On the handling of automated vehicles: modeling, bifurcation analysis, and experiments. (English) Zbl 1472.70007
Summary: The dynamics of automated vehicles are studied and the existence and stability of steady state cornering maneuvers are investigated. Utilizing tools from analytical mechanics, namely the Appellian approach, vehicle models are constructed which incorporate geometrical nonlinearities and differentiate between front wheel drive (FWD) and rear wheel drive (RWD) automobiles. The dynamics of these models are studied using bifurcation analysis. Stable and unstable steady states are mapped out as a function of speed and steering angle. It is demonstrated that RWD and FWD vehicles exhibit different behavior, especially when they operate close to their handling limits. The theoretical results are verified experimentally using an automated vehicle performing safety critical maneuvers.
MSC:
| 70B15 | Kinematics of mechanisms and robots |
| 70K50 | Bifurcations and instability for nonlinear problems in mechanics |
Keywords:
automated vehicles; bicycle model; nonholonomic dynamics; bifurcation analysis; steady state corneringSoftware:
DDE-BIFTOOLReferences:
| [1] | Beregi, S.; Takács, D., Analysis of the tyre-road interaction with a non-smooth delayed contact model, Multibody Syst. Dyn., 45, 185-201 (2019) |
| [2] | Berntorp, K.; Quirynen, R.; Uno, T.; Cairano, S. D., Trajectory tracking for autonomous vehicles on varying road surfaces by friction-adaptive nonlinear model predictive control, Veh. Syst. Dyn., 58, 5 (2020) |
| [3] | De Sapio, V., Advanced Analytical Dynamics: Theory and Applications (2017), Cambridge University Press · Zbl 1416.70002 |
| [4] | Della Rossa, F.; Mastinu, G.; Piccardi, C., Bifurcation analysis of an automobile model negotiating a curve, Veh. Syst. Dyn., 50, 10, 1539-1562 (2012) |
| [5] | Erlien, S. M.; Fujita, S.; Gerdes, J. C., Safe driving envelopes for shared control of ground vehicles, IFAC Proc. Vol., 46, 21, 831-836 (2013) |
| [6] | Ersal, T.; Kolmanovsky, I.; Masoud, N.; Ozay, N.; Scruggs, J.; Vasudevan, R.; Orosz, G., Connected and automated road vehicles: state of the art and future challenges, Veh. Syst. Dyn., 58, 5, 672-704 (2020) |
| [7] | Farroni, F.; Russo, M.; Russo, R.; Terzo, M.; Timpone, F., A combined use of phase plane and handling diagram method to study the influence of tyre and vehicle characteristics on stability, Veh. Syst. Dyn., 51, 8, 1265-1285 (2013) |
| [8] | Fiala, E., Seitenkräfte am rollenden Luftreifen, Zeitschrift Der Vereines Deutscher Ingenieure, 96, 973-979 (1954) |
| [9] | Gantmacher, F., Lectures in Analytical Mechanics (1975), MIR Publishers |
| [10] | Goh, J. Y.; Goel, T.; Gerdes, J. C., Toward automated vehicle control beyond the stability limits: drifting along a general path, J. Dyn. Syst. Measur. Control, 142, 2, Article 021004 pp. (2020) |
| [11] | Guckenheimer, J.; Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Applied Mathematical Sciences (1983), Springer · Zbl 0515.34001 |
| [12] | Hwan Jeon, J., Cowlagi, R.V., Peters, S.C., Karaman, S., Frazzoli, E., Tsiotras, P., Iagnemma, K., Optimal motion planning with the half-car dynamical model for autonomous high-speed driving, in: American Control Conference, 2013, pp. 188-193. |
| [13] | Kuznetsov, Y. A., Elements of Applied Bifurcation Theory, Applied Mathematical Sciences (2004), Springer · Zbl 1082.37002 |
| [14] | Li, S. E.; Chen, H.; Li, R.; Liu, Z.; Wang, Z.; Xin, Z., Predictive lateral control to stabilise highly automated vehicles at tire-road friction limits, Veh. Syst. Dyn., 58, 5 (2020) |
| [15] | Liu, J.; Jayakumar, P.; Stein, J. L.; Ersal, T., A study on model fidelity for model predictive control-based obstacle avoidance in high-speed autonomous ground vehicles, Veh. Syst. Dyn., 54, 11, 1629-1650 (2016) |
| [16] | Lu, H.; Stépán, G.; Lu, J.; Takács, D., The effect of time delay on vehicle stability control, Veh. Syst. Dyn. (2021), submitted |
| [17] | Mi, T.; Stépán, G.; Takács, D.; Chen, N., Vehicle shimmy modeling with Pacejka’s magic formula and the delayed tire model, J. Comput. Nonlinear Dyn., 15, 3, Article 031005 pp. (2020) |
| [18] | Ono, E.; Hosoe, S.; Tuan, H. D.; Doi, S., Bifurcation in vehicle dynamics and robust front wheel steering control, IEEE Trans. Control Syst. Technol., 6, 3, 412-420 (1998) |
| [19] | Pacejka, H., Tire and Vehicle Dynamics (2005), Elsevier |
| [20] | Paden, B.; Čáp, M.; Yong, S. Z.; Yershov, D.; Frazzoli, E., A survey of motion planning and control techniques for self-driving urban vehicles, IEEE Trans. Intell. Veh., 1, 1, 33-55 (2016) |
| [21] | Popp, K.; Schiehlen, W., Ground Vehicle Dynamics (2010), Springer |
| [22] | Rajamani, R., Vehicle Dynamics and Control (2012), Springer · Zbl 1268.70002 |
| [23] | Riekert, P.; Schunck, T.-E., Zur fahrmechanik des gummibereiften kraftfahrzeugs, Ing.-Arch., 11, 3, 210-224 (1940) |
| [24] | Schramm, D.; Hiller, M.; Bardini, R., Ground Vehicle Dynamics (2014), Springer |
| [25] | Sieber, J.; Engelborghs, K.; Luzyanina, T.; Samaey, G.; Roose, D., DDE-BIFTOOL Manual-bifurcation analysis of delay differential equations (2014), ArXiv Preprint ArXiv:1406.7144 |
| [26] | Ulsoy, A. G.; Peng, H.; Cakmakci, M., Automotive Control Systems (2012), Cambridge University Press |
| [27] | Várszegi, B.; Takács, D.; Orosz, G., On the nonlinear dynamics of automated vehicles – a nonholonomic approach, Eur. J. Mech. A, 74, 371-380 (2019) · Zbl 1406.70021 |
| [28] | Velenis, E.; Katzourakis, D.; Frazzoli, E.; Tsiotras, P.; Happee, R., Steady-state drifting stabilization of RWD vehicles, Control Eng. Pract., 19, 11, 1363-1376 (2011) |
| [29] | Voser, C.; Hindiyeh, R. Y.; Gerdes, J. C., Analysis and control of high sideslip manoeuvres, Veh. Syst. Dyn., 48, S1, 317-336 (2010) |
| [30] | Wurts, J.; Stein, J. L.; Ersal, T., Collision imminent steering at high speed using nonlinear model predictive control, IEEE Trans. Control Syst. Technol., 69, 8, 8278-8289 (2020) |
| [31] | Zhang, H.; Cao, D.; Du, H., Modeling, Dynamics, and Control of Electrified Vehicles (2018), Springer |
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