Lioi Altered Version

Simulations of Robotic Pursuit Using Matlab and Simulink: 

Simulations of Robotic Pursuit Using Matlab and Simulink Joshua Lioi ISR Summer REU 2006 Advisor: Dr. P. S. Krishnaprasad

Outline: 

Outline Classical Pursuit & Mice Problem Robots being modeled Simulations Cyclic Pursuit & Cyclic mice problem Motion Camouflage Robot Motion Camouflage Collaboration Applications

Classical Pursuit: 

Classical Pursuit Pierre Bouger 1732 Predator always moves toward prey Spiral Trajectory Capture requirements for the speed Allows for no constraints of motion Pursuit Curve. Retrieved June 20, 2006, from Wolfram MathWorld Web site: http://mathworld.wolfram.com/PursuitCurve.html

Mice Problem: 

Mice Problem All mice have equal speed Counterclockwise and constant speed Similar shape at each instant Meet at Brocard point Irregular polygons and relative speeds Pursuit Curve. Retrieved June 20, 2006, from Wolfram MathWorld Web site: http://mathworld.wolfram.com/PursuitCurve.html

Meet the Robots: 

Meet the Robots Genghis and Lola Controls: speed and angular velocity Nonholonomic Crickets Traditional Equations

Matlab & Simulink: 

Matlab & Simulink

Classical Example: 

Classical Example

Cyclic Pursuit: 

Cyclic Pursuit Marshall, Broucke, and Francis Relative coordinates r, α, and β Proportional angular velocity Similar to Classical, but more realistic Marshall, J. A., Broucke, M. E., Francis, B. A. (2004). “Formations of Vehicles in Cyclic Pursuit”. IEEE Trans. Automat. Contr. 49, 1963-1974.

Cyclic Pursuit: 

Cyclic Pursuit Classical versus Cyclic in Circular Pursuit

Mice Problem Simulation: 

Mice Problem Simulation Equilateral Triangle

Mice Problem Simulation: 

Mice Problem Simulation Irregular Triangle

Motion Camouflage: 

Motion Camouflage Dragonflies and echolocating bats Optic Flow Two Styles Model used (constant speed) Equations: Justh, E. W., Krishnaprasad, P. S. (2006). “Steering Laws for Motion Camouflage”. Proc. R. Soc. A FirstCite Early Online Publishing Ghose, Kaushlik (2006, Apr 28). Retrieved August 9, 2006, from Kaushlik Ghose research page Web site: http://www.glue.umd.edu/%7Ekghose/

Motion Camouflage: 

Motion Camouflage Successes of Robot Motion Camouflage

Motion Camouflage: 

Motion Camouflage Failures of Robot Motion Camouflage

Collaboration: 

Collaboration