G ³ -splines for the path planning of wheeled mobile robots

Abstract

This paper deals with generation of smooth paths for the navigation of wheeled mobile robots by means of the iterative steering technique. A new motion planning primitive called G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> -spline or η-spline is proposed. It is a seventh order polynomial spline that permits the interpolation of an arbitrary sequence of points with associated arbitrary direction, curvature and curvature derivative. Adopting this path planning, the robot's control inputs can be obtained by means of a dynamic path inversion procedure ensuring the continuity of velocities and accelerations. This new spline depends on a vector with six parameters (η) that can be used to finely shape the path. The paper includes both theoretical results and path planning examples.