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Research Papers

Preview Horizon Analysis for Vehicle Rollover Prevention Using the Zero-Moment Point

[+] Author and Article Information
Paul G. Stankiewicz

Department of Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: pgs5031@gmail.com

Alexander A. Brown

Department of Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: alexanderallenbrown@gmail.com

Sean N. Brennan

Associate Professor
Mem. ASME
Department of Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: sbrennan@psu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 29, 2014; final manuscript received March 30, 2015; published online May 29, 2015. Assoc. Editor: Junmin Wang.

J. Dyn. Sys., Meas., Control 137(9), 091002 (Sep 01, 2015) (12 pages) Paper No: DS-14-1043; doi: 10.1115/1.4030390 History: Received January 29, 2014; Revised March 30, 2015; Online May 29, 2015

This research estimates the minimum preview time needed to prevent untripped wheel lift events by analyzing simple maneuvers that are idealizations of a human driver's response in collision avoidance situations. To predict a vehicle's future rollover propensity, the zero-moment point (ZMP) metric is applied to projected vehicle trajectories. Comparing different amounts of preview, the results show that short-range predictions, ranging from 0.1 s to 0.7 s, are sufficient to prevent nearly all dynamics-induced rollovers in typical highway curves. These results are useful to determine the minimum preview horizons, with respect to rollover, that may be necessary for more advanced vehicle control methods, such as model predictive control (MPC).

Copyright © 2015 by ASME
Topics: Vehicles , Wheels , Tires
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References

Figures

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Fig. 1

Vehicle models viewed along the body-fixed x-axis for (a) 2DOF rigid model (b) 3DOF roll model. CG refers to the rigid model's center-of-gravity for the total mass. CGu and CGs, meanwhile, refer to the unsprung mass and sprung mass, respectively, of the roll model.

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Fig. 2

Free-body diagram illustrating the vehicle's lateral and yaw dynamics

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Fig. 3

Roll model on banked slope with zero moment point illustration

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Fig. 4

Generalized example of corrective steering maneuver #1 simulations

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Fig. 5

Example of the iterative calculation of the preview time for corrective steering #1

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Fig. 6

yZMP (a) with and (b) without corrective steering #1

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Fig. 7

Minimum preview times needed to prevent wheel lift for corrective steering #1. The “Tire Skid Threshold” indicates the steering frequencies above which skidding is likely to precede rollover.

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Fig. 8

Contour plots of minimum preview times (s) needed to prevent wheel lift for corrective steering #1 for (a) linear roll model and (b) carsim. The Tire Skid Threshold indicates the steering frequencies above which skidding is likely to precede rollover. The “No Rollover” zone indicates where steering combinations did not induce wheel lift.

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Fig. 9

Bode plot of steering angle and yZMP

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Fig. 10

Generalized example of corrective steering maneuver #2 simulations

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Fig. 11

Example of the iterative calculation of the preview time for corrective steering #2

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Fig. 12

yZMP (a) with and (b) without corrective steering #2

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Fig. 13

Minimum preview times needed to prevent wheel lift for corrective steering #2. The Tire Skid Threshold indicates the steering frequencies above which skidding is likely to precede rollover.

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Fig. 14

Contour plot of minimum preview times (s) needed to prevent wheel lift for corrective steering #2 for (a) linear roll model and (b) carsim. The Tire Skid Threshold indicates the steering frequencies above which skidding is likely to precede rollover. The No Rollover zone indicates where steering combinations did not induce wheel lift.

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Fig. 15

Preview times needed to prevent wheel lift for varying longitudinal velocities (−23 deg, 0.2 Hz steering combination)

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Fig. 16

Contour plot of minimum preview times (s) needed to prevent wheel lift for corrective steering #1 for (a) vehicle variation #2 and (b) vehicle variation #3. The Tire Skid Threshold indicates the steering frequencies above which skidding is likely to precede rollover. The No Rollover zone indicates where steering combinations did not induce wheel lift.

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Fig. 17

Minimum preview times needed to prevent wheel lift for corrective steering #1 for each vehicle variation (−23 dev, 0.2 Hz steering combination)

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Fig. 18

Contour plot of minimum preview times (s) needed to prevent wheel lift for corrective steering #1 for (a) a flat road (0 deg bank angle) and (b) an intermediate slope (4 deg bank angle). The Tire Skid Threshold indicates the steering frequencies above which skidding is likely to precede rollover. The No Rollover zone indicates where steering combinations did not induce wheel lift.

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