A Nonlinear Modeling Framework for Autonomous Cruise Control

A nonlinear modeling framework is presented for autonomous cruise control (ACC) equipped vehicles which allows one to analyze car-following scenarios in a wide range of velocities and headways. By designing the range policy as well as the controller one can improve the ride qualities for individual vehicles and increase the throughput of the overall traffic systems. INTRODUCTION Vehicular traffic has been studied for many decades and many different control methods has been developed (traffic lights, variable message signs) to regulate transportation systems; see [1] for a review. While traditional traffic control increases the efficiency, further improvement are possible by exploiting advanced vehicle technologies. In particular, one may use autonomous cruise control (ACC) devices to regulate the flow [2]. We propose a modeling framework for ACC equipped vehicles that allows one to implement nonlinear range policies that can be used for the entire velocity and headway range. Such vehicles are able to operate in stop-and-go conditions. To achieve this one needs to take into account nonlinearities in the system (like air drag). On the other hand, we also exploit nonlinearities when designing and implementing the range policy, so that it provides a smooth ride and also increases the road capacity. We propose a particular nonlinear range policy which is easy to handle analytically. We show that both plant and string stability can be ensured by appropriate choice of control gains. Such controller can be implemented in vehicles independent of the powertrain specifications (internal combustion engine, hybrid-electric vehicles, electric vehicles, etc.) and allows optimization in the entire torque and engine speed range (e.g., for energy consumption). NONLINEAR ACC MODEL We consider vehicles on a single lane as represented in the top panel of Fig. 1 where the positions xn, the velocities vn and the headways hn are shown together with the vehicle length . We focus our attention on two consecutive vehicles and for simplicity we drop the indexes for the follower and use the subscript L for the leader. To model the longitudinal dynamics of the follower we assume no slip condition on the wheels and neglect the flexibility of the tires and the suspension. Applying the power law we obtain the differential equation for the velocity v meffv=−mgsinφ− γmgcosφ− k(v+ vw)+ η Ren . (1) The effective mass meff = m+ J/R2 contains the mass of the vehicle m, the moment of inertia J of the rotating elements, and the wheel radius R. Furthermore, g is the gravitational constant, φ is the inclination angle, γ is the rolling resistance coefficient, k is the air drag constant, vw is the velocity of the headwind, η is the gear ratio, and Ten is the engine torque [3]. For simplicity, we consider φ = 0, vw = 0 and J = 0 =⇒ meff = m, while the other parameters are shown in Table 1 in the Appendix. When units are not spelled out, quantities should be understood in SI units. Our goal is to implement a given range policy v = V (h) which is achieved by the vehicle in steady state. While a variety of range policies can be considered we assume the following general properties: (i) V is continuous and monotonously increasing (the more sparse traffic is, the faster the driver wants to travel); (ii) V (h)≡ 0 for h≤ hst (in dense traffic, drivers intend to stop); (iii)V (h)≡ vmax for h≥ hgo (in very sparse traffic, drivers intend to drive with maximum speed – often called free flow speed). Indeed, vehicles that implement such range policy are capable of handling stop-and-go situations. Two examples are shown in the ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference DSCC2012-MOVIC2012 1 Copyright © 2012 by ASME DSCC2012-MOVIC2012-8871 October 17-19, 2012, Fort Lauderdale, Florida, USA n n+ 1 n+ 2 vn vn+1 vn+2 xn xn+1 xn+2 hn hn+1