Nonlinear state and tire force estimation for advanced vehicle control

<div class="htmlview paragraph">Various vehicle dynamic simulation software programs have been developed for use in reconstructing accidents. Typically these are used to analyze and reconstruct preimpact and postimpact vehicle motion. These simulation programs range from proprietary programs to commercially available packages. While the basic theory behind these simulations is Newton's laws of motion, some component modeling techniques differ from one program to another. This is particularly true of the modeling of tire force mechanics. Since tire forces control the vehicle motion predicted by a simulation, the tire mechanics model is a critical feature in simulation use, performance and accuracy. This is particularly true for accident reconstruction applications where vehicle motions can occur over wide ranging kinematic wheel conditions. Therefore a thorough understanding of the nature of tire forces is a necessary aspect of the proper formulation and use of a vehicle dynamics program.</div> <div class="htmlview paragraph">This paper includes a discussion of tire force terminology, tire force mechanics, the measurement and modeling of tire force components and combined tire force models currently used in simulation software for the reconstruction of accidents. The paper discusses the difference between the idealized tire force ellipse and an actual tire friction ellipse. Equations are presented for five tire force models from three different simulation programs. Each model uses a different method for computing tire forces for combined braking and steering. Some experimentally measured light vehicle tire properties are examined.</div> <div class="htmlview paragraph">Some tire force models begin with a specified level of braking force and use the friction ellipse to determine the corresponding steering force; this produces steering forces and a resultant tire force equal in magnitude to full skidding for combined steering and braking. Comparisons are presented of results from simulation programs using different tire models for vehicle motions involving two types of severe yaw. The comparisons in this paper are not of reconstructions where the user seeks initial conditions to match an existing trajectory. The first comparison is a hypothetical postimpact motion with a given initial velocity and initial angular velocity and the other is a sudden steer maneuver. In some cases, the simulations and their tire models predict the vehicle motion closely. In most cases, however, the results differ significantly between simulation programs.</div> <div class="htmlview paragraph">The example simulations presented in this paper are not intended to reflect the way vehicle dynamic simulation programs are used typically in accident reconstruction.</div>

This paper presents an in-depth analysis of the application of different techniques for vehicle state and tyre force estimation using the same experimental data and vehicle models, except for the tyre models. Four schemes are demonstrated: (i) an Extended Kalman Filter (EKF) scheme using a linear tyre model with stochastically adapted cornering stiffness, (ii) an EKF scheme using a Neural Network (NN) data-driven linear tyre model, (iii) a tyre model-less Suboptimal-Second Order Sliding Mode (S-SOSM) scheme, and (iv) a Kinematic Model (KM) scheme integrated in an EKF. The estimation accuracy of each method is discussed. Moreover, guidelines for each method provide potential users with valuable insight into key properties and points of attention.

Nonlinear state estimation is a pre-requisite for advanced process control and fault diagnosis tasks. In literature, various recursive nonlinear filtering techniques have been proposed and used for state estimation of nonlinear systems. Over the last few years, Moving Horizon Estimation (MHE) is increasingly being used for state estimation of nonlinear systems. Moving horizon estimation works with a window of data and hence requires additional online computation compared to recursive nonlinear filters. However, MHE performs both smoothing and filtering and thus has the potential to obtain more accurate state estimates as compared to the recursive filters. Most of the available comparisons of MHE with recursive filters are based on simulation case studies where the true states and parameters, as well as noise processes are exactly known. In this work, we apply MHE to a three-tank experimental setup and compare its performance with various nonlinear filters available in literature such as Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Gaussian Sum EKF (GSEKF). We present some of the challenges in experimental implementation of state estimation approaches. These include presence of unknown disturbances, non-whiteness of noise signals as well as lack of accurate measurements. We then discuss the approach followed for obtaining model parameters and noise characterization to make the models amenable for filter implementation. It is found that EKF, GSEKF and UKF perform as well as MHE as far as accuracy is concerned, but require significantly lower computational efforts.

The concept of intelligent tires has drawn attention of researchers in the areas of autonomous driving, advanced vehicle control, and artificial intelligence. The focus of this paper is on intelligent tires and the application of machine learning techniques to tire force estimation. We present an intelligent tire system with a tri-axial acceleration sensor, which is installed onto the inner liner of the tire, and Neural Network techniques for real-time processing of the sensor data. The accelerometer is capable of measuring the acceleration in x,y, and z directions. When the accelerometer enters the tire contact patch, it starts generating signals until it fully leaves it. Simultaneously, by using MTS Flat-Trac test platform, tire actual forces are measured. Signals generated by the accelerometer and MTS Flat-Trac testing system are used for training three different machine learning techniques with the purpose of online prediction of tire forces. It is shown that the developed intelligent tire in conjunction with machine learning is effective in accurate prediction of tire forces under different driving conditions. The results presented in this work will open a new avenue of research in the area of intelligent tires, vehicle systems, and tire force estimation.

Estimation of Nonlinear Tire Forces and Road Friction for Modeling and Control

A robust method to estimate tire forces for a passenger vehicle with the Unscented Kalman Filter (UKF) is provided. Only standard vehicle sensors were used and no a priori knowledge of tire and road properties was required. The estimator uses the bicycle model and a random walk tire force model. The tire force estimates were compared to a CarSim reference model for combined slip maneuvers. The results showed a good overall tracking performance of the estimator. In addition, the UKF-estimator demonstrated a high convergence rate and good stability properties. The performed robustness studies showed that the estimator performs well even in the presence of disturbances such as changes in tire-road friction. This method enables a cost-effective and robust implementation for future real time vehicle applications.

Longitudinal and lateral forces acting on tyres are known to be closely related to tractive ability, braking characteristics, handling stability and manoeuvrability of ground vehicles. However, it is not feasible in the operating vehicles to measure the tyre forces directly because of the high cost of sensors, the limitations in sensor technology, interference with tyre rotation and the harsh environment. Another approach is the indirect monitoring technique that can estimate the tyre forces based on remote sensor outputs and vehicle dynamics models. In this paper, in order to develop tyre force-monitoring systems, a monitoring model is proposed utilizing not only the yawing motion but also the roll motion. Based on the monitoring model, a monitoring system is designed to estimate the lateral tyre force acting on each tyre. The monitoring system is constructed on the basis of a new scaled Kalman filter with model error compensator (SKFMEC) technique that is developed in this study to improve the robustness performance of Kalman filter methods. The SKFMEC technique adopts both the well-conditioned observer and the model error compensator concepts. Tyre force estimation performance of the monitoring system is evaluated in the MATLAB simulations where true tyre force data are generated from a 14-degree-of-freedom vehicle model with the combined-slip ‘magic formula’ tyre model.

The direct yaw moment control system is able to greatly enhance the vehicle stability when driving on challenging road surfaces. This paper introduces a direct control approach for managing the vehicle yaw moment, utilizing terminal sliding mode control and a square root cubature Kalman filter (SRCKF). Initially, the longitudinal and lateral forces acting on the vehicle’s tires are estimated through a sliding mode observer. Subsequently, the SRCKF algorithm and the four-wheel tire force are employed to accurately estimate the yaw rate and sideslip angle. Based on these estimations, additional yaw moments are determined using the terminal sliding mode control algorithm, and a combined control of yaw rate and sideslip angle is achieved through a threshold method. A rule-based braking force distribution strategy is then implemented to ensure vehicle stability control. Simulation results demonstrate that the tire force estimations from the sliding mode observer and the vehicle yaw rate and sideslip angle estimations from the SRCKF algorithm closely align with the output results from Carsim, with an error margin of less than 15%. The braking force distribution strategy, based on the direct yaw moment control using the terminal sliding mode algorithm, effectively tracks the desired yaw rate and sideslip angle.

Corner-based estimation of tire forces and vehicle velocities robust to road conditions

This paper presents an innovative application of the particle filtering techniques to the vertical gyro problem, which is a highly nonlinear and non Gaussian recursive state estimation problem. The classical approach to recursive state estimation problem of nonlinear and/or non Gaussian systems is based on the extended Kalman filter (EKF), which is a heuristic method based on the linearization of the state dynamics and observations near a nominal path. Depending on the amount of nonlinearities and non Gaussian noise, the EKF often provides a solution far from acceptable. The vertical gyro is an instrument adopted to measure the tilt angles (pitch and roll) of an aircraft with respect to local vertical. It is composed by three orthogonal gyros that are used as process sensors and by three orthogonal accelerometers that are used as aiding sensors. The output of accelerometers is filtered using a proper low-pass filter to allow for the estimation of the local direction of the gravity vector that is assumed the same of the local vertical. In the application to the vertical gyro, Gordon's version of the particle filter was used. The relevant dynamical model is based on non-linear attitude rate equation using Euler angles rather than quaternions. The algorithm, developed in Matlab environment, was first calibrated and tested in simulations, obtaining very appealing performances. Subsequently, it was implemented using real data, acquired by means of an inertial unit produced by Crossbow <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TM</sup> (model DMU-HDX <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TM</sup> ), and its results were compared to those provided by the proprietary EKF embedded in the unit. First of all, stationary tests were performed. Sensor data were input to the particle filter that outputs the tilt angles (roll and pitch) with respect to the local geodetic reference. The results were compared to those provided by the internal EKF. Subsequently, the same operation was done using data that were acquired with moving platform. The accuracy of the filter was tested also for degraded operating conditions (lower data rates) and large initial errors. The main advantage of the methodology is that, while the internal filter works with 7 states (quaternions, biases and temperature), the particle filter ensures the convergence with 3 states, and provides acceptable performances with 1000 particles only, appearing promising for a real time application.

This brief reports single degrees of freedom nonlinear dynamic model-based state estimators for the navigation of remotely operated vehicles (ROVs)-unmanned, tethered robots commonly used for underwater commercial and scientific tasks. These methods exploit knowledge of the vehicle's nonlinear dynamics, the forces and moments acting on the vehicle, and disparate position and velocity measurements. The position and velocity of the ROV are estimated using two methods: 1) a nonlinear observer (NLO) and 2) an extended Kalman filter (EKF). The NLO is derived and its stability proven using Lyapunov techniques. A high-precision 300-kHz acoustic positioning system provided a ground truth for the laboratory experiments and our results show that both the NLO and EKF position estimates possess lower standard deviations than the measurements from conventional 12-kHz long-baseline systems. A dynamic model sensitivity analysis is included for the laboratory experiments. Field experiments obtained with the Jason2 ROV at 2300-m depth demonstrate that the NLO and EKF work in the field. These experiments are, to the best of our knowledge, the first reported experiments of an NLO and EKF using a nonlinear model of ROV dynamics. The performance of the NLO and EKF are compared using the criteria of convergence, accuracy, precision, parameter sensitivity, and robustness to velocity measurement outages, and our results show that the NLO provides superior performance. The impact of these results includes more robust state estimation for underwater robots and an increased operating range that will provide new capabilities.

Good vehicle handling characteristics are essential to ensure traffic safety. In the integrated system of electric power steering (EPS) and active front steering (AFS), the steering wheel torque may change abruptly with the interference of active steering. The additional front road wheel angle generated by AFS gives rise to the change of tyre lateral force, which results in the change of steering wheel torque finally. Although the tyre forces are difficult to measure, the extended Kalman filter (EKF) algorithm can be used to estimate it. The problem of steering wheel torque change can be resolved by tyre forces estimate based on the EKF observer in nonlinear system. The vehicle nonlinear mathematical model is presented and a nonlinear tyre lateral force estimator is also established basing on EKF. The estimated tyre lateral forces can be applied to compensate the abrupt change of steering wheel torque, which realises the combination of vehicle states estimation and vehicle control. The simulation results in MATLAB/Simulink show the effectiveness of proposed control strategy.

Autonomous vehicle navigation in an unfamiliar environment is a challenging task. This investigation presents two algorithms for autonomous vehicle navigation in unknown environments with obstacles. Basic building blocks of the path-planning algorithms are the behaviour-based controller and nonlinear state estimator. Measurements from the sensor mounted on the vehicle are used as the input to the state estimator, whereas the estimated position of the vehicle with respect to the obstacle is the output. The estimate is then used to decide the possible control action from a family of behaviour-based controllers for navigating the vehicle. The first path-planning algorithm uses the extended Kalman filter (EKF) for estimating the vehicle position using measurements of the obstacle position. The second path-planning algorithm uses the unscented Kalman filter (UKF) to estimate the vehicle position. Our results indicate that UKF-based path-planning algorithm performs better than the EKF-based algorithm both in terms of performance and fuel consumption. This is indicated by a 9% reduction of the control effort. Path-planning algorithms presented in this investigation can be used to build reliable autonomous vehicle navigation systems.

A real-time optimization technique is proposed for optimal state estimation of general nonlinear systems. A state estimation algorithm is determined so that a receding-horizon performance index is minimized. Application of the stabilized continuation method results in a real-time solution technique that does not involve any approximation or iterative algorithms in principle. The discretization of the algorithm is the only approximation required in the actual implementation on digital computers. The structure of the state estimation algorithm is clarified based on the present solution technique, and a simple model of a nonlinear space vehicle is employed as an application example. Results of simulation and experiment validate the effectiveness of the proposed algorithm.

The ability to reliably maximize tire force usage would improve the safety of autonomous vehicles, especially in challenging edge cases. However, vehicle control near the limits of handling has many challenges, including robustly contending with tire force saturation, balancing model fidelity and computational efficiency, and coordinating inputs with the lower level chassis control system. This work studies nonlinear model predictive control for limit handling, specifically adapting to changing tire-road conditions and maximally allocating tire force utilization. We present a novel hierarchical framework that combines a single-track model with longitudinal weight transfer dynamics in the predictive control layer, with lateral brake distribution occurring at the chassis control layer. This vehicle model is simultaneously used in the unscented Kalman filter for online friction estimation. Comparative experiments on a full-scale vehicle operating on a race track at up to 95% of maximum tire force usage demonstrate the overall practical effectiveness of this approach.