Effective parametrization of low order Bézier motion primitives for continuous-curvature path-planning applications

Blažič, Sašo (author), Klančar, Gregor (author)

We propose a new parametrization of motion primitives based on Bézier curves that suits perfectly path-planning applications (and environment exploration) of wheeled mobile robots. The individual motion primitives can simply be calculated taking into account the requirements of path planning and the constraints of a vehicle, given in the form of the starting and ending orientations, velocities, turning rates, and curvatures. The proposed parametrization provides a natural geometric interpretation of the curve. The solution of the problem does not require optimization and is obtained by solving a system of simple polynomial equations. The resulting planar path composed of the primitives is guaranteed to be C2 continuous (the curvature is therefore continuous). The proposed primitives feature low order Bézier (third order polynomial) curves. This not only provides the final path with minimal required turns or unwanted oscillations that typically appear when using higher-order polynomial primitives due to Runge’s phenomenon but also makes the approach extremely computationally efficient. When used in path planning optimizers, the proposed primitives enable better convergence and conditionality of the optimization problem due to a low number of required parameters and a low order of the polynomials. The main contribution of the paper therefore lies in the analytic solution for the third-order Bézier motion primitive under given boundary conditions that guarantee continuous curvature of the composed spline path. The proposed approach is illustrated on some typical scenarios of path planning for wheeled mobile robots.

• Language: English
• Keywords: path planning, motion primitive, Bernstein-Bézier curve, continuous curvature, mobile robots
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FE - Faculty of Electrical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2022
• Number of pages: Str. 1-20
• Numbering: iss. 11, 1709
• PID: 20.500.12556/RUL-138620
• UDC: 007.52
• ISSN on article: 2079-9292
• DOI: 10.3390/electronics11111709
• COBISS.SI-ID: 112016643
• Publication date in RUL: 03.08.2022

Record is a part of a journal

• Title: Electronics
• Shortened title: Electronics
• Publisher: MDPI
• ISSN: 2079-9292
• COBISS.SI-ID: 523068953

Licences

• License: CC BY-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
• Link: http://creativecommons.org/licenses/by-nc/4.0/
• Description: A creative commons license that bans commercial use, but the users don’t have to license their derivative works on the same terms.
• Licensing start date: 03.08.2022

Secondary language

• Language: Slovenian
• Keywords: planiranje poti, primitivi gibanja, Bernstein-Bézier krivulja, zvezna ukrivljenost, mobilni roboti

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0219-2019
• Name: Modeliranje, simulacija in vodenje procesov

• Funder: ARRS - Slovenian Research Agency
• Project number: L2-3168-2021
• Name: Razvoj samo-učečega sistema za optimizacijo pravil vožnje avtonomnih transportnih vozil in njihovih časovno-prostorsko usklajenih aktivnosti