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Technical Brief

Three-Dimensional Curve Tracking for Particles Using Gyroscopic Control

[+] Author and Article Information
Chuanfeng Wang

Western Digital Corporation,
Irvine, CA 92612
e-mail: chuanfengwang@gmail.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 27, 2016; final manuscript received June 20, 2017; published online August 28, 2017. Assoc. Editor: Zongxuan Sun.

J. Dyn. Sys., Meas., Control 139(12), 124503 (Aug 28, 2017) (5 pages) Paper No: DS-16-1159; doi: 10.1115/1.4037284 History: Received March 27, 2016; Revised June 20, 2017

Curve-tracking control is challenging and fundamental in many robotic applications for an autonomous agent to follow a desired path. In this paper, we consider a particle, representing a fully actuated autonomous robot, moving at unit speed under steering control in the three-dimensional (3D) space. We develop a feedback control law that enables the particle to track any smooth curve in the 3D space. Representing the 3D curve in the natural Frenet frame, we construct the control law under which the moving direction of the particle will be aligned with the tangent direction of the desired curve and the distance between the particle and the desired curve will converge to zero. We demonstrate the effectiveness of the proposed 3D curve-tracking control law in simulations.

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Figures

Grahic Jump Location
Fig. 1

Simulation result in nominal condition: (a) actual trajectory and desired curve and (b) control input magnitude and components along three axes

Grahic Jump Location
Fig. 2

Simulation result with noise injected into control effort: (a) actual trajectory and desired curve and (b) control input magnitude and components along three axes

Grahic Jump Location
Fig. 3

Simulation results under different natural Frenet frame selections

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