Static output feedback control for lane change maneuver

International audienceThis paper addresses the lateral control of a vehicle during lane change maneuvers. The proposed design procedure aims to answer the questions of control using cost-effective sensors implementation, adaptation to measured variables and robustness to unmeasured varying parameters. This is achieved through a static output feedback controller with preview information. The only used measurements are the lateral displacement at sensor location and the yaw angle relative to the lane centerline. The vehicle lateral model is augmented with an integral action, the error signal and the preview reference signal. The controller is synthesized using the LMI framework thanks to a relaxation method that removes the nonlinear terms. Simulations are conducted for various scenarios showing the ability of the design method to handle different performance objectives

Global existence for wave and beam equations with double damping and a new power nonlinearity

We consider the Cauchy problem in $\mathbb{R}^{n}$ for wave and beam equations with frictional, viscoelastic damping, and a new power nonlinearity. In addition to the solution and its total energy, we define the following quantity: $$Q[u](t):=\|u_{t}(t,\cdot)+(-\Delta)^{\sigma}u(t,\cdot)\|_{L^{2}(\mathbb{R}^{n})}.$$ Our aim is to show that the interaction between frictional and viscoelastic damping in a linear model leads to an exponential decay of $Q[u](t)$ as $t\to \infty$. This decay motivates us to define a new power nonlinearity of the form $N[u]:=|u_{t}+(-\Delta)^{\sigma}u|^{p}$. Surprisingly, $N[u]$ can be considered a small perturbation for any $p>1$, in the sense that, the decay estimates of the unique global solution, the total energy and $Q[u](t)$ coincide with those for solutions to the corresponding linear Cauchy problem with vanishing right-hand side.Comment: A new nonlinearity is define

A new gap in the critical exponent for semi-linear structurally damped evolution equations

Our aim in this paper is to discuss the critical exponent in semi-linear structurally damped wave and beam equations with additional dispersion term. The special model we have in mind is $$u_{tt}(t,x)+(-\Delta)^{\sigma}u(t,x)+(-\Delta)^{2\delta}u(t,x)+2(-\Delta)^{\delta}u_{t}(t,x)=\left|u(t,x)\right| ^{p}$$ where the initial displacement $u(0,x)=u_{0}(x)$, the initial velocity $u_{t}(0,x)=u_{1}(x)$ and the parameters $t\in [0,\infty)$, $x\in \mathbb{R}^{n}$, $\sigma\geq 1$, $\delta\in(0,\frac{\sigma}{2})$, $p>1$. The solution to the linear equation at low frequency region involves an interplay of diffusion and oscillation phenomena represented by a real-complex Fourier multiplier of the form $$m(t,\xi)=\frac{e^{-|\xi|^{2\delta}t\pm i|\xi|^{\sigma}t}}{2i|\xi|^{\sigma}}, \ \ \xi\in \mathbb{R}^{n}, \ \ i=\sqrt{-1}.$$ The scaling argument shows that the diffusive part leads to faster decay rates compared to the oscillatory one. This interplay creates a new gap in the critical exponent between the blow up (in finite time) result when $1<p<1+\frac{4\delta}{n-2\delta}$ (sub-critical case) and the global (in time) existence result when $p>1+\frac{\sigma+2\delta}{n-\sigma}$ (super-critical case). We leave an open to show if this gap will be closed at least in low or high space dimensions because, to the best of authors knowledge, the necessary Fourier multiplier that leads to the sub-critical case does not explicitly appear in $m(t,\xi)$.Comment: Wave equation, beam equation, structural damping, dispersion terms, global existence, blow up, critical exponen

Lateral & Steering Dynamics Estimation for Single Track Vehicle: Experimental Tests * *This work is supported by National Agency of Research under the framework VIROLO++.

International audienceThis paper deals with lateral and steering dynamics estimation of powered two-wheeled (PTW) vehicles. It presents an experimental validation of the Unknown Input Observer (UIO) addressed in Damon et al. (2016). A small scooter equipped with a multi-sensor architecture used to performed the test is introduced. A mathematical model of the scooter is derived using measured parameters on a Computer-Aided Design (CAD) model. Then the main design steps of the UIO are shortly remind. Finally, an urban driving scenario is presented to show the effectiveness of the proposed observer to estimate the lateral dynamics and the rider's action in real riding scenario

Powered Two-Wheeled Vehicles Steering Behavior Study: Vision-Based Approach

International audienceThis paper presents a vision-based approach to prevent dangerous steering situations when riding a motorcycle in turn. In other words, the proposed algorithm is capable of detecting under, neutral or over-steering behavior using only a conventional camera and an inertial measurement unit. The inverse perspective mapping technique is used to reconstruct a bird-eye-view of the road image. Then, filters are applied to keep only the road markers which are, afterwards, approximated with the well-known clothoid model. That allows to predict the road geometry such that the curvature ahead of the motorcycle. Finally, from the predicted road curvature, the measures of the Euler angles and the vehicle speed, the proposed algorithm is able to characterize the steering behavior. To that end, we propose to estimate the steering ratio and we introduce new pertinent indicators such that the vehicle relative position dynamics to the road. The method is validated on the advanced simulator BikeSim during a steady turn

Rider weight consideration for observer design with an application to the estimation of the lateral motorcycle dynamics and rider's action

International audienceThis paper highlights the necessity of the rider weight consideration during observer's design for motorcycle dynamics estimation or control. It presents a novel approach using a linear parameter varying (LPV) model associated with the well-know Takagi-Sugeno (TS) methods to derive a robust observer regarding the rider weight uncertainty. Then the proposed solution is illustrated with an application to a proposed observer in our previous works by comparing results of estimation between a nominal, a heavier and a lighter rider. Finally, a complete simulation scenario shows the ability of the proposed method to estimate the lateral motorcycle dynamic states considering an uncertain rider weight

Road Geometry and Steering Reconstruction for Powered Two Wheeled Vehicles

International audienceThis paper deals with the estimation of both motorcycle lateral dynamics and road geometry reconstruction. A linear parameter varying (LPV) unknown input observer is designed to estimate the whole motorcycle dynamic states including road banking angles and the rider's steering torque taken into account the variation of the forward velocity. The road bank angle and the lateral slip angle are relevant parameters for improving rider's safety and handling, thus, it is interesting to estimate the road geometry. The observer convergence study is based on Lyapunov theory and the established convergence conditions are expressed in linear matrix inequalities (LMIs) formalism. The main idea consists in getting a set of conditions to design an observer transformed into a polytopic form, which estimates a part of the motorcycle dynamics states independently of some inputs (rider torque) and/or other states (zeros dynamics: roll angle) taken into account the variation of the longitudinal velocity