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Research Papers

Motion Planning and Control of a Tractor With a Steerable Trailer Using Differential Flatness

[+] Author and Article Information
Ji-Chul Ryu

Mechanical Systems Laboratory, Department of Mechanical Engineering, University of Delaware, Newark, DE 19716jcryu@udel.edu

Sunil K. Agrawal1

Mechanical Systems Laboratory, Department of Mechanical Engineering, University of Delaware, Newark, DE 19716agrawal@udel.edu

Jaume Franch

Department of Applied Mathematics 4, Universitat Politecnica de Catalunya, Barcelona 08034, Spainjfranch@mat.upc.es

1

Corresponding author.

J. Comput. Nonlinear Dynam 3(3), 031003 (Apr 30, 2008) (8 pages) doi:10.1115/1.2908178 History: Received February 22, 2007; Revised December 02, 2007; Published April 30, 2008

This paper presents a methodology for trajectory planning and tracking control of a tractor with a steerable trailer based on the system’s dynamic model. The theory of differential flatness is used as the basic approach in these developments. Flat outputs are found that linearize the system’s dynamic model using dynamic feedback linearization, a subclass of differential flatness. It is demonstrated that this property considerably simplifies motion planning and the development of controller. Simulation results are presented in the paper, which show that the developed controller has the desirable performance with exponential stability.

FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A tractor with a steerable trailer described by six configuration variables x,y,θ,ψ,δ1,δ2

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Figure 7

The tractor’s desired and actual trajectories with the end conditions in Table 2. Initial error of 1.0m for x is given to observe the controller performance. The actual trajectory converges to the desired one.

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Figure 6

The computed original torque inputs with the end conditions in Table 1. τv is the torque input for the tractor’s front wheel and τδ1, τδ2 are for steering of the tractor’s front wheel and the trailer’s rear wheel, respectively.

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Figure 5

Desired and actual trajectories for θ, ψ, δ1, and δ2 with the end conditions in Table 1. The desired trajectories of θ and δ1 are calculated from the planned trajectories of the flat outputs (F1,F2)=(x,y), and the desired trajectory of δ2 is calculated from (F1,F2,F3) using the diffeomorphism constructed in Sec. 3.

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Figure 4

The tractor’s desired and actual trajectories with the end conditions in Table 1. Initial error of 1.0m for x is given to observe the controller performance. The actual trajectory converges to the desired one.

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Figure 3

Integrated planner and controller with the dynamic model of the tractor with a steerable trailer

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Figure 2

Instantaneous centers of rotation of the tractor and trailer segments

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Figure 8

Desired and actual trajectories for θ, ψ, δ1, and δ2 with the end conditions in Table 2. The desired trajectories of θ and δ1 are calculated from the planned trajectories of the flat outputs (F1,F2)=(x,y), and the desired trajectory of δ2 is calculated from (F1,F2,F3) using the diffeomorphism constructed in Sec. 3.

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Figure 9

The computed original torque inputs with the end conditions in Table 2. τv is the torque input for the tractor’s front wheel and τδ1, τδ2 are for steering of the tractor’s front wheel and the trailer’s rear wheel, respectively.

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