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.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Woolsey, C. A. , and Techy, L. , 2009, “ Cross-Track Control of a Slender, Underactuated AUV Using Potential Shaping,” Ocean Eng., 36(1), pp. 82–91. [CrossRef]
Farrell, J. A. , Pang, S. , Li, W. , and Arrieta, R. , 2003, “ Chemical Plume Tracing Experimental Results With a Remus AUV,” IEEE Oceans Conference (OCEANS), San Diego, CA, Sept. 22–26, pp. 962–968.
Zhang, F. , Fiorelli, E. , and Leonard, N. E. , 2007, “ Exploring Scalar Fields Using Multiple Sensor Platforms: Tracking Level Curves,” 46th IEEE Conference on Decision and Control (CDC), New Orleans, LA, Dec. 12–14, pp. 3579–3584.
Zhang, F. , Fratantoni, D. M. , Paley, D. , Lund, J. , and Leonard, N. E. , 2007, “ Control of Coordinated Patterns for Ocean Sampling,” Int. J. Control, 80(7), pp. 1186–1199. [CrossRef]
Yoshizawa, K. , Hashimoto, H. , Wada, M. , and Mori, S. , 1996, “ Path Tracking Control of Mobile Robots Using a Quadratic Curve,” IEEE Intelligent Vehicles Symposium (IV), Tokyo, Japan, Sept. 19–20, pp. 58–63.
Yang, J.-M. , and Kim, J.-H. , 1999, “ Sliding Mode Control for Trajectory Tracking of Nonholonomic Wheeled Mobile Robots,” IEEE Trans. Rob. Autom., 15(3), pp. 578–587. [CrossRef]
Gu, D. , and Hu, H. , 2006, “ Receding Horizon Tracking Control of Wheeled Mobile Robots,” IEEE Trans. Control Syst. Technol., 14(4), pp. 743–749. [CrossRef]
Aguiar, A. P. , and Hespanha, J. P. , 2007, “ Trajectory-Tracking and Path-Following of Underactuated Autonomous Vehicles With Parametric Modeling Uncertainty,” IEEE Trans. Autom. Control, 52(8), pp. 1362–1379. [CrossRef]
Borhaug, E. , and Pettersen, K. Y. , 2005, “ Adaptive Way-Point Tracking Control for Underactuated Autonomous Vehicles,” 44th IEEE Conference on Decision and Control, European Control Conference (CDC-ECC), Seville, Spain, Dec. 15, pp. 4028–4034.
Do, K. D. , Jiang, Z. P. , and Pan, J. , 2004, “ Robust Adaptive Path Following of Underactuated Ships,” Automatica, 40(6), pp. 929–944. [CrossRef]
Andersson, S. B. , 2007, “ Curve Tracking for Rapid Imaging in AFM,” IEEE Trans. NanoBiosci., 6(4), pp. 354–361. [CrossRef]
Chang, D. E. , Shadden, S. C. , Marsden, J. E. , and Olfati-Saber, R. , 2003, “ Collision Avoidance for Multiple Agent Systems,” 42nd IEEE Conference on Decision and Control (CDC), Maui, HI, Dec. 9–12, pp. 539–543.
Singh, L. , Stephanou, H. , and Wen, J. , “ Real-Time Robot Motion Control With Circulatory Fields,” IEEE International Conference on Robotics and Automation (ICRA), Minneapolis, MN, Apr. 22–28, pp. 2737–2742.
Zhang, F. , Justh, E. , and Krishnaprasad, P. S. , 2004, “ Boundary Following Using Gyroscopic Control,” 43rd IEEE Conference on Decision and Control (ICDC), Nassau, Bahamas, Dec. 14–17, pp. 5204–5209.
Fiorelli, E. , Leonard, N. E. , and Pradeep, B. , 2003, “ Adaptive Sampling Using Feedback Control of an Autonomous Underwater Glider Fleet,” 13th International Symposium on Unmanned Untethered Submersible Technology (UUST), Durham, NH, Aug. 24–27, pp. 1–16. http://www.princeton.edu/~naomi/uust03FBLSp.pdf
Fiorelli, E. , Leonard, N. E. , Bhatta, P. , Paley, D. A. , Bachmayer, R. , and Fratantoni, D. M. , 2006, “ Multi-AUV Control and Adaptive Sampling in Monterey Bay,” IEEE J. Oceanic Eng., 31(4), pp. 935–948. [CrossRef]
Austyn Mair, W. , and Birdsall, D. L. , 1996, Aircraft Performance (Cambridge Aerospace Series), Cambridge University Press, Cambridge, UK.
Kidono, K. , Miura, J. , and Shirai, Y. , 2002, “ Autonomous Visual Navigation of a Mobile Robot Using a Human-Guided Experience,” Rob. Auton. Syst., 40(2–3), pp. 121–130. [CrossRef]
Malisoff, M. , Mazenc, F. , and Zhang, F. , 2012, “ Stability and Robustness Analysis for Curve Tracking Control Using Input-to-State Stability,” IEEE Trans. Autom. Control, 57(5), pp. 1320–1326. [CrossRef]
Mukhopadhyay, S. , Wang, C. , Patterson, M. , Malisoff, M. , and Zhang, F. , 2014, “ Collaborative Autonomous Surveys in Marine Environments Affected by Oil Spills,” Cooperative Robots and Sensor Networks (Studies in Computational Intelligence), A. Koubaa and A. Khelil , eds., Vol. 554, Springer, Berlin, pp. 87–113. [CrossRef] [PubMed] [PubMed]
Mukhopadhyay, S. , Wang, C. , Bradshaw, S. , Maxon, S. , Patterson, M. , and Zhang, F. , 2012, “ Controller Performance of Marine Robots in Reminiscent Oil Surveys,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vilamoura, Portugal, Oct. 7–12, pp. 1766–1771.
Wu, W. , and Zhang, F. , 2011, “ Cooperative Exploration of Level Surfaces of Three Dimensional Scalar Fields,” Autom. IFAC J., 47(9), pp. 2044–2051. [CrossRef]


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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In