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TECHNICAL PAPERS

Motorcycle Steering Control by Road Preview

[+] Author and Article Information
R. S. Sharp

Department of Electrical and Electronic Engineering, Imperial College, London SW7 2AZ, UKrobin.sharp@imperial.ac.uk

J. Dyn. Sys., Meas., Control 129(4), 373-381 (Dec 14, 2006) (9 pages) doi:10.1115/1.2745842 History: Received September 26, 2005; Revised December 14, 2006

The main objectives of the work described are to devise an effective path-based motorcycle simulation capability and to add to understanding of how riders control motorcycles. Optimal linear preview control theory was previously applied to the tracking of a roadway by a car, using a simple car model operating in fixed control. Similar theory is applied to path control of motorcycles. The simple car previously employed is replaced by a much more elaborate motorcycle. The steering angle control used previously is changed into steering torque control. Rider upper body lean torque is also allowed as a control input. The machine speed is considered constant but is a parameter of the motion. The objective of the optimal control is to minimize a weighted sum of tracking errors, rider lean angle and control power. The time-invariant optimal control corresponding to a white noise disturbance and to an infinite optimization horizon is found for many situations, involving variations in machine speed and performance priorities. Tight controls, corresponding to high weightings on performance, and loose controls, corresponding to high weightings on control power, are identified. Results show the expected pattern for preview control, that information well into the future is of limited value in determining the present control inputs. Full system performance is achievable with only finite preview. The extent of the preview necessary for full performance is determined as a function of machine speed and performance priorities. This necessary preview is found to be in accord with conventional wisdom of motorcycle riding and rider training. Optimal path tracking preview controls are shown to represent the inverse dynamics of the motorcycle. New light is shed on the relative effectiveness of steering torque and body lean torque controls. Simulations of an optimally controlled motorcycle and rider combination are conducted. A typical lane change path and an S-shaped path from the literature are used. For a chosen speed, optimal controls are installed on the machine for which they were derived and simulation results showing tracking performance, control inputs, and other responses are included. Transformation of the problem from a global description, in which the optimal control is found, to a local description corresponding to the rider’s view, is described. It is concluded that a motorcycle rider model representing a useful combination of steering control capability and computational economy has been established. The model yields new insights into rider and motorcycle behavior.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Optimal preview steer torque gains for tight single-control system with 500 preview points, q1=104, q2=4×104, q3=0, r1=1, and three speeds, as functions of the distance ahead

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Figure 2

Optimal preview steer torque gains for loose single-control system with 500 preview points, q1=100, q2=400, q3=0, r1=1, and three speeds, as functions of the distance ahead

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Figure 3

Optimal preview gains for tight dual-control system with 500 preview points and with equal weights on the two controls, q1=104, q2=4×104, q3=0, r1=r2=1, and three speeds, as functions of the distance ahead

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Figure 4

Optimal preview steer torque and upper body lean torque gains for loose dual-control system with 500 preview points and with equal weights on the two controls, q1=100, q2=400, q3=0, r1=r2=1, and three speeds, as functions of the distance ahead

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Figure 5

Optimal preview steer torque and upper body lean torque gains for tight dual-control system with 500 preview points and with unequal weights on the two controls, q1=104, q2=4×104, q3=0, r1=1, r2=0.1, and three speeds, as functions of the distance ahead

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Figure 6

Optimal preview steer torque and upper body lean torque gains for loose dual-control system with 500 preview points and with unequal weights on the two controls, q1=100, q2=400, q3=0, r1=1, r2=0.1, and three speeds, as functions of the distance ahead

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Figure 7

Required preview distances (99% criterion) for tight controls, q1=104, q2=4×104, q3=0. Circles show steer torque and crosses show lean torque for r1=r2=1. Pluses show steer torque and stars show lean torque for r1=1, r2=0.1. The squares are for the single-control system.

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Figure 8

Required preview distances (99% criterion) for loose controls, q1=100, q2=400, q3=0. Circles show steer torque and crosses show lean torque for r1=r2=1. Pluses show steer torque and stars show lean torque for r1=1, r2=0.1. The squares are for the single-control system.

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Figure 9

Lane change to the right at 30m∕s, with the upper graph showing the roadway and the motorcycle path and the lower graph showing the steering torque and the rider’s upper body lean torque applied. The controls presume 180m rider preview and weightings of q1=104, q2=4×104, q3=0, and r1=r2=1.

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Figure 10

Lane change to the right at 30m∕s, showing various aspects of the motions, scaled for clarity. The controls presume 180m preview and weightings of q1=104, q2=4×104, q3=0, and r1=r2=1.

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Figure 11

Lane change to the right at 30m∕s, with the upper graph showing the roadway and the motorcycle path and the lower graph showing the steering torque and the rider’s upper body lean torque applied. The controls presume 180m preview and weightings of q1=104, q2=4×104, q3=0 and r1=1, r2=0.1.

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Figure 12

Lane change at 30m∕s, showing various aspects of the motions, scaled for clarity. The controls presume 180m preview and weightings of q1=104, q2=4×104, q3=0, and r1=1, r2=0.1.

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Figure 13

Lane change at 30m∕s, with the upper graph showing the roadway and the motorcycle path and the lower graph showing the steering torque and the rider’s upper body lean torque applied. The controls presume 250m preview and weightings of q1=100, q2=400, q3=0 and r1=r2=1.

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Figure 14

Lane change to the right at 30m∕s, showing various aspects of the motions, scaled for clarity. The controls presume 250m rider preview and weightings of q1=100, q2=400, q3=0 and r1=r2=1.

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Figure 15

S-maneuver simulation at 30m∕s, with the upper graph showing the roadway and the motorcycle path and the lower graph showing the steering torque and the rider’s upper body lean torque applied. The controls presume 90m preview and weightings of q1=104, q2=0, q3=105 and r1=r2=1. With these weightings, the rider lean torque is small compared with the steering torque.

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Figure 16

S-maneuver simulation at 30m∕s, showing various aspects of the motion, scaled for clarity. The controls presume 90m rider preview and weightings of q1=104, q2=0, q3=105 and r1=r2=1, as in Fig. 1. The weightings cause the rider to lean just a little relative to the motorcycle.

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Figure 17

Path tracking error in S-maneuver of Figs.  1516

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