“…Hence, estimation of tire forces independent of road conditions would be a remedy. Longitudinal force estimation independent of the road friction may be classified on the basis of wheel dynamics into the nonlinear and sliding mode observers [22]- [24], Kalman-based estimation [25], [26], and unknown input observers [27], [28]. This section provides two force estimation approaches, an unknown input observer and a Kalman-based method.…”
Abstract-This article seeks to develop a longitudinal vehicle velocity estimator robust to road conditions by employing a tire model at each corner. Combining the lumped LuGre tire model and the vehicle kinematics, the tires internal deflection state is used to gain an accurate estimation. Conventional kinematicbased velocity estimators use acceleration measurements, without correction with the tire forces. However, this results in inaccurate velocity estimation because of sensor uncertainties which should be handled with another measurement such as tire forces that depend on unknown road friction. The new Kalman-based observer in this paper addresses this issue by considering tire nonlinearities with a minimum number of required tire parameters and the road condition as uncertainty. Longitudinal forces obtained by the unscented Kalman filter on the wheel dynamics is employed as an observation for the Kalman-based velocity estimator at each corner. The stability of the proposed time-varying estimator is investigated and its performance is examined experimentally in several tests and on different road surface frictions. Road experiments and simulation results show the accuracy and robustness of the proposed approach in estimating longitudinal speed for ground vehicles.
“…Hence, estimation of tire forces independent of road conditions would be a remedy. Longitudinal force estimation independent of the road friction may be classified on the basis of wheel dynamics into the nonlinear and sliding mode observers [22]- [24], Kalman-based estimation [25], [26], and unknown input observers [27], [28]. This section provides two force estimation approaches, an unknown input observer and a Kalman-based method.…”
Abstract-This article seeks to develop a longitudinal vehicle velocity estimator robust to road conditions by employing a tire model at each corner. Combining the lumped LuGre tire model and the vehicle kinematics, the tires internal deflection state is used to gain an accurate estimation. Conventional kinematicbased velocity estimators use acceleration measurements, without correction with the tire forces. However, this results in inaccurate velocity estimation because of sensor uncertainties which should be handled with another measurement such as tire forces that depend on unknown road friction. The new Kalman-based observer in this paper addresses this issue by considering tire nonlinearities with a minimum number of required tire parameters and the road condition as uncertainty. Longitudinal forces obtained by the unscented Kalman filter on the wheel dynamics is employed as an observation for the Kalman-based velocity estimator at each corner. The stability of the proposed time-varying estimator is investigated and its performance is examined experimentally in several tests and on different road surface frictions. Road experiments and simulation results show the accuracy and robustness of the proposed approach in estimating longitudinal speed for ground vehicles.
“…The lateral dynamics with the tire model can be expressed as follows after putting the tire forces of each track Several studies focuses on normal force calculation on each axle using load transfer and acceleration measurements [28], [33], [34]. Calculated normal forces on the front and rear axles F zf and F zr can then be utilized in (13) whenever lateral/longitudinal acceleration measurements are available.…”
Section: A Lateral Dynamics With the Pure-slip Conditionmentioning
Abstract-In this paper, a vehicle's lateral dynamic model is developed based on the pure and the combined-slip LuGre tire models. Conventional vehicle's lateral dynamic methods derive handling models utilizing linear tires and pure-slip assumptions. The current article proposes a general lateral dynamic model, which takes the linear and nonlinear behaviors of the tire into account using the pure and combined-slip assumptions separately. The developed methodology also incorporates various normal loads at each corner and provides a proper tire-vehicle platform for control and estimation applications. Steady-state and transient LuGre models are also used in the model development and their responses are compared in different driving scenarios. Considering the fact that the vehicle dynamics is time-varying, the stability of the suggested time-varying model is investigated using an affine quadratic stability approach, and a novel approach to define the critical longitudinal speed is suggested and compared with that of conventional lateral stability methods. Simulations have been conducted and the results are used to validate the proposed method.
“…in which B c = [0 1 1] T , the estimation input is u = R eω −v xt , the output y = µ x is the normalized longitudinal force, which can be obtained from road friction-independent approaches using nonlinear and sliding mode observers [22]- [24], Kalman-based estimation [25], [26], and unknown input observers [27]- [29]. The measurement and process noises are denoted by w m and w p = [w 1 w 2w1 ]…”
Section: Corners' State Estimation By Unscented Kalman Filtermentioning
Abstract-A distributed estimation approach based on opinion dynamics is proposed to enhance the reliability of vehicle corners' velocity estimates, which are obtained by an unscented Kalman filter. The corners' estimates from a Kalman observer, which is formed by integrating the model-based and kinematic-based velocity estimation approaches, are utilized as opinions with different levels of confidence in the developed algorithm. More reliable estimates robust to disturbances and time delay are achieved via solving a convex optimization problem. Road tests confirm the robustness of the methods independent of the powertrain configuration on surfaces with various friction conditions in pure and combined-slip maneuvers, which are arduous for the current vehicle state estimators.
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