2003
DOI: 10.1016/s0010-4485(03)00045-9
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Polynomial approximation to clothoids via s-power series

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Cited by 41 publications
(21 citation statements)
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“…Using MATLAB Optimization and Symbolic toolboxes it is obtained that C m in = 5.9447 · 10 −4 . The maximum scaling is obtained using (15), which bounds error of approximating a clothoid by a line so that it is obtained C m ax = 144.34. We suppose that we do not need the case when κ 0 = 0 so that K m ax = 0.…”
Section: Resultsmentioning
confidence: 99%
See 3 more Smart Citations
“…Using MATLAB Optimization and Symbolic toolboxes it is obtained that C m in = 5.9447 · 10 −4 . The maximum scaling is obtained using (15), which bounds error of approximating a clothoid by a line so that it is obtained C m ax = 144.34. We suppose that we do not need the case when κ 0 = 0 so that K m ax = 0.…”
Section: Resultsmentioning
confidence: 99%
“…One could also use other interpolation curves instead of circular arcs, e.g., s-power series [15]. However, up to now we have not found a curve that is better in terms of efficiency, implementation complexity, and accuracy, until higher order approximations are used, in which case we lose efficiency.…”
Section: Interpolationmentioning
confidence: 88%
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“…These make use of clothoids [32] and higher order polynomial curves [33][34][35], or curves with closed form expressions such as Bézier curves [36,37] or -splines [38]. Unfortunately these are not treating issues such as topological admissibility or convergence guarantees in general planning tasks.…”
Section: Related Workmentioning
confidence: 99%