Efficient continuous curvature path generation with pseudo-parametrized algebraic splines

Abstract

This paper investigates a method to achieve computationally efficient path generation and tracking, suitable for manned operations. To provide an adequate level of comfort to the passengers, path geometric continuity of the second order ( $$G^2$$ ) is used. Thus, generalized 3D $$G^2$$ Dubins paths are proposed as a template, later approximated with algebraic polynomial splines of the third order. This allows to leverage the strengths of both Dubins paths and spline-based methods. The proposed splines pseudo-parametrization avoids explicit numerical evaluation of elliptic integrals, while achieving a good approximation of arc-length parametrization. The method is first applied to planar maneuvers, and then extended to complete 3D ones, such as climbing turns. The strategy leads to facilitated 4D planning, that can be either velocity or time-based, re-planning is a local problem, and path tracking convergence is enhanced. The technique has been demonstrated on a certifiable fly-by-wire platform both in laboratory tests and in flights, including landings. Flight results will be shown and discussed at the end of the paper.