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

Blažič, Sašo (avtor), Klančar, Gregor (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: path planning, motion primitive, Bernstein-Bézier curve, continuous curvature, mobile robots
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FE - Fakulteta za elektrotehniko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2022
• Št. strani: Str. 1-20
• Številčenje: iss. 11, 1709
• PID: 20.500.12556/RUL-138620
• UDK: 007.52
• ISSN pri članku: 2079-9292
• DOI: 10.3390/electronics11111709
• COBISS.SI-ID: 112016643
• Datum objave v RUL: 03.08.2022

BLAŽIČ, Sašo in KLANČAR, Gregor, 2022, Effective parametrization of low order Bézier motion primitives for continuous-curvature path-planning applications. Electronics [na spletu]. 2022. Vol. 11, no. 1709, p. 1–20. [Dostopano 3 maj 2025]. DOI 10.3390/electronics11111709. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=138620

Gradivo je del revije

• Naslov: Electronics
• Skrajšan naslov: Electronics
• Založnik: MDPI
• ISSN: 2079-9292
• COBISS.SI-ID: 523068953

Licence

• Licenca: CC BY-NC 4.0, Creative Commons Priznanje avtorstva-Nekomercialno 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc/4.0/deed.sl
• Opis: Licenca Creative Commons, ki prepoveduje komercialno uporabo, vendar uporabniki ne rabijo upravljati materialnih avtorskih pravic na izpeljanih delih z enako licenco.
• Začetek licenciranja: 03.08.2022

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: planiranje poti, primitivi gibanja, Bernstein-Bézier krivulja, zvezna ukrivljenost, mobilni roboti

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P2-0219-2019
• Naslov: Modeliranje, simulacija in vodenje procesov

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: L2-3168-2021
• Naslov: Razvoj samo-učečega sistema za optimizacijo pravil vožnje avtonomnih transportnih vozil in njihovih časovno-prostorsko usklajenih aktivnosti