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Research Papers

Near Time-Optimal Real-Time Path Following Under Error Tolerance and System Constraints

[+] Author and Article Information
Yen-Chi Chang

Mechanical and Aerospace Engineering,
University of California, Los Angeles,
Los Angeles, CA 90095
e-mail: yenchichang@ucla.edu

Cheng-Wei Chen

Mechanical and Aerospace Engineering,
University of California, Los Angeles,
Los Angeles, CA 90095
e-mail: jwster@ucla.edu

Tsu-Chin Tsao

Professor
Mechanical and Aerospace Engineering,
University of California, Los Angeles,
Los Angeles, CA 90095
e-mail: ttsao@ucla.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 6, 2017; final manuscript received November 17, 2017; published online January 16, 2018. Assoc. Editor: Soo Jeon.

J. Dyn. Sys., Meas., Control 140(7), 071004 (Jan 16, 2018) (11 pages) Paper No: DS-17-1138; doi: 10.1115/1.4038651 History: Received March 06, 2017; Revised November 17, 2017

An online fast path following control algorithm subject to contouring error tolerance and other prototypical constraints, analogous to a racing car within track boundaries, is presented. A receding horizon quadratic programming (QP) for real-time implementation on electromechanical systems is proposed. A key feature of the algorithm is that the challenging constrained minimal-time optimization is approximated by minimizing the distance between an unattainable target and actual location when moving along the contour, mimicking pursuing rabbit lures in greyhound racing. Modeling errors and other uncertainties in implementation are compensated for by observer state feedback, which provides real-time updates of initial states for every receding horizon optimization. Applying the proposed online method, the requirement of an accurate model from conventional offline trajectory planning methods is relaxed. The proposed method is demonstrated by experimental results from a 1 kHz sampling rate implementation on a multi-axis nanolithographic position system.

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Figures

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Fig. 1

Block diagram of the fast contour tracking system

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Fig. 2

Block diagram of the proposed MPC structure

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Fig. 3

Schematic diagram of the approximated time-optimal receding horizon control

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Fig. 11

Simulated (black solid line) contour error, axial velocities, and feed rate with aggressive δθmax (case 3)

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Fig. 4

Multiscale alignment and positioning system

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Fig. 8

Simulated and measured contour error, axial velocities, and feed rate with conservative δθmax (case 2). Solid thick lines: simulation results, solid thin lines: experimental results, dash lines: constraints.

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Fig. 9

Measured position and boundary with moderate δθmax (case 2)

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Fig. 10

Cycle time of different horizon length when using moderate δθmax (case 2)

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Fig. 5

The 12-segment diamond-shape contour

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Fig. 6

Effect of modeling error on contour error

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Fig. 7

Simulated and measured contour error, axial velocities, and feed rate with conservative δθmax (case 1). Solid thick lines: simulation results, solid thin lines: experimental results, dash lines: constraints.

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