Vehicle Planar Motion Research Articles

Optimal coordinated control of active steering and direct yaw moment for distributed-driven electric vehicles

This paper considers the problem of optimal coordination of active steering and direct yaw moment for general electric vehicles equipped with in-wheel motors and steer-by-wire devices. As a typical over-actuated system, vehicle planar motion shows flexible control performance under different wheel actuations, thus achieving the optimal integration among them is of critical significance. Based on the modeling from wheel actuations of motor torques and wheel angles to vehicle planar motion states, this paper proposes an optimal hierarchical control framework composed of a reference state generator, a linear time-varying model predictive controller (LTV-MPC), and an optimal control allocator. Motor torques and wheel angles are decoupled as equivalent distributed variables by linearization technique. Then an optimal allocation framework is formed towards the trade-off between driving security and power saving, and a compensation module based on the back-propagation neural network (BPNN) is designed to guarantee the control allocation accuracy. Holistic multi-objective optimization is demonstrated through Co-simulations with Matlab/Simulink and TruckSim. Results verify the effectiveness of the proposed control strategy.

Coordinated motion and powertrain control of a series-parallel hybrid 8 × 8 vehicle with electric wheels

This article deals with the coordinated motion and powertrain control of a series-parallel hybrid 8 × 8 vehicle equipped with mechanical transmission and electric wheels. With six wheels driven by in-wheel motors and two driven by an AMT, the 8 × 8 vehicle has enormous potential to improve its dynamic performance, fuel economy, off-road mobility, maneuverability, gradeability, etc. On the other hand, as vehicle motion dynamics and powertrain components are closely coupled in the complex hybrid system, appropriate control strategy is urgently desired to deal with the torque distribution problem. Continuous control variables such as wheel torque, engine torque, generator torque, and discrete variable like transmission gear should be determined properly to achieve optimum control of the vehicle. A hierarchical control strategy constructed by tracking controller and allocation algorithm is proposed. Integral sliding mode control is adopted in the upper layer to track desired vehicle planar motion. The allocation problem is handled by a three-step control allocation algorithm based on quadratic programming, with carefully consideration of vehicle and powertrain features. Co-simulations with Matlab/Simulink® and TruckSim® show that the proposed coordinated control approach is capable of controlling vehicle planar motion and managing the complex series-parallel hybrid system simultaneously.

Simultaneous Estimation of Vehicle’s Center of Gravity and Inertial Parameters Based on Ackermann’s Steering Geometry

Onboard vehicle parameter estimation is an important procedure for advanced vehicle control tasks, especially for vehicles whose payload configurations vary in day-to-day use. This study presents a newly proposed estimation method based on the Ackermann’s steering geometry (ASG) that aims to estimate multiple vehicle's center of gravity (CG) position and inertial parameters at the same time. In this method, the vehicle planar motion equations are first synthesized into a form where only the lateral force of one front wheel and longitudinal forces appear. This way, the influence of uncertainties in the tire lateral force models is greatly reduced. Then, the condition of eliminating the remaining front wheel lateral force term can be derived, which is exactly the Ackermann’s steering geometry. When the influence of lateral tire force terms are eliminated, regression technique is applied to estimate the needed vehicle parameters. Vehicle’s suspension kinematics is also considered in the processing of dynamic signals. Unlike conventional methods in estimating vehicle’s payload related parameters, the new method requires neither lateral tire force model nor accurate suspension property parameters. Simulations in CarSim®-Simulink environment verified that the proposed method is capable of estimating vehicle parameters such as CG position and inertial parameters at the same time.

A Stability Estimation Approach in Vehicle Planar Motion Considering Longitudinal Dynamics

A stability estimation approach is proposed to support complementary stability criterion design in vehicle planar motion. The comprehensive effect of tangential force and axle load transfer on tire cornering characteristics is considered corresponding to the longitudinal dynamics effects. The effectiveness of different stability concept is discussed in terms of the physical meaning of state variables in 3DOF differential systems. Based on the sense of technical stability, the 3DOF model is simplified according to longitudinal dynamics characteristic within definite observation time interval. The central equilibrium points continuum properties of the simplified model can be used to estimate the vehicle behavior in planar motion.

Vehicle Planar Motion Stability Study for Tyres Working in Extremely Nonlinear Region

Many researches on vehicle planar motion stability focus on two degrees of freedom(2DOF) vehicle model, and only the lateral velocity (or side slip angle) and yaw rate are considered as the state variables. The stability analysis methods, such as phase plane analysis, equilibriums analysis and bifurcation analysis, are all used to draw many classical conclusions. It is concluded from these researches that unbounded growth of the vehicle motion during unstable operation is untrue in reality thus one limitation of the 2DOF model. The fundamental assumption of the 2DOF model is that the longitudinal velocity is treated as a constant, but this is intrinsically incorrect. When tyres work in extremely nonlinear region, the coupling between the vehicle longitudinal and lateral motion becomes significant. For the purpose of solving the above problem, the effect of vehicle longitudinal velocity on the stability of the vehicle planar motion when tyres work in extremely nonlinear region is investigated. To this end, a 3DOF model which introducing the vehicular longitudinal dynamics is proposed and the 3D phase space portrait method is employed for visualization of vehicle dynamics. Through the comparisons of the 2DOF and 3DOF models, it is discovered that the vehicle longitudinal velocity greatly affects the vehicle planar motion, and the vehicle dynamics represented in phase space portrait are fundamentally different from that of the 2DOF model. The vehicle planar motion with different front wheel steering angles is further represented by the corresponding vehicle route, yaw rate and yaw angle. These research results enhance the understanding of the stability of the vehicle system particularly during nonlinear region, and provide the insight into analyzing the attractive region and designing the vehicle stability controller, which will be the topics of future works.

LTV-MPC for Yaw Rate Control and Side Slip Control with Dynamically Constrained Differential Braking

In this paper a novel vehicle lateral dynamic control approach is presented. A differential braking control law based on vehicle planar motion has been designed using a two-degrees-of-freedom vehicle model. On the basis of the estimate of tire longitudinal forces we estimate the range of lateral forces which the tire can exert. Using this constraints a model predictive control (MPC) based on a two-track model is designed in order to stabilize the vehicle. The performances are estimated comparing the results with standard manoeuvers. Simulation results show the benefits of the control methodology used: in particular we show how very effective distribution of braking torque are obtained as a result of this feedback policy.

Parametric method for determination of motion characteristics of underwater vehicles, applicable in preliminary designing

Parametric method for determination of motion characteristics of underwater vehicles, applicable in preliminary designingThis paper describes a method for preliminary designing the autonomous underwater vehicles (AUV), especially useful in the case when requirements concerning kinematic and dynamic parameters of vehicle motion are given in design assumptions. Concept of the method is based on dynamic equations which describe vehicle planar motion in vertical and horizontal directions, resulting from action of screw propellers or water ballast, respectively. The motion equations were determined by applying simplifications concerning both geometrical description of vehicle's form and flow phenomena. Their solutions were obtained in the form of closed analytical expressions which are both of cognitive and practical merits as they can serve to assess influence of vehicle's design parameters on its motion characteristics and simultaneously are convenient to formulate design optimization problems. Application of the method was illustrated by the attached examples dealing with determination of kinematic and dynamic characteristics of motion of the vehicle "Scylla" of set geometrical configuration and propulsion parameters.

Nonlinear dynamics and stability analysis of vehicle plane motions

In this article, the problems of dynamics and stability for vehicle planar motion systems have been investigated. By introducing a so-called joint-point locus approach, equilibria of the system and their associated stability properties are given geometrically. With this method, it is discovered that the difference between the front and the rear steering angles plays a key role in vehicle system dynamics and that the topological structure of the phase portrait and the types of bifurcations are different from those published previously. In particular, the vehicle system could still be stabilized even when pushed to work in a certain severely nonlinear region, by applying extremely large steering angles. However, it is worth noticing that the attractive domain of the stable equilibrium is very narrow. These developments might prove to be important in active steering control design. Numerical experiments are carried out to illustrate the potentials of the proposed techniques.

Design and evaluation of side slip angle-based vehicle stability control scheme on a virtual test track

This paper describes the development of side slip angle-based vehicle stability control (VSC) schemes and the evaluation of the control schemes on a virtual test track. A differential braking control law based on vehicle planar motion has been designed using a three-degree-of-freedom yaw plane vehicle model. The control threshold for the VSC is designed based on the vehicle body side slip angle. Since VSC always works with the driver, the overall vehicle performance will depend not on how well the VSC works but rather on its interaction with the human driver. Vehicle behavior and interactions between the vehicle, the controller, and the human driver are investigated using a vehicle simulator on a virtual test track (VTT). The VTT consists of a real-time vehicle simulator, a visual animation engine, a visual display, and human-vehicle interfaces. The VTT has been developed and used for the evaluation of the VSC under various realistic conditions in the laboratory. In this paper, the effects of the different control threshold on the vehicle-driver-controller interaction for a novice and expert driver are compared. Test results obtained using the VTT establish the need for a variable control threshold. The VTT makes it possible to perform exhaustive design trials and evaluations in the laboratory without risk of injury before field testing and promises to significantly reduce development cost and cycle time.

Side slip angle based control threshold of vehicle stability control system

Vehicle Stability Control (VSC) system prevents vehicle from spinning or drifting out mainly by braking intervention. Although a control threshold of conventional VSC is designed by vehicle characteristics and centered on average drivers, it can be a redundancy to expert drivers in critical driving conditions. In this study, a manual adaptation of VSC is investigated by changing the control threshold. A control threshold can be determined by phase plane analysis of side slip angle and angular velocity which is established with various vehicle speeds and steering angles. Since vehicle side slip angle is impossible to be obtained by commercially available sensors, a side slip angle is designed and evaluated with test results. By using the estimated value, phase plane analysis is applied to determine control threshold. To evaluate an effect of control threshold, we applied a 23-DOF vehicle nonlinear model with a vehicle planar motion model based sliding controller. Controller gains are tuned as the control threshold changed. A VSC with various control thresholds makes VSC more flexible with respect to individual driver characteristics.