Obstacle and Collision Avoidance Control Laws of a Swarm of Boids

Authors: Bibhya Sharma, Jito Vanualailai, Jai Raj

Abstract:

This paper proposes a new obstacle and collision avoidance control laws for a three-dimensional swarm of boids. The swarm exhibit collective emergent behaviors whilst avoiding the obstacles in the workspace. While flocking, animals group up in order to do various tasks and even a greater chance of evading predators. A generalized algorithms for attraction to the centroid, inter-individual swarm avoidance and obstacle avoidance is designed in this paper. We present a set of new continuous time-invariant velocity control laws is presented which is formulated via the Lyapunov-based control scheme. The control laws proposed in this paper also ensures practical stability of the system. The effectiveness of the proposed control laws is demonstrated via computer simulations

 

Keywords: Lyapunov-based Control Scheme, Motion planning, Practical stability, Swarm.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1336999

References:

[1] C. Blum and D. Merkle. Swarm Intelligence: Introduction and Applications. Springer - Verlag Berlin Heidelberg, Germany, 2008.
[2] M. Dorigo, L.M. Gambardella, M. Birattari, A. Martinoli, R. Poli, and T. Stützle. Ant Colony Optimization and Swarm Intelligence: 5th International Workshop, ANTS 2006, Brussels, Belgium, September 4-7, 2006, Proceedings, volume 4150. Springer, 2006.
[3] Q.K. Pan, M. Fatih Tasgetiren, and Y.C. Liang. A discrete particle swarm optimization algorithm for the no-wait flowshop scheduling problem. Computers & Operations Research, 35(9):2807–2839, 2008.
[4] G.J. Gelderblom, G. Cremers, M. de Wilt, W. Kortekaas, A. Thielmann, K. Cuhls, A. Sachinopoulou, and I. Korhonen. The opinions expressed in this study are those of the authors and do not necessarily reflect the views of the european commission. 2008.
[5] B. Sharma, J. Vanualailai, and S. Singh. Tunnel passing maneuvers of prescribed formations. International Journal of Robust and Nonlinear Control, 2012.
[6] B. Sharma, J. Vanualailai, and S. Singh. Lyapunov-based nonlinear controllers for obstacle avoidance with a planar -link doubly nonholonomic manipulator. Robotics and Autonomous Systems, 2012.
[7] B. Sharma, J. Vanualailai, and U. Chand. Flocking of multi-agents in constrained environments. European Journal of Pure and Applied Mathematics, 2(3):401–425, 2009.
[8] B. Sharma. New Directions in the Applications of the Lyapunov-based Control Scheme to the Findpath Problem. PhD thesis, University of the South Pacific, Suva, Fiji Islands, July 2008. PhD Dissertation.
[9] O. Lefebvre, F. Lamiraux, and C. Pradalier. Obstacles avoidance for car-like robots: Integration and experimentation on two robots. In IEEE International Conference on Robotics and Automation, New Orleans, April 26th - May 1st 2004.
[10] V. Lakshmikantham, S. Leela, and A. A. Martynyuk. Practical Stability of Nonlinear Systems. World Scientific, Singapore, 1990.
[11] C. W. Reynolds. Flocks, herds, and schools: A distributed behavioral model, in computer graphics. In Proceedings of the 14th annual conference on Computer graphics and interactive techniques, pages 25–34, New York, USA, 1987.
[12] A. Ordemann, G. Balazsi, and F. Moss. Pattern formation and stochastic motion of the zooplankton Daphina in a light field. Physica A, 325:260–266, 2003.
[13] F. Moss. Into the Daphina vortex. Chaos, 14(4):S10, 2004.
[14] M. T. Butler, Q. Wang, and R. M Harshy. Cell density and mobility protect swarming bacteria against antibiotics. Proceedings of the National Academy of Sciences, 107(8):3776–3781, 2010.
[15] P. C-Y. Sheu and Q. Xue. Intelligent Robotic Planning Systems. World Scientific, Singapore, 1993.