Local Path Planning for Nonholonomic Mobile Robots Based on Planar G 2 Pythagorean Hodograph Degree 7 Bezier Transition Curves

The paper proposes a method that joins two line segments using planar Pythagorean hodograph (PH) degree 7 Bezier transition curves. The objective is to make use of such curvature-continuous curves for the path planning of nonholonomic constrained vehicles moving in 2D space, which requires designing a smooth path while satisfying the constraint of minimum turning radius. We initially present a novel idea that employs PH degree 7 Bezier transition curves for dealing with curvature constraints, the result of which proves to be better than the traditional method based on the "forward simulation". The properties of PH degree 7 Bezier transition curves are then fully analyzed showing that the curves can be determined by a minimum of three parameters, each of which has an intuitive geometric meaning. The paper also proposes a path planner with direct curvature constraints during the process of path generation in 2D space. The objective function of the optimal path generation can be adjusted to minimize the length of the whole path or to closely follow the original global nonsmooth sequences of line segments. Here, the optimization problem is tactfully converted to a linear programming problem that can be solved efficiently. Finally, we use a kinematic bicycle model for simulation and compare the results with those from Dubins path showing that a G2 curve is easier to follow than a G1 one.