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.
Issue Section:
Technical Brief
References
1.
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
.2.
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
. 3.
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
.4.
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
.5.
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
.6.
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
.7.
Gu
, D.
, and Hu
, H.
, 2006
, “Receding Horizon Tracking Control of Wheeled Mobile Robots
,” IEEE Trans. Control Syst. Technol.
, 14
(4
), pp. 743
–749
.8.
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
.9.
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
.10.
Do
, K. D.
, Jiang
, Z. P.
, and Pan
, J.
, 2004
, “Robust Adaptive Path Following of Underactuated Ships
,” Automatica
, 40
(6
), pp. 929
–944
.11.
Andersson
, S. B.
, 2007
, “Curve Tracking for Rapid Imaging in AFM
,” IEEE Trans. NanoBiosci.
, 6
(4
), pp. 354
–361
.12.
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
.13.
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
.14.
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
.15.
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.pdf16.
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
.17.
Austyn Mair
, W.
, and Birdsall
, D. L.
, 1996
, Aircraft Performance
(Cambridge Aerospace Series), Cambridge University Press
, Cambridge, UK
.18.
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
.19.
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
.20.
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
.21.
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
.22.
Wu
, W.
, and Zhang
, F.
, 2011
, “Cooperative Exploration of Level Surfaces of Three Dimensional Scalar Fields
,” Autom. IFAC J.
, 47
(9
), pp. 2044
–2051
.Copyright © 2017 by ASME
You do not currently have access to this content.
