Effective Parametrization of Low Order Bezier Motion Primitives for Continuous-Curvature Path-Planning Applications

We propose a new parametrization of motion primitives based on Bezier 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 C-2 continuous (the curvature is therefore continuous). The proposed primitives feature low order Bezier (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 Bezier 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.

Automated summary

This paper proposes a new parametrization of motion primitives based on Bezier curves for path-planning applications. The method allows for simple calculation of individual motion primitives while ensuring curve continuity, improving efficiency and convergence in path planning.