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Research Papers

Implementation of Reversing Control on a Doubly Articulated Vehicle

[+] Author and Article Information
Amy J. Rimmer

Department of Engineering,
University of Cambridge,
Cambridge CB2 1TN, UK
e-mail: amyrimmer@gmail.com

David Cebon

Department of Engineering,
University of Cambridge,
Cambridge CB2 1TN, UK
e-mail: dc@eng.cam.ac.uk

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 2, 2016; final manuscript received December 4, 2016; published online April 13, 2017. Assoc. Editor: Tesheng Hsiao.

J. Dyn. Sys., Meas., Control 139(6), 061011 (Apr 13, 2017) (9 pages) Paper No: DS-16-1225; doi: 10.1115/1.4035456 History: Received May 02, 2016; Revised December 04, 2016

The problem of reversing vehicles with two trailers could be solved with a semi-autonomous assistance system for automatically steering the vehicle. In the literature found, no controllers have been implemented on a full-size vehicle with two trailers. In this paper, two simple path-tracking controllers are presented for automating the reversing of a “B-double” vehicle, consisting of a tractor and two trailers. One of the controllers is a heuristic “preview point” controller; the other uses a state feedback approach. The controllers steer the wheels on the front axle so as to stabilize the vehicle in reverse and control the path of the rearmost axle to follow a prescribed path. A tuning strategy is outlined where both controllers are tuned using the linear quadratic regulator and have the same closed-loop poles. The two controllers are implemented on a full-size B-double test vehicle. Experimental results are discussed, and the controller performances are evaluated against criteria. With the state feedback controller, the test vehicle was able to track target paths, consisting of a roundabout and a lane change, to within 50 mm.

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Figures

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Fig. 1

B-double test vehicle: The Denby extra ecolink B-trailer was loaned by Denby transport. The other vehicle units are part of the CVDC test vehicle fleet. Distances shown between the front axle and the hitch point for the tractor unit, hitch-to-hitch for the B-trailer, and hitch to equivalent rear axle for the tanker.

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Fig. 2

Vehicle diagram illustrating preview point controller, shown here for a doubly articulated vehicle

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Fig. 3

Control loop for preview point controller shown for a doubly articulated vehicle. Quantities are defined in Sec. 2.2.

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Fig. 4

Vehicle diagram illustrating state feedback controller, for a doubly articulated vehicle

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Fig. 5

Control loop for a state feedback controller shown for a doubly articulated vehicle. Here, κ denotes the curvature of the path and the other quantities are defined in Sec. 2.3.

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Fig. 6

Vehicle diagram showing dimensions and velocities for doubly articulated vehicle

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Fig. 7

Diagram of test equipment for B-double test vehicle (vehicles separated for clarity)

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Fig. 8

Block diagram representing global controller software code. The implementation of the “controller” block can be either of the two paths following controllers (preview point or state feedback).

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Fig. 9

Lane change maneuver showing the positions of the equivalent axle of the B-double rear trailer when state feedback and preview point controllers are used

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Fig. 10

Roundabout maneuver showing the positions of the equivalent axle of the B-double rear trailer when state feedback and preview point controllers are used

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Fig. 11

Comparison of state feedback and preview point controllers implemented on B-double for lane change path, tuned with LQR weighting (w) of 5, showing (a) rear trailer effective axle lateral offset, (b) front axle steer angle, (c) first articulation angle, (d) second articulation angle, (e) front axle steer rate, and (f) vehicle swept path. Gray lines indicate the state feedback controller, and black lines indicate the preview point controller.

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Fig. 12

Comparison of state feedback and preview point controllers implemented on B-double for roundabout path, tuned with LQR weighting (w) of 5, showing (a) rear trailer effective axle lateral offset, (b) front axle steer angle, (c) first articulation angle, (d) second articulation angle, (e) front axle steer rate, and (f) vehicle swept path. Gray lines indicate the state feedback controller, and black lines indicate the preview point controller.

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Fig. 13

Summary of B-double experimental results when preview point and state feedback controllers are implemented on lane change and roundabout paths. LQR weighting (w) ranged from 0.1 to 10. (a) RMS offsets of the rear trailer equivalent axle and (b) RMS steer rates.

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