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- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Springer Science+Business Media New York
- Subject
- Engineering; Robotics and Automation; Artificial Intelligence (incl. Robotics); Computer Imaging, Vision, Pattern Recognition and Graphics; Control, Robotics, Mechatronics
- ISSN
- 0929-5593
- eISSN
- 1573-7527
- DOI
- 10.1007/s10514-015-9538-9
- Publisher site
- See Article on Publisher Site
Abstract
This paper considers the synthesis of pseudo time optimal paths for a mobile robot navigating among obstacles subject to uniform braking safety constraints. The classical Brachistochrone problem studies the time optimal path of a particle moving in an obstacle free environment subject to a constant force field. By encoding the mobile robot’s braking safety constraint as a force field surrounding each obstacle, the paper generalizes the Brachistochrone problem into safe time optimal navigation of a mobile robot in environments populated by polygonal obstacles. Convexity of the safe travel time functional, a path dependent function, allows efficient construction of a speed graph for the environment. The speed graph consists of safe time optimal arcs computed as convex optimization problems in $$O(n^3 \log (1/\epsilon ))$$ O ( n 3 log ( 1 / ϵ ) ) total time, where n is the number of obstacle features in the environment and $$\epsilon $$ ϵ is the desired solution accuracy. Once the speed graph is constructed for a given environment, pseudo time optimal paths between any start and target robot positions can be computed along the speed graph in $$O(n^2\log n)$$ O ( n 2 log n ) time. The results are illustrated with examples and described as a readily implementable procedure.
Journal
Autonomous Robots – Springer Journals
Published: Feb 12, 2016