This paper proposes a solution to the motion planning
and control problem of car-like mobile robots which is required to
move safely to a designated target in a priori known workspace
cluttered with swarm of boids exhibiting collective emergent
behaviors. A generalized algorithm for target convergence and
swarm avoidance is proposed that will work for any number of
swarms. The control laws proposed in this paper also ensures
practical stability of the system. The effectiveness of the proposed
control laws are demonstrated via computer simulations of an
emergent behavior.
[1] J-C. Latombe, "Robot Motion Planning", Kluwer Academic Publishers,
USA, 1991.
[2] 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.
[3] B. Sharma, J. Vanualailai, and A. Prasad, "New collision avoidance
scheme for multi-agents: A solution to the blindman-s problem",
Advances in Differential Equations and Control Processes, vol. 3, no. 2,
pp. 141-169, 2009.
[4] M. Erdmann and T. Lozano-Perez, "On multiple moving objects", in
Proc. IEEE International Conference on Robotics and Automation, pp.
1419 1424, 1986.
[5] L. E. Parker, "A robot navigation algorithm for moving obstacles",
Master-s thesis, The University of Tennessee, Knoxville, 1988.
[6] M. Egerstedt and C. F. Martin, "Conflict resolution for autonomous
vehicles: A case study in hierarchical control design", International
Journal of Hybrid Systems, vol. 2, no. 3, pp. 221-234, 2002.
[7] E. Klavins and D. E. Koditschek, "A formalism for the composition of
concurrent robot behaviors", in Proc. IEEE International Conference on
Robotics & Automation, pp 3395-3402, San Francisco, CA, 2000.
[8] Alami, S. Fleury, M. Herrb, F. Ingrand, and F. Robert, "Multirobot
cooperation in the martha project", IEEE Robotics & Automation
Magazine, vol. 5, pp. 36-47, 1998.
[9] B. P. Gerkey and M. J. Mataric, "Auction methods for multirobot
coordination", in IEEE Transactions on Robotics & Automation, vol. 18,
pp. 758-768, 2002.
[10] D. Kostic, S. Adinandra, J. Caarls, and H. Nijmeijer, "Collision free
motion coordination of unicycle multi-agent systems", in 2010 American
Control Conference, America, 2010.
[11] K. Kant and S. W. Zucker, "Toward efficiency trajectory planning: The
path-velocity decomposition", International Journal of Robotics
Research, vol. 5, no. 3, pp. 72-89, 1986.
[12] B. Sharma, J. Vanualailai, and A. Prasad, "Trajectory planning and
posture control of multiple mobile manipulators", International Journal
of Applied Mathematics and Computation, vol. 2, no. 1, pp. 11-31,
2010.
[13] B. Kreczmer, "Robot local motion planning among moving obstacles",
in Proc. 8th IEEE International Conference on Intelligent
Transportation Systems, pp. 419-424, Vienna, Austria, Sept. 13-16
2005.
[14] P. C-Y. Sheu and Q. Xue, "Intelligent Robotic Planning Systems",
World Scientific, Singapore, 1993.
[15] C. W. Reynolds, "Flocks, herds, and schools: A distributed behavioral
model, in computer graphics", in Proc. 14th annual conference on
Computer graphics and interactive techniques, pp. 25-34, New York,
USA, 1987.
[16] A. Mogilner, L. Edelstein-Keshet, L. Bent, and A. Spiros, "Mutual
interactions, potentials, and individual distance in asocial aggregation",
Journal of Mathematical Biology, vol. 47, pp. 353-389, 2003.
[17] V. Gazi and K.M. Passino, "Stability analysis of social foraging
swarms", in IEEE Transactions on Systems, Man and Cybernetics - Part
B, vol. 34, no. 1, pp 539-557, 2004.
[18] V. Lakshmikantham, S. Leela, and A. A. Martynyuk, "Practical Stability
of Nonlinear Systems", World Scientific, Singapore, 1990.
[19] B. Sharma and J. Vanualailai, "Lyapunov stability of a nonholonomic
car-like robotic system", Nonlinear Studies, vol. 14, no. 2, pp. 143- 160,
2007.
[20] K. S. Hwang and M. D. Tsai, "On-line collision avoidance trajectory
planning of two planar robots based on geometric modeling", Journal of
Information Science and Engineering, vol. 15, pp. 131-152, 1999.
[21] B. Sharma, J. Vanualailai, and A. Chandra, "Dynamic trajectory
planning of a standard trailer system", Far East Journal of Applied
Mathematics, vol. 28, no. 3, pp. 465-486, 2007.
[1] J-C. Latombe, "Robot Motion Planning", Kluwer Academic Publishers,
USA, 1991.
[2] 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.
[3] B. Sharma, J. Vanualailai, and A. Prasad, "New collision avoidance
scheme for multi-agents: A solution to the blindman-s problem",
Advances in Differential Equations and Control Processes, vol. 3, no. 2,
pp. 141-169, 2009.
[4] M. Erdmann and T. Lozano-Perez, "On multiple moving objects", in
Proc. IEEE International Conference on Robotics and Automation, pp.
1419 1424, 1986.
[5] L. E. Parker, "A robot navigation algorithm for moving obstacles",
Master-s thesis, The University of Tennessee, Knoxville, 1988.
[6] M. Egerstedt and C. F. Martin, "Conflict resolution for autonomous
vehicles: A case study in hierarchical control design", International
Journal of Hybrid Systems, vol. 2, no. 3, pp. 221-234, 2002.
[7] E. Klavins and D. E. Koditschek, "A formalism for the composition of
concurrent robot behaviors", in Proc. IEEE International Conference on
Robotics & Automation, pp 3395-3402, San Francisco, CA, 2000.
[8] Alami, S. Fleury, M. Herrb, F. Ingrand, and F. Robert, "Multirobot
cooperation in the martha project", IEEE Robotics & Automation
Magazine, vol. 5, pp. 36-47, 1998.
[9] B. P. Gerkey and M. J. Mataric, "Auction methods for multirobot
coordination", in IEEE Transactions on Robotics & Automation, vol. 18,
pp. 758-768, 2002.
[10] D. Kostic, S. Adinandra, J. Caarls, and H. Nijmeijer, "Collision free
motion coordination of unicycle multi-agent systems", in 2010 American
Control Conference, America, 2010.
[11] K. Kant and S. W. Zucker, "Toward efficiency trajectory planning: The
path-velocity decomposition", International Journal of Robotics
Research, vol. 5, no. 3, pp. 72-89, 1986.
[12] B. Sharma, J. Vanualailai, and A. Prasad, "Trajectory planning and
posture control of multiple mobile manipulators", International Journal
of Applied Mathematics and Computation, vol. 2, no. 1, pp. 11-31,
2010.
[13] B. Kreczmer, "Robot local motion planning among moving obstacles",
in Proc. 8th IEEE International Conference on Intelligent
Transportation Systems, pp. 419-424, Vienna, Austria, Sept. 13-16
2005.
[14] P. C-Y. Sheu and Q. Xue, "Intelligent Robotic Planning Systems",
World Scientific, Singapore, 1993.
[15] C. W. Reynolds, "Flocks, herds, and schools: A distributed behavioral
model, in computer graphics", in Proc. 14th annual conference on
Computer graphics and interactive techniques, pp. 25-34, New York,
USA, 1987.
[16] A. Mogilner, L. Edelstein-Keshet, L. Bent, and A. Spiros, "Mutual
interactions, potentials, and individual distance in asocial aggregation",
Journal of Mathematical Biology, vol. 47, pp. 353-389, 2003.
[17] V. Gazi and K.M. Passino, "Stability analysis of social foraging
swarms", in IEEE Transactions on Systems, Man and Cybernetics - Part
B, vol. 34, no. 1, pp 539-557, 2004.
[18] V. Lakshmikantham, S. Leela, and A. A. Martynyuk, "Practical Stability
of Nonlinear Systems", World Scientific, Singapore, 1990.
[19] B. Sharma and J. Vanualailai, "Lyapunov stability of a nonholonomic
car-like robotic system", Nonlinear Studies, vol. 14, no. 2, pp. 143- 160,
2007.
[20] K. S. Hwang and M. D. Tsai, "On-line collision avoidance trajectory
planning of two planar robots based on geometric modeling", Journal of
Information Science and Engineering, vol. 15, pp. 131-152, 1999.
[21] B. Sharma, J. Vanualailai, and A. Chandra, "Dynamic trajectory
planning of a standard trailer system", Far East Journal of Applied
Mathematics, vol. 28, no. 3, pp. 465-486, 2007.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55267", author = "Jai Raj and Jito Vanualailai and Bibhya Sharma and Shonal Singh", title = "Swarm Navigation in a Complex Environment", abstract = "This paper proposes a solution to the motion planning
and control problem of car-like mobile robots which is required to
move safely to a designated target in a priori known workspace
cluttered with swarm of boids exhibiting collective emergent
behaviors. A generalized algorithm for target convergence and
swarm avoidance is proposed that will work for any number of
swarms. The control laws proposed in this paper also ensures
practical stability of the system. The effectiveness of the proposed
control laws are demonstrated via computer simulations of an
emergent behavior.", keywords = "Swarm, practical stability, motion planning,
emergent.", volume = "6", number = "12", pages = "1676-7", }
