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

Sašo Blažič (Author), Gregor Klančar (Author)

Abstract

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.

Keywords

planiranje poti;primitivi gibanja;Bernstein-Bézier krivulja;zvezna ukrivljenost;mobilni roboti;path planning;motion primitive;Bernstein-Bézier curve;continuous curvature;mobile robots;

Data

Language:	English
Year of publishing:	2022
Typology:	1.01 - Original Scientific Article
Organization:	UL FE - Faculty of Electrical Engineering
UDC:	007.52
COBISS:	112016643
ISSN:	2079-9292
Views:	58
Downloads:	33
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	planiranje poti;primitivi gibanja;Bernstein-Bézier krivulja;zvezna ukrivljenost;mobilni roboti;
Type (COBISS):	Article
Pages:	str. 1-20
Volume:	ǂiss. ǂ11
Issue:	1709
Chronology:	Jun.-1 2022
DOI:	10.3390/electronics11111709
ID:	16077872