TY - GEN
T1 - Smoothly blending vector fields for global robot navigation
AU - Lindemann, Stephen R.
AU - LaValle, Steven M.
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2005
Y1 - 2005
N2 - We introduce a new algorithm for constructing smooth vector fields for global robot navigation. Given a d-dimensional cell complex with each cell a convex polygon, our algorithm defines a number of local vector fields: one for each cell, and one for each face connecting two cells together. We smoothly blend these component vector fields together using bump functions; the precomputation of the component vector field and all queries can be done in linear time. The integral curves of the resulting globally-defined vector field are guaranteed to arrive at a neighborhood of the goal state in finite time. Except for a set of measure zero, the vector field is smooth. The resulting vector field can be used directly to control kinematic systems or can be used to develop dynamic control policies. We prove convergence for the integral curves of the vector fields produced by our algorithm and give examples illustrating the practical advantages of our technique.
AB - We introduce a new algorithm for constructing smooth vector fields for global robot navigation. Given a d-dimensional cell complex with each cell a convex polygon, our algorithm defines a number of local vector fields: one for each cell, and one for each face connecting two cells together. We smoothly blend these component vector fields together using bump functions; the precomputation of the component vector field and all queries can be done in linear time. The integral curves of the resulting globally-defined vector field are guaranteed to arrive at a neighborhood of the goal state in finite time. Except for a set of measure zero, the vector field is smooth. The resulting vector field can be used directly to control kinematic systems or can be used to develop dynamic control policies. We prove convergence for the integral curves of the vector fields produced by our algorithm and give examples illustrating the practical advantages of our technique.
UR - http://www.scopus.com/inward/record.url?scp=33847180512&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2005.1582713
DO - 10.1109/CDC.2005.1582713
M3 - Conference contribution
AN - SCOPUS:33847180512
SN - 0780395689
SN - 9780780395688
T3 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
SP - 3553
EP - 3559
BT - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
T2 - 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Y2 - 12 December 2005 through 15 December 2005
ER -