Technical Brief

Robot Path Planning in Uncertain Environments: A Language-Measure-Theoretic Approach

[+] Author and Article Information
Devesh K. Jha

Mechanical & Nuclear Engineering Department
Pennsylvania State University,
University Park, PA 16802
e-mail: dkj5042@psu.edu

Yue Li

Mechanical & Nuclear Engineering Department
Pennsylvania State University,
University Park, PA 16802
e-mail: yol5214@psu.edu

Thomas A. Wettergren

Naval Undersea Warfare Center,
Newport, RI 02841;
Mechanical & Nuclear Engineering Department
Pennsylvania State University,
University Park, PA 16802
e-mail: t.a.wettergren@ieee.org

Asok Ray

Fellow ASME
Mechanical & Nuclear Engineering Department
Pennsylvania State University,
University Park, PA 16802
e-mail: axr2@psu.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 23, 2014; final manuscript received May 31, 2014; published online October 21, 2014. Assoc. Editor: Jongeun Choi. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Dyn. Sys., Meas., Control 137(3), 034501 (Oct 21, 2014) (7 pages) Paper No: DS-14-1028; doi: 10.1115/1.4027876 History: Received January 23, 2014; Revised May 31, 2014

This paper addresses the problem of goal-directed robot path planning in the presence of uncertainties that are induced by bounded environmental disturbances and actuation errors. The offline infinite-horizon optimal plan is locally updated by online finite-horizon adaptive replanning upon observation of unexpected events (e.g., detection of unanticipated obstacles). The underlying theory is developed as an extension of a grid-based path planning algorithm, called ν, which was formulated in the framework of probabilistic finite state automata (PFSA) and language measure from a control-theoretic perspective. The proposed concept has been validated on a simulation test bed that is constructed upon a model of typical autonomous underwater vehicles (AUVs) in the presence of uncertainties.

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Garau, B., Alvarez, A., and Oliver, G., 2005, “Path Planning of Autonomous Underwater Vehicles in Current Fields With Complex Spatial Variability: An A* Approach,” IEEE International Conference on Robotics and Automation (ICRA), Barcelona, Spain, April 18–22, pp. 194–198. [CrossRef]
Pêtrès, C., Pailhas, Y., Patrón, P., Petillot, Y., Evans, J., and Lane, D., 2007, “Path Planning for Autonomous Underwater Vehicles,” IEEE Trans. Rob. Autom., 23(2), pp. 331–341. [CrossRef]
Rhoads, B., Mezić, I., and Poje, A., 2010, “Minimum Time Feedback Control of Autonomous Underwater Vehicles,” IEEE Conference on Decision and Control (CDC), Atlanta, GA, Dec. 15–17, pp. 5828–5834. [CrossRef]
Lolla, T., Ueckermann, P., Yiğit, K., Haley, P. J.Jr., and Lermusiaux, P. F. J., 2012, “Path Planning in Time Dependent Flow Fields Using Level Set Methods,” IEEE International Conference on Robotics and Automation (ICRA), St. Paul, MN, May 14–18, pp. 166–173.
Majumdar, A., and Tedrake, R., 2013, “Robust Online Motion Planning With Regions of Finite Time Invariance,” Algorithmic Foundations of Robotics X, Springer, Berlin, Germany, pp. 543–558.
Blackmore, L., Ono, M., Bektassov, A., and Williams, B. C., 2010, “A Probabilistic Particle-Control Approximation of Chance-Constrained Stochastic Predictive Control,” IEEE Trans. Rob., 26(3), pp. 502–517. [CrossRef]
Chakravorty, S., and Kumar, S., 2011, “Generalized Sampling-Based Motion Planners,” IEEE Trans. Syst. Man Cybern. Part B Cybern., 41(3), pp. 855–866. [CrossRef]
LaValle, S. M., 2006, Planning Algorithms, Cambridge University, Cambridge, UK.
Chattopadhyay, I., Mallapragada, G., and Ray, A., 2009, “ν*: A Robot Path Planning Algorithm Based on Renormalized Measure of Probabilistic Regular Languages,” Int. J. Control., 82(5), pp. 849–867. [CrossRef]
Ray, A., 2005, “Signed Real Measure of Regular Languages for Discrete-Event Supervisory Control,” Int. J. Control., 78(12), pp. 949–967. [CrossRef]
Chattopadhyay, I., and Ray, A., 2007, “Language-Measure-Theoretic Optimal Control of Probabilistic Finite-State Systems,” Int. J. Control., 80(8), pp. 1271–1290. [CrossRef]
Miettinen, K. M., 1999, Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, Boston, MA.
Ray, A., 2004, “Symbolic Dynamic Analysis of Complex Systems for Anomaly Detection,” Signal Process., 84(7), pp. 1115–1130. [CrossRef]
Gill, A., 1976, Applied Algebra for the Computer Sciences, Prentice-Hall, Englewood Cliffs, NJ.
Bapat, R. B., and Raghavan, T. E. S., 1997, Non-negative Matrices and Applications, Cambridge University, Cambridge, UK.
Rudin, W., 1988, Real and Complex Analysis, 3rd ed., McGraw Hill, New York.
Fossen, T. I., 1994, Guidance and Control of Ocean Vehicles, John Wiley, Chichester, West Sussex, UK.
Chattopadhyay, I., and Ray, A., 2011, “GODDeS: Globally ϵ-Optimal Routing Via Distributed Decision-Theoretic Self-Organization,” American Control Conference, San Francisco, CA, June 29–July 1, pp. 3215–3220.


Grahic Jump Location
Fig. 1

Illustration of the effects of uncontrollable transitions due to the disturbances. It is shown how uncontrollable transitions may cause the robot to end up in a different neighboring state of the origin cell, thus interfering with control actions.

Grahic Jump Location
Fig. 2

Optimal paths under different directions of the ocean current. (The vehicle is constrained to stay in the box and not hit the walls.)

Grahic Jump Location
Fig. 3

Real-time replanning over a finite time horizon T

Grahic Jump Location
Fig. 4

Replanning with |T|=2 for different characteristic weights



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