zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Formation control of multiple elliptical agents with limited sensing ranges. (English) Zbl 1246.93005
Summary: This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptical shape and with limited sensing ranges to perform a desired formation. The controllers guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on an algebraic separation condition between ellipses, Lyapunov’s method, and smooth or p-times differentiable step functions. These functions are introduced and incorporated into novel potential functions to solve the collision avoidance problem without the need for switchings under the agents’ limited sensing ranges.
93A14Decentralized systems
68T40Robotics (AI aspects)
[1]Balch, T.; Arkin, R. C.: Behavior-based formation control for multirobot teams, IEEE transactions on robotics and automation 14, 926-939 (1998)
[2]Choi, Y.; Wang, W.; Liu, Y.; Kim, M.: Continuous collision detection for two moving elliptic disks, IEEE transactions on robotics 22, 213-224 (2006)
[3]Das, A.; Fierro, R.; Kumar, V.; Ostrowski, J.; Spletzer, J.; Taylor, C.: A vision based formation control framework, IEEE transactions on robotics and automation 18, 813-825 (2002)
[4]Dimarogonas, D. V.; Loizou, S. G.; Kyriakopoulos, K. J.; Zavlanos, M. M.: A feedback stabilization and collision avoidance scheme for multiple independent non-point agents, Automatica 42, 229-243 (2006) · Zbl 1099.93029 · doi:10.1016/j.automatica.2005.09.019
[5]Do, K. D.: Bounded controllers for formation stabilization of mobile agents with limited sensing ranges, IEEE transactions on automatic control 52, 569-576 (2007)
[6]Do, K. D.: Output-feedback formation tracking control of unicycle-type mobile robots with limited sensing ranges, Robotics and autonomous systems 57, 34-47 (2009)
[7]Do, K. D.: Practical control of underactuated ships, Ocean engineering 37, 1111-1119 (2010)
[8]Do, K.D. (2012). Formation control of underactuated ships with elliptical shape approximation and limited communication ranges. Automatica, in press (http://dx.doi.org/10.1016/j.automatica.2011.11.013).
[9]Do, K. D.; Pan, J.: Control of ships and underwater vehicles: design for underactuated and nonlinear marine systems, (2009)
[10]Egerstedt, M.; Hu, X.: Formation constrained multiagent control, IEEE transactions on robotics and automation 17, 947-951 (2001)
[11]Hu, J.; Feng, G.: Distributed tracking control of leader follower multi-agent systems under noisy measurement, Automatica 46, 1382-1387 (2010) · Zbl 1204.93011 · doi:10.1016/j.automatica.2010.05.020
[12]Hussein, I.; Bloch, A.: Optimal control of underactuated nonholonomic mechanical systems, IEEE transactions on automatic control 53, 668-681 (2008)
[13]Hussein, I.; Stipanovic, D.: Effective coverage control for mobile sensor networks with guaranteed collision avoidance, IEEE transactions on control systems technology 15, 642-657 (2007)
[14]Jonathan, R. T.; Beard, R. W.; Young, B.: A decentralized approach to formation maneuvers, IEEE transactions on robotics and automation 19, 933-941 (2003)
[15]Khalil, H.: Nonlinear systems, (2002) · Zbl 1003.34002
[16]Ogren, P.; Fiorelli, E.; Leonard, N. E.: Cooperative control of mobile sensor networks: adaptive gradient climbing in a distributed environment, IEEE transactions on automatic control 49, 1292-1302 (2004)
[17]Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory, IEEE transactions on automatic control 51, 401-420 (2006)
[18]Rimon, E.; Koditschek, D. E.: Exact robot navigation using artificial potential functions, IEEE transactions on robotics and automation 8, 501-518 (1992)
[19]Stipanovic, D. M.; Inalhan, G.; Teo, R.; Tomlin, C. J.: Decentralized overlapping control of a formation of unmanned aerial vehicles, Automatica 40, 1285-1296 (2004) · Zbl 1073.93556 · doi:10.1016/j.automatica.2004.02.017
[20]Tanner, H. G., & Kumar, A. (2005). Towards decentralization of multi-robot navigation functions. In Proceedings of the 2005 IEEE international conference on robotics and automation, Barcelona, Spain (pp. 4132–4137).
[21]Wang, P.: Navigation strategies for multiple autonomous mobile robots moving in formation, Journal of robotic systems 8, 177-195 (1991) · Zbl 0716.70035 · doi:10.1002/rob.4620080204