Trajectory generation for aircraft based on differential flatness and spline theory

Abstract

An efficient approach based on differential flatness and spline theory for the aircraft trajectory generation in the target area is proposed. It is well known that the traditional feedback control approach frequently fails for a large class of nonlinear mechanical systems with constraints. The aircraft dynamics system is a nonlinear system restrained by the nonholonomic constraints, dynamic constraints, etc., where a global asymptotically stable solution that satisfies the constraints does not exist. The salient features of differential flatness have been found compatible for the nonlinear systems of aircraft; besides, the flat output could be parameterized with the basis function of Bezier curve, one of the basic spline curves. Then it changes an optimal control problem — the problem of trajectory generation for aircraft, into a general nonlinear programming problem, to ensure the enforceability of the generated trajectory and reduce the problem solving difficulty. Experiments indicate that it is very effective to solve the trajectory generation problem for aircraft in the target area.