Region of attraction estimation for a perching aircraft: A Lyapunov method exploiting barrier certificates

Dynamic perching maneuvers for fixed-wing aircraft are becoming increasingly plausible due to recent progress in perching using `micro-spines´ mounted on tuned suspensions and, separately, on feedback motion planning techniques for post-stall maneuvering. In this paper, we bring these complementary techniques together by efficiently estimating the mechanical stability of the plane when it makes contact with a vertical surface; the resulting landing funnel can then be used in a feedback motion planning algorithm for the flight controller. We consider a simplified model of the perching dynamics and report an extension of the region of attraction techniques, using sums-of-squares optimization, which combines polynomial approximations of barrier constraints with the traditional Lyapunov methods to achieve tight estimation of the true region of attraction for the model. We demonstrate the new method on a variety of design parameters for the perching system, suggesting a potential use as a mechanical system or controller design tool.