@article{44c2a4f252ff4d4a90d3874ddd721227,
title = "On minimum-time paths of bounded curvature with position-dependent constraints",
abstract = "We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with constraints on the minimum turning radius of the particle over multiple regions of the state space. Necessary conditions for optimality of these paths are derived to characterize the nature of optimal paths, both when the particle is inside a region and when it crosses boundaries between neighboring regions. These conditions are used to characterize families of optimal and nonoptimal paths. Among the optimality conditions, we derive a {"}refraction{"} law at the boundary of the regions that generalizes the so-called Snell's law of refraction in optics to the case of paths with bounded curvature. Tools employed to deduce our results include recent principles of optimality for hybrid systems. A numerical example is given to demonstrate the derived results.",
keywords = "Dubins vehicle, Hybrid control, Motion planning, Optimal control",
author = "Sanfelice, {Ricardo G.} and Yong, {Sze Zheng} and Emilio Frazzoli",
note = "Funding Information: This research has been partially supported by ARO through grant W911NF-07-1-0499 and MURI grant W911NF-11-1-0046 , by NSF through grants 0715025 and CAREER Grant ECS-1150306 , and by AFOSR through grant FA9550-12-1-0366 . The material in this paper was partially presented at the 11th International Conference on Hybrid Systems: Computation and Control (HSCC{\textquoteright}08), April 22–24, 2008, St. Louis, Missouri, USA. This paper was recommended for publication in revised form by Associate Editor Kok Lay Teo under the direction of Editor Ian R. Petersen. Funding Information: Ricardo G. Sanfelice received the B.S. degree in Electronics Engineering from the Universidad Nacional de Mar del Plata, Buenos Aires, Argentina, in 2001. He joined the Center for Control, Dynamical Systems, and Computation at the University of California, Santa Barbara in 2002, where he received his M.S. and Ph.D. degrees in 2004 and 2007, respectively. During 2007 and 2008, he was a Postdoctoral Associate at the Laboratory for Information and Decision Systems at the Massachusetts Institute of Technology. He visited the Centre Automatique et Systemes at the Ecole de Mines de Paris for four months. In 2009, he joined the faculty of the Department of Aerospace and Mechanical Engineering, where he is currently an Assistant Professor. Prof. Sanfelice is the recipient of the 2013 SIAM Control and Systems Theory Prize, the National Science Foundation (NSF) CAREER award, the Air Force Young Investigator Research Award (YIP), and the 2010 IEEE Control Systems Magazine Outstanding Paper Award. His research interests are in modeling, stability, robust control, observer design, and simulation of nonlinear and hybrid systems with applications to power systems, aerospace, and biology. ",
year = "2014",
month = feb,
doi = "10.1016/j.automatica.2013.11.016",
language = "English (US)",
volume = "50",
pages = "537--546",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier Limited",
number = "2",
}