Cornering Stiffness Parameters Research Articles

Trajectory tracking of an autonomous vehicle using immersion and invariance control

An Immersion and Invariance [I & I] controller is designed to control the nonlinear lateral vehicle’s motion, using the steering angle as the only input. Similar to most of the lateral vehicle’s dynamics control law, the cornering stiffness parameters are involved in our proposed controller. Because of the tight relation between tire/road properties and the cornering stiffness parameters, they are not available from the outputs of the sensors and therefore, should be estimated for utilizing in the control law. An online data-driven identification is employed for estimating the cornering stiffness parameters. In addition, a robust model-based fault detection and approximation method in the presence of uncertainties via neural networks is presented. The performance of the obtained control law is investigated via simulation tests in different situations and in the presence of the disturbance. Moreover, some validation tests are performed using the CarSim software to show the effectiveness of our algorithm.

An Adaptive Approach to Real-Time Estimation of Vehicle Sideslip, Road Bank Angles, and Sensor Bias

Robust estimation of vehicle sideslip angle is essential for stability control applications. However, the direct measurement of sideslip angle is expensive for production vehicles. This paper presents a novel sideslip estimation algorithm which relies only on sensors available on passenger and commercial vehicles. The proposed method uses both kinematics and dynamics vehicle models to construct extended Kalman filter observers. The estimate relies on the results provided from the dynamics model observer where the tire cornering stiffness parameters are updated using the information provided from the kinematics model observer. The stability property of the proposed algorithm is discussed and proven. Finally, multiple experimental tests are conducted to verify its performance in practice. The results show that the proposed approach provides smooth and accurate sideslip angle estimation. In addition, our novel algorithm provides reliable estimates of bank angles and lateral acceleration sensor bias.

Robust gain-scheduled output feedback yaw stability control for in-wheel-motor-driven electric vehicles with external yaw-moment

This paper presents a robust gain-scheduled output feedback yaw stability H∞ controller design to improve vehicle yaw stability and handling performance for in-wheel-motor-driven electric vehicles. The main control objective is to track the desired yaw references by managing the external yaw moment. Since vehicle lateral states are difficult to obtain, the state feedback controller normally requires vehicle full-state feedback is a critical challenge for vehicle lateral dynamics control. To deal with the challenge, the robust gain-scheduled output feedback controller design only uses measurements from standard sensors in modern cars as feedback signals. Meanwhile, parameter uncertainties in vehicle lateral dynamics such as tire cornering stiffness and vehicle inertial parameters are considered and handled via the norm-bounded uncertainty, and linear parameter-varying polytope vehicle model with finite vertices is established through reducing conservative. The resulting robust gain-scheduled output feedback yaw stability controller is finally designed, and solved in term of a set of linear matrix inequalities. Simulations for single lane and double lane change maneuvers are implemented to verify the effectiveness of developed approach with a high-fidelity, CarSim®, full-vehicle model. It is confirmed from the results that the proposed controller can effectively preserve vehicle yaw stability and lateral handling performance.

Robust Lateral Control of an A-double combination via H∞ and Generalized H2 Static Output Feedback

A robust static output feedback controller is developed for improving the high speed lateral performance of an A-double combination by active steering of the dolly unit. The controller is designed to be robust against the uncertainty in the cornering stiffness parameters of the tires in the semitrailers. Both H∞ and generalized H2 synthesis approaches are discussed together with their solutions in the form of linear matrix inequality (LMI) optimizations. The control syntheses are then applied to both a fixed system and an uncertain parameter-dependent system. The verification results confirm a significant reduction in rearward amplification of yaw rates and high speed transient off-tracking. To validate the simulation results, an advanced high-fidelity vehicle model is used.

Interval observer design for LPV systems with parametric uncertainty

Observer design for dynamical systems with both known and unknown time-varying parameters is of significant interest in a number of real-world applications. This class of systems has been rarely addressed in the existing literature. This paper develops an interval observer design methodology for linear parameter varying (LPV) systems with parametric uncertainty. With information on upper and lower bounds of the uncertain parameters, an interval observer that produces an envelope covering all possible state trajectories is presented. The application of the proposed algorithm in an important vehicle state estimation problem which aims at minimizing the worst-case envelope of the side-slip-angle estimate in the presence of uncertain tire cornering stiffness parameters and varying vehicle speed is presented. The obtained observer is evaluated in simulation using CarSim, a commercial industry-standard vehicle simulation software. The results verify the value of the developed observer design method.

Aircraft-on-ground path following control by dynamical adaptive backstepping

The necessity of improving the air traffic and reducing the aviation emissions drives to investigate automatic steering for aircraft to effectively roll on the ground. This paper addresses the path following control problem of aircraft-on-ground and focuses on the task that the aircraft is required to follow the desired path on the runway by nose wheel automatic steering. The proposed approach is based on dynamical adaptive backstepping so that the system model does not have to be transformed into a canonical triangular form which is necessary in conventional backstepping design. This adaptive controller performs well despite the lack of information on the aerodynamic load and the tire cornering stiffness parameters. Simulation results clearly demonstrate the advantages and effectiveness of the proposed approach.

Parameter estimation and validation of a tractor and single axle towed implement dynamic system model

Developing models and estimating model parameters for a tractor and implement system is important for rapid development and improvement of precision implement guidance systems. A dynamic model for a tractor with a towed implement was developed. This model contained a tire lateral force model with several parameters that are varying and difficult to measure accurately. Several field experiments were conducted to collect trajectory data for a tractor with a single axle grain cart. Data from these experiments were used to estimate the tire lateral force model parameters. Three different replicates of the experimental trajectories were collected with each of the step, random and chirp steering inputs. The data was collected at 4.5 m/s forward velocity in two different fields. A two-step optimization process was used to estimate the tire model parameters. First, the experimental data and a set of steady state model equations were used to estimate cornering stiffness parameters. Second, a prediction error minimization method and a dynamic model were used to estimate relaxation length parameters. The parameter estimation process was repeated with each replicate of the experimental data, and the individual estimates were combined using a weighted averaging method. The vehicle model responses with estimated parameters represented the system responses with reasonable accuracy. With the parameters estimated from three different trajectories, the RMSEs for trajectories of tractor and implement CGs varied from 0.05 to 0.83 m. The model-based frequency responses also closely matched with the experimental frequency responses.

Local and global sensitivity analysis of a tractor and single axle grain cart dynamic system model

Tractor and towed implement system models have become increasingly important for model-based guidance controller design , virtual prototyping , and operator-and-hardware-in-loop simulation. Various tractor and towed implement models have been proposed in the literature which contain uncertain or time-varying parameters. Sensitivity analysis was used to identify the effect of system parameter uncertainty/variation on system responses and to identify the most critical parameters of the lateral dynamics model for a tractor and single axle grain cart system. Both local and global sensitivity analyses were performed with respect to three tyre cornering stiffness parameters, three tyre relaxation length parameters, and two implement inertial parameters. Overall, the system was most sensitive to the tyre cornering stiffness parameters and least sensitive to the implement inertial parameters. In general, the uncertainty in the input parameters and the system output responses were related in a non-linear fashion. With the nominal parameter values for a Mechanical Front Wheel Drive (MFWD) tractor, a single axle grain cart, and maize stubble surface conditions, a 10% uncertainty in cornering stiffness parameters caused a 2% average uncertainty in the system responses whereas a 50% uncertainty in cornering stiffness parameters caused a 20% average uncertainty at 4.5 m s −1 forward velocity . If a 5% average uncertainty in system responses is acceptable, the cornering stiffness parameters must be estimated within 25% of actual/nominal values. The output uncertainty increased as the forward velocity was increased.

Recursive Identification of Cornering Stiffness Parameters for an Enhanced Single Track Model

The current development of safety systems within the automotive industry heavily relies on the ability to perceive the environment. This is accomplished by using measurements from several different sensors within a sensor fusion framework. One important part of any system of this kind is an accurate model describing the motion of the vehicle. The most commonly used model for the lateral dynamics is the single track model, which includes the so called cornering stiffness parameters. These parameters describe the tire-road contact and are unknown and even time-varying. Hence, in order to fully make use of the single track model, these parameters have to be identified. The aim of this work is to provide a method for recursive identification of the cornering stiffness parameters to be used on-line while driving.

GPS-based real-time identification of tire-road friction coefficient

Vehicle control systems such as collision avoidance, adaptive cruise control, and automated lane-keeping systems as well as ABS and stability control systems can benefit significantly from being made road-adaptive. The estimation of tire-road friction coefficient at the wheels allows the control algorithm in such systems to adapt to external driving conditions. This paper develops a new tire-road friction coefficient estimation algorithm based on measurements related to the lateral dynamics of the vehicle. A lateral tire force model parameterized as a function of slip angle, friction coefficient, normal force and cornering stiffness is used. A real-time parameter identification algorithm that utilizes measurements from a differential global positioning system (DGPS) system and a gyroscope is used to identify the tire-road friction coefficient and cornering stiffness parameters of the tire. The advantage of the developed algorithm is that it does not require large longitudinal slip in order to provide reliable friction estimates. Simulation studies indicate that a parameter convergence rate of 1 s can be obtained. Experiments conducted on both dry and slippery road indicate that the algorithm can work very effectively in identifying a slippery road.