012938 design process Methods 0.000 description 1
- 230000005484 gravity Effects 0.000 description 1
- 230000007774 longterm Effects 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Computer Hardware Design (AREA)
- General Engineering & Computer Science (AREA)
- Evolutionary Computation (AREA)
- Aviation & Aerospace Engineering (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Automation & Control Theory (AREA)
- Steering Control In Accordance With Driving Conditions (AREA)
Abstract
The invention relates to a vehicle dynamics model precision evaluation method based on errors in a prediction time domain, which is characterized in that a continuous vehicle dynamics model is discretized, only one prediction time domain is simulated at each sampling time according to a set prediction time domain, a sampling period and a given control amount time sequence, and the prediction precision of an error evaluation model between the output and true values of the vehicle model in the prediction time domain in a nonlinear model prediction controller is realized according to the prediction precision of the model, so that the problem that the model evaluation method based on the global errors can not reflect the model prediction precision of the vehicle dynamics model in an NMPC controller is solved, and the selection basis of the vehicle dynamics model, the prediction time domain and the sampling period is provided for an NMPC controller designer.
Description
Technical Field
The invention belongs to the technical field of automobile dynamics and the field of model predictive control, and particularly relates to a vehicle dynamics model precision evaluation method based on errors in a prediction time domain.
Background
The nonlinear model predictive control (Nonlinear Model Predictive Control), namely a nonlinear predictive model, is called NMPC for short, is a closed-loop optimization control strategy based on the nonlinear model, and is an effective means for solving the vehicle control problem. However, when the NMPC controller controls the vehicle, the model is required to be simple enough to meet the real-time performance of control, and accurate enough to ensure the validity of the control sequence solved by the optimization algorithm. Therefore, the vehicle dynamics model is evaluated by using an effective means, and is important for the realization of the NMPC controller.
At present, in the field of nonlinear model predictive control, a model precision evaluation method based on global errors in the traditional vehicle dynamics field is used, namely continuous model output under actual measurement input data is compared with real output, a smaller step length is generally set for continuous vehicle dynamics models during simulation comparison, and global error comparison in the whole simulation time period is carried out. However, when predicting, the NMPC controller needs to discretize the dynamics model and find a displayed iteration equation to perform larger-step approximate solution on the differential equation, and the NMPC controller is concerned about predicting the prediction accuracy of the model in the time domain, rather than the global error. Therefore, the model accuracy evaluation method of the global error of the continuous model focuses on the long-time simulation accuracy of the continuous model, cannot evaluate the discretized and short-time-domain model accuracy in the NMPC, and has quite large limitations.
Disclosure of Invention
The invention aims to provide a vehicle dynamics model precision evaluation method based on errors in a prediction time domain, which solves the problem of quantitative calculation of the steering stability of an automobile design simulation analysis stage.
The aim of the invention is realized by the following technical scheme:
a vehicle dynamics model precision evaluation method based on prediction time domain errors comprises the following steps:
step one, measuring and testing parameters of a real vehicle
According to the controlled target vehicle, each structural parameter of the target vehicle is measured, then a vehicle test of corresponding typical working conditions is carried out, and after the test is finished, the time sequence of the state quantity and the control quantity in the test is recorded. The state variables X include, but are not limited to, lateral velocity, yaw rate, longitudinal velocity, roll angle velocity, and front and rear wheel angular velocity. The control amount time series includes, but is not limited to, the front wheel steering angle, the drive torque, and the brake torque. Typical operating conditions include, but are not limited to, steering wheel sinusoidal input tests, steering wheel step input tests.
Step two, constructing a vehicle dynamics model as follows:
in the formula (1), X is a state variable;for the derivative of X, f is a relational expression for the state variable value;
discretizing the vehicle dynamics model, namely obtaining an iterative equation of n+1 time relative to n time by adopting a formula (2) for a differential equation shown in the formula (1):
X n+1 ＝X n +T·f(X n ,U n ) (2)
x in formula (2) n As state variable at time n, X n+1 The state variable is the state variable at the time of n+1, and T is the sampling period;
setting a simulation evaluation working condition, a sampling period T and a prediction time domain N in the NMPC controller p Wherein the prediction time domain is a positive integer multiple of the sampling period;
step five, giving a control quantity time sequence in a prediction time domain after the starting time t and the vehicle state;
step six, simulating a prediction time domain through the vehicle dynamics model in the formula (2) to obtain a prediction result X of the vehicle state p The method comprises the steps of carrying out a first treatment on the surface of the Repeating the fourth step, and giving a vehicle state at the time t+T and a control quantity time sequence in a prediction time domain until a termination condition t=N is reached, wherein N is the termination time and is a positive integer multiple of a sampling period T;
step seven, predicting result X of vehicle state p And vehicle state X as true value real Comparing, calculating the absolute value X of the state single point error error ＝|X p -X real I, and counting the average value and variance of the errors;if the state error is within the allowable range, the vehicle dynamics model, the corresponding sampling period and the predicted time domain parameter can be used for designing an NMPC controller, and if the state error is not within the allowable range, the parameters are required to be adjusted.
Further, the state variables X include lateral velocity, yaw rate, longitudinal velocity, roll angle velocity, and front and rear wheel angular velocity.
Further, the control quantity time sequence comprises a front wheel rotation angle, a driving moment and a braking moment.
Further, the typical working conditions include a steering wheel sine input test and a steering wheel step input test.
Still another object of the present invention is to provide a system for evaluating accuracy of a model of vehicle dynamics in a prediction time domain based on a nonlinear prediction model, comprising:
a coordinate system acquisition module; the method comprises the steps of acquiring a vehicle coordinate system, a tire coordinate system, a geographic coordinate system and a tire model;
the force and moment balance motion equation building module; the system is used for carrying out stress analysis on the vehicle when the vehicle runs at a fixed speed, and establishing a force and moment balance motion equation according to the vehicle coordinate system;
a vehicle suspension characteristic parameter acquisition module; the method comprises the steps of acquiring vehicle suspension characteristic parameters when the vehicle runs along a curve;
a vehicle dynamics model building module; the method comprises the steps of establishing a vehicle dynamics model according to the tire coordinate system, the force and moment balance motion equation and vehicle suspension characteristic parameters;
a vehicle dynamics model discretization module; the method comprises the steps of discretizing a vehicle dynamics model to obtain an iteration equation;
a simulation module; the method comprises the steps of firstly selecting a simulation evaluation working condition, setting a sampling period and a prediction time domain in an NMPC controller, then giving a starting time t the vehicle state and a control quantity time sequence in a prediction time domain after the t time, and simulating a prediction time domain through a discretized vehicle dynamics model;
a computing module; and comparing the predicted result of the vehicle state with the vehicle state serving as a true value, calculating the absolute value of the single-point error of the state, and counting the average value and the variance of the error.
The beneficial effects are as follows:
according to the vehicle dynamics model precision evaluation method provided by the invention, the continuous vehicle dynamics model is discretized, only one prediction time domain is simulated at each sampling time according to the set prediction time domain, the sampling period and the given control quantity time sequence, the error between the vehicle model state output and the true value in the prediction time domain is calculated, and the prediction precision of the model in the NMPC controller is evaluated according to the error. The evaluation method solves the problem that the traditional model precision evaluation method based on global errors can not reflect the evaluation of model prediction precision of the vehicle dynamics model in the NMPC controller, and can provide the selection basis of the vehicle dynamics model, the prediction time domain and the sampling period for the NMPC controller designer, thereby reducing the time and the cost of the controller design.
Drawings
FIG. 1 is a flow chart of a vehicle dynamics model accuracy evaluation method based on errors in a prediction time domain;
FIG. 2 is a control amount input time series for model evaluation in example 1 of the present invention;
FIG. 3 is a model evaluation result based on an error in a prediction horizon and a comparison with a conventional model evaluation result based on a global error in example 1 of the present invention (taking a yaw rate as an example, the following is the same);
FIG. 4 is an evaluation of prediction accuracy of a model under different prediction time domains in embodiment 1 of the present invention;
fig. 5 is an evaluation of prediction accuracy of the model at different sampling periods in embodiment 1 of the present invention.
Detailed Description
Example 1 accuracy evaluation was performed on a six degree of freedom vehicle dynamics model built with reference to a certain type of two-axis commercial vehicle.
And step one, measuring vehicle structural parameters.
Measuring a controlled vehicle, acquiring structural parameters such as the mass, the mass center position, the rotational inertia, the transverse and longitudinal mechanical properties of the tire and the like of the vehicle, performing a corresponding steering wheel sine input test, and recording time sequences of state quantity and control quantity in the test after the test is finished. In this embodiment, the simulation vehicle test is performed by inputting the real vehicle structural parameters into the truckim software, and the time sequence of the corresponding control quantity and state quantity is obtained.
And step two, building a vehicle dynamics model.
2.1 six-degree-of-freedom continuous dynamics model construction of automobile
According to basic dynamic characteristics of plane motion of a commercial vehicle, a six-degree-of-freedom continuous dynamic model differential equation comprising longitudinal motion, lateral motion, yaw motion around a Z axis, roll motion around an X axis and front and rear wheel rotation motion in the X, Y axis direction in a vehicle coordinate system is established, and is shown in a formula (3):
wherein v is x ,v y The mass center of the sprung mass is longitudinal and lateral; omega z Yaw rate for the sprung mass;is the roll angle. g is gravity acceleration; m is m s Is the sprung mass, m uf Is the front; i x ,I z Moment of inertia for sprung mass roll and yaw; r is R e The rolling radius of the wheel; a is the distance from the mass center to the front axle; b is the center of mass to rear axis distance; h is the distance from the sprung mass centroid to the center of rotation; h is a f ,h r Distance from sprung mass center to rotation center; t (T) di Is the external moment acting on each wheel; the front and rear wheels are simplified into two wheels, I wf ，I wr For the moment of inertia of the front and rear wheels, T df ，T dr Is an external moment acting on front and rear wheels; f (F) xf ,F xr Longitudinal force for ground facing front and rear wheels; sigma M z ＝F yf ·a+F yr ·b；m uf ,m ur Is the front and rear unsprung mass;for simplicity of the equivalent stiffness and damping of the rear and front axles.
2.2 calculation of longitudinal and lateral tire forces of front and rear wheels. In the case, the influence of the camber angle and the correcting moment of the wheel is ignored, and the longitudinal force and the lateral force of the tire are calculated by using the Pacejka89 model. Longitudinal force F under pure slip x0 Pure lateral deflection downward force F y0 The calculations of (1) are shown in formulas (8) - (9):
F x0 ＝D x sin(C x arctan(B x ·x 1 -E x (B x x 1 -arctan(B x ·x 1 )))) (8)
F y0 ＝D y sin(C y arctan(B y ·x 2 -E y (B y x 2 -arctan(B y ·x 2 )))) (9)
calculating a tire slip ratio using a tire slip ratio model suitable for all conditions, as shown in formula (3):
wherein S is the slip ratio of the tire slip ratio; omega w Is the rotational angular velocity of the wheel; r is R e The rolling radius of the wheel; v xw Is the wheel center longitudinal velocity in the plane of the wheel.
In order to cope with the situations of large tire slip angle and wheel backward, the uniform slip angle model of the formula (11) can be adopted to express the slip angle calculation of the tire under all working conditions
Wherein alpha is the tire slip angle; v yw Is the wheel center lateral velocity in the plane of the wheel.
In order to fully describe the transverse and longitudinal coupling dynamics of the automobile, the mixing slip characteristic of the tire, namely the 'attaching ellipse' relation between the tire and the ground, is fully considered, and the specific calculation mode of the tire force under the mixing slip working condition is shown as a formula (12).
2.3 discretization of vehicle dynamics model:
discretizing the continuous vehicle dynamics model represented by the formula (12) by adopting a one-step Euler method represented by the formula (2) to obtain an iterative equation of n+1 time relative to n time:
step three, simulation in prediction time domain of discrete vehicle dynamics model
3.1 setting of simulation evaluation Condition of model
In this case, the following working conditions are taken as examples: the vehicle was subjected to sinusoidal tests with front wheel angles of 3.6deg, 5.4deg and 7.2deg at an initial speed of 80 km/h. The steering wheel angle input time is shown in fig. 2. Setting a sampling period N p 0.05s, the predicted time domain is T0.5 s.
3.2 determination of the time series of the initial State and the control quantity of the Single simulation
Given a starting time of 0, six degrees of freedom vehicle state: longitudinal speed, lateral speed, transverse standard angular speed, side dip angle speed, front and rear wheel rotation angular speed and control quantity time sequence in a prediction time domain after t moment.
3.3 simulating a prediction horizon using the discretized vehicle dynamics model of equation (2) to obtain a prediction result X of the vehicle state p
3.4 repeating step 2.2, giving the vehicle state and the control quantity time sequence in a prediction time domain at 0.05s, 0.1s and 0.15s …, and so on until the termination condition t=n is reached, wherein the sampling cut-off time n=6 in the present case, as shown in fig. 2, is the simulation result of the discrete vehicle dynamics model in the prediction time domain and the comparison of the simulation result with the simulation result of the model precision evaluation method based on the global error (the conventional method is aimed at the continuous vehicle dynamics model established in step two, so that the simulation is carried out by the conventional method, the conventional fourth-order longgrid tower method is adopted for solving, and the solving step length is 0.001 s.
Fourth, evaluating vehicle dynamics model based on prediction time domain error
Example 1 State output of Trucksims at the same control amount time series input is used as a true value, and the absolute value of the state error X is calculated by comparing the predicted vehicle state with this error ＝|X p -X real And (3) obtaining the average error corresponding to each starting moment under the case working condition.
As shown in FIG. 3, during a sinusoidal input condition with a front wheel angle of 5.4deg, the Trucksim vehicle, which is the true value, produces a phenomenon of side slip instability after 2s, whereas the six degree of freedom model does not reveal this phenomenon due to the simplification of the model, and produces a distinct trend of motion during subsequent motions due to accumulated errors.
If the result is analyzed by the conventional method, the accuracy of the established six-degree-of-freedom model cannot meet the control requirement. However, in the prediction of a nonlinear MPC controller, only the accuracy of the model in a short prediction time domain needs to be guaranteed, not the long-term global model accuracy, and it is obviously inappropriate to use the conventional model evaluation result based on global error to illustrate the insufficient simplified model accuracy.
The model precision evaluation method based on the prediction time domain error can start from the real state of the vehicle at each moment to avoid accumulated errors, so that the error of the vehicle model in one prediction time domain is obtained, and the precision of the six-degree-of-freedom vehicle dynamics model in the prediction time domain can be completely used for designing the NMPC controller from the evaluation result based on the new method.
As shown in fig. 4 and 5, the prediction accuracy of the model at different sampling periods and different prediction time domains gradually increases with the increase of the sampling period and the prediction time domain. But the larger sampling period can obtain better control instantaneity, the larger prediction time domain can obtain longer vehicle running state, and the design process of the NMPC controller can determine the corresponding parameters of the controller by selecting according to the prediction error obtained by the optimization method disclosed by the invention, so that the traditional model precision evaluation method cannot be realized.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
Finally, it should be noted that the above-mentioned embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (4)
1. A vehicle dynamics model precision evaluation method based on prediction time domain errors is characterized by comprising the following steps:
step one, measuring and testing parameters of a real vehicle
According to the controlled target vehicle, measuring various structural parameters of the target vehicle, then carrying out vehicle test under corresponding typical working conditions, and recording time sequences of state quantity and control quantity in the test after the test is finished;
step two, constructing a vehicle dynamics model as follows:
in the formula (1), X is a state variable;for the derivative of X, f is a relational expression for the state variable value;
discretizing the vehicle dynamics model, namely obtaining an iterative equation of n+1 time relative to n time by adopting a formula (2) for a differential equation shown in the formula (1):
X n+1 ＝X n +T·f(X n ,U n ) (2)
x in formula (2) n As state variable at time n, X n+1 The state variable is the state variable at the time of n+1, and T is the sampling period;
setting a simulation evaluation working condition, a sampling period T and a prediction time domain N in the NMPC controller p Wherein the prediction time domain is a positive integer multiple of the sampling period;
step five, giving a control quantity time sequence in a prediction time domain after the starting time t and the vehicle state;
step six, simulating a prediction time domain through the vehicle dynamics model in the formula (2) to obtain a prediction result X of the vehicle state p The method comprises the steps of carrying out a first treatment on the surface of the Repeating the fourth step, and giving a vehicle state at the time t+T and a control quantity time sequence in a prediction time domain until a termination condition t=N is reached, wherein N is the termination time and is a positive integer multiple of a sampling period T;
step seven, predicting result X of vehicle state p And vehicle state X as true value real Comparing, calculating the absolute value X of the state single point error error ＝|X p -X real I, and counting the average value and variance of the errors; if the state error is within the allowable range, the vehicle dynamics model, the corresponding sampling period and the predicted time domain parameter can be used for designing an NMPC controller, and if the state error is not within the allowable range, the parameters are required to be adjusted.
2. The vehicle dynamics model accuracy evaluation method based on the prediction time domain error as set forth in claim 1, wherein: the state variables X include lateral velocity, yaw velocity, longitudinal velocity, roll angle velocity and front and rear wheel angular velocity.
3. The vehicle dynamics model accuracy evaluation method based on the prediction time domain error as set forth in claim 1, wherein: the control quantity time sequence comprises a front wheel rotation angle, a driving moment and a braking moment.
4. The vehicle dynamics model accuracy evaluation method based on the prediction time domain error as set forth in claim 1, wherein: the typical working conditions comprise a steering wheel sine input test and a steering wheel step input test.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211051623.2A CN115563694B (en) | 2022-08-31 | 2022-08-31 | Vehicle dynamics model precision evaluation method based on prediction time domain error |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211051623.2A CN115563694B (en) | 2022-08-31 | 2022-08-31 | Vehicle dynamics model precision evaluation method based on prediction time domain error |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115563694A CN115563694A (en) | 2023-01-03 |
| CN115563694B true CN115563694B (en) | 2024-04-12 |
Family
ID=84738572
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211051623.2A Active CN115563694B (en) | 2022-08-31 | 2022-08-31 | Vehicle dynamics model precision evaluation method based on prediction time domain error |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115563694B (en) |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105045102A (en) * | 2015-06-30 | 2015-11-11 | 吉林大学 | Vehicle lateral stability nonlinear integration control method |
| CN109597308A (en) * | 2019-01-15 | 2019-04-09 | 天津大学 | Pilotless automobile model predictive controller design method based on kinetic model |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110395120A (en) * | 2019-08-14 | 2019-11-01 | 厦门金龙联合汽车工业有限公司 | A kind of weaving control method of four-wheel distribution driving car |
| US11679759B2 (en) * | 2021-01-27 | 2023-06-20 | Mitsubishi Electric Research Laboratories, Inc. | System and method for adaptive control of vehicle dynamics |
-
2022
- 2022-08-31 CN CN202211051623.2A patent/CN115563694B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105045102A (en) * | 2015-06-30 | 2015-11-11 | 吉林大学 | Vehicle lateral stability nonlinear integration control method |
| CN109597308A (en) * | 2019-01-15 | 2019-04-09 | 天津大学 | Pilotless automobile model predictive controller design method based on kinetic model |
Non-Patent Citations (2)
| Title |
|---|
| Modeling and validation of 7-DOF ride model for heavy vehicle;Sulaiman 等;International Conference on Automotive, Mechanical and Materials Engineering;20121231;108-112 * |
| 基于MPC与EKF算法的电动汽车状态估计与横向稳定性控制;邓涛;罗俊林;汪明明;;汽车安全与节能学报;20170915(第03期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN115563694A (en) | 2023-01-03 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Zhao et al. | Design of a nonlinear observer for vehicle velocity estimation and experiments | |
| JP6842112B2 (en) | Road surface profile estimation device, road surface profile estimation system, road surface profile estimation method and road surface profile estimation program | |
| CN109131351B (en) | Vehicle stability evaluation method based on random time lag | |
| CN103279675B (en) | Tire-road attachment coefficient and the method for estimation of slip angle of tire | |
| CN110884499B (en) | Method and system for determining vehicle mass center slip angle | |
| CN113570057B (en) | Vehicle wheel center vertical displacement measuring method and device based on model training | |
| CN110497915B (en) | Automobile driving state estimation method based on weighted fusion algorithm | |
| CN116702096B (en) | Method and device for measuring and calculating road sliding resistance of vehicle plateau environment | |
| CN112270039A (en) | Distributed asynchronous fusion-based nonlinear state estimation method for drive-by-wire chassis vehicle | |
| Widner et al. | Framework for vehicle dynamics model validation | |
| CN115563694B (en) | Vehicle dynamics model precision evaluation method based on prediction time domain error | |
| CN112287289A (en) | Vehicle nonlinear state fusion estimation method for cloud control intelligent chassis | |
| CN116409327A (en) | Road surface adhesion coefficient estimation method considering transient characteristics of tire under lateral working condition | |
| AU2016294674B2 (en) | Method and system for determining the aerodynamic resistance of a cyclist | |
| CN114953886A (en) | Manned lunar vehicle suspension state calculation method and system | |
| Pastorino et al. | Validation of a multibody model for an X-by-wire vehicle prototype through field testing | |
| CN113325849A (en) | Motion control method for high-ground-clearance plant protection machine | |
| Kim et al. | Estimation of lateral tire force from objective measurement data for handling analysis | |
| Unjhawala | A Set of Reduced Order Vehicle Models for Applications in Machine Learning, State Estimation, and Control | |
| Pütz et al. | Simulation of the Handling Dynamics | |
| CN110641474B (en) | Automobile control stability robustness quantitative calculation method based on dissipation energy | |
| CN113264054B (en) | Vehicle parameter and control model-based vehicle control method, device and equipment | |
| Li et al. | Tire Force Allocation with Different Vertical Load Estimation Methods for 4WID-4WIS Vehicles | |
| CN116394956A (en) | Estimation method and estimation system for cornering stiffness and rotational inertia of vehicle | |
| Zhujie et al. | Vehicle state and parameter estimation based on improved adaptive dual extended Kalman filter with variable sliding window |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |