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2 2011

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Real-time coordinated trajectory planning and obstacle avoidance for mobile robots

McNinch L. C., Soltan R. A., Muske K. R., Ashrafiuon H., Peyton J. C.

Journal of Automation Mobile Robotics and Intelligent Systems

2011

Vol. 5, No. 1

23-29

A novel method for real-time coordinated trajectory planning and obstacle avoidance of autonomous mobile robot systems is presented. The desired autonomous system trajectories are generated from a set of first order ODEs. The solution to this system of ODEs converges to either a desired target position or a closed orbit de.ned by a limit cycle. Coordinated control is achieved by utilizing the nature of limit cycles where independent, non-crossing paths are automatically generated from different initial positions that smoothly converge to the desired closed orbits. Real-time obstacle avoidance is achieved by specifying a transitional elliptically shaped closed orbit around the nearest obstacle blocking the path. This orbit determines an alternate trajectory that avoids the obstacle. When the obstacle no longer blocks a direct path to the original target trajectory, a transitional trajectory that returns to the original path is defined. The coordination and obstacle avoidance methods are demonstrated experimentally using differential-drive wheeled mobile robots.

Comparison ODE theorems related to the method of lines

Leszczyński H.

Journal of Applied Analysis

2011

Vol. 17, nr 1

137-154

We prove a comparison theorem for an ODE and DAE system which arises from the method of lines. Under a Perron comparison condition on the functional dependence and a specific Lipschitz and (W+) condition on the classical argument, we obtain strong uniqueness criteria.