# zbMATH — the first resource for mathematics

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.

##### MSC:
 93A14 Decentralized systems 68T40 Artificial intelligence for robotics
Full Text:
##### References:
 [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 [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) · Zbl 1366.93496 [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). · Zbl 1246.93006 [9] Do, K.D.; Pan, J., Control of ships and underwater vehicles: design for underactuated and nonlinear marine systems, (2009), Springer [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 [12] Hussein, I.; Bloch, A., Optimal control of underactuated nonholonomic mechanical systems, IEEE transactions on automatic control, 53, 668-681, (2008) · Zbl 1367.49017 [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), Prentice Hall [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) · Zbl 1365.93243 [17] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE transactions on automatic control, 51, 401-420, (2006) · Zbl 1366.93391 [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 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.