An optimal curvature smoothing method and the associated real-time interpolation for the trajectory generation of flying robots

Abstract

This paper presents a trajectory smoothing approach and corresponding real-time interpolation for the flying robot. To smoothly transit between straight line segments, the Bézier curve is introduced to guarantee continuous curvature. Subsequently, considering the constraints on approximation errors and lengths of the original straight line segments, an optimization problem pursuing maximal curvature radius of the Bézier curves is proposed to reduce the potential fluctuation in the real-time flights. With the established geometric profile of continuous curvature, a fast real-time interpolation approach that ensures smooth acceleration profile in real-time flights is proposed. To verify the effectiveness of this development, extensive simulations and experiments are conducted at last. The results show that the proposed trajectory generation approach can effectively generate reference trajectories in real-time both at two-dimensional and three-dimensional spaces with continuous curvature and smooth acceleration. With well-generated trajectory, the flying robot can closely track the reference with maximum cross-tracking error of 0.05 m.