Real-time Approximation of Clothoids With Bounded Error for Path Planning Applications

We present a method for real-time computation of clothoid coordinates that guarantees bounded approximation error over a wide range of clothoid parameters provided that the clothoid's orientation change and length areReal-time approximation bounded. It is shown that coordinates of clothoid with...

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Bibliographic Details
Published in:IEEE transactions on robotics 2014-04, Vol.30 (2), p.507-515
Main Authors: Brezak, Misel, Petrovic, Ivan
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Approximation
Approximation algorithms
Approximation error
Clothoid approximation
Computation
Computational efficiency
Errors
Eulers equations
Fresnel integrals
Geometry
Interpolation
Mathematical analysis
Mathematical models
Measurement errors
motion control
Parameter estimation
Path planning
Real time
Real-time systems
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Summary:We present a method for real-time computation of clothoid coordinates that guarantees bounded approximation error over a wide range of clothoid parameters provided that the clothoid's orientation change and length areReal-time approximation bounded. It is shown that coordinates of clothoid with any parameters can be computed from those of a single clothoid (with fixed parameters), using appropriate geometrical transformations. A comprehensive analysis is given on how to determine a required set of clothoids and, based on this, how to sample a clothoid in a lookup table in order to achieve required approximation precision. The algorithm is computationally very efficient and therefore suitable for real-time path planning, as well as for other applications that benefit from fast clothoid computation.
ISSN:1552-3098
1941-0468
DOI:10.1109/TRO.2013.2283928