Feedback equivalence of control systems
Systems & Control Letters
Joint triangulations and triangulation maps
SCG '87 Proceedings of the third annual symposium on Computational geometry
Feedback equivalence for general control systems
Systems & Control Letters
Subset warping: rubber sheeting with cuts
CVGIP: Graphical Models and Image Processing
Constructing piecewise linear homeomorphisms of simple polygons
Journal of Algorithms
Planning Algorithms
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In this paper a piecewise linear homeomorphism is presented that maps a strictly monotone polygonal chain to a straight line. This mapping enables one to reduce the path tracking task for mobile robots to straight line tracking. Due to the simplicity of the transformation, closed form solutions for the direct and inverse mapping are presented. Furthermore, the transformation also defines a feedback equivalence relation between the original and the transformed system equations of the mobile robot. It is shown that the form of the system equations is preserved and that the transformation essentially maps a car-like robot in the original domain, to a car-like robot in the transformed domain. This enables one to use straight line trackers developed solely for this system, for the tracking of arbitrary strictly monotone polygonal curves. Finally, it is shown that the use of this mapping can also simplify the application of existing path tracking controllers since they only need to track straight line paths. In general, one can eliminate from the existing path controllers all parameters that are needed for non-straight paths, thus obtaining respective simplified controllers. For example, it is shown that a fuzzy path controller with 135 rules can be reduced to an equivalent fuzzy straight line tracking controller with 45 rules.