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Research Papers

Convolution-Based Trajectory Generation Methods Using Physical System Limits

[+] Author and Article Information
Geon Lee

Korean Institute of Science and
Technology (KIST),
Seoul, 136-791, Republic of Korea
e-mail: 022454@kist.re.kr

Jinhyun Kim

Department of Mechanical Engineering,
Seoul National University of
Science and Technology,
Seoul, 139-743, Republic of Korea
e-mail: jinhyun@seoultech.ac.kr

Youngjin Choi

Department of Electronic Systems Engineering,
Hanyang University,
Ansan, 426-791, Republic of Korea
e-mail: cyj@hanyang.ac.kr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 29, 2010; final manuscript received June 22, 2012; published online October 29, 2012. Assoc. Editor: Warren E. Dixon.

J. Dyn. Sys., Meas., Control 135(1), 011001 (Oct 29, 2012) (8 pages) Paper No: DS-10-1354; doi: 10.1115/1.4007551 History: Received November 29, 2010; Revised June 22, 2012

This paper proposes two novel convolution-based trajectory generation methods using physical system limits such as maximum velocity, maximum acceleration, and maximum jerk. Convolution is a mathematical operation on two functions of an input function and a convoluted function, producing an output function that is typically viewed as a modified version of input function. Time duration parameters of the convoluted functions with a unit area are determined from the given physical system limits. The convolution-based trajectory generation methods to be proposed in this paper have three advantages; first, a continuously differentiable trajectory is simply obtained by applying successive convolution operations; second, a resultant trajectory is always generated satisfying the given physical system limits; third, the suggested methods have low computational burden thanks to recursive form of convolution operation. The suggested methods consider both zero and nonzero initial/terminal conditions. Finally, the effectiveness of the suggested methods is shown through numerical simulations.

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Figures

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Fig. 1

Convolution-based trajectory generation method: zero states

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Fig. 2

Convolution-based trajectory generation method: nonzero terminal condition

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Fig. 3

Decomposition of the trajectory with nonzero states into a rectangular initial velocity function and the nonzero final velocity function

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Fig. 4

Four possible trajectories according to the given distance, initial and terminal conditions

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Fig. 5

Criterion distance Sn* obtained as t0 →0 in the Fig. 2, in the case of zero initial velocity

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Fig. 6

The distance to be moved is equal to the area of polygon

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Fig. 7

Block diagram of the whole algorithm

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Fig. 8

Block diagram of the convolution

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Fig. 9

Simulation results of the method I

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Fig. 10

Simulation results of the method II

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