Robust post-stall perching with a simple fixed-wing glider using LQR-Trees

Abstract

Abstract. Birds routinely execute post-stall maneuvers with a speed and precision far beyond the capabilities of our best aircraft control systems. One remarkable example is a bird exploiting post-stall pressure drag in order to rapidly decelerate to land on a perch. Stall is typically associated with a loss of control authority, and it is tempting to attribute this agility of birds to the intricate morphology of the wings and tail, to their precision sensing apparatus, or their ability to perform thrust vectoring. Here we ask whether an extremely simple fixed-wing glider (no propeller) with only a single actuator in the tail is capable of landing precisely on a perch from a large range of initial conditions. To answer this question, we focus on the design of the flight control system; building upon previous work which used linear feedback control design based on quadratic regulators (LQR), we develop nonlinear feedback control based on nonlinear model-predictive control (NMPC) and "LQR-Trees". Through simulation using a flat-plate model of the glider, we find that both nonlinear methods are capable of achieving an accurate bird-like perching maneuver from a large range of initial conditions; the "LQR-Trees" algorithm is particularly useful due to its low computational burden at runtime and its inherent performance guarantees. With this in mind, we then implement the "LQR-Trees" algorithm on real hardware and demonstrate a 95 percent perching success rate over 147 flights for a wide range of initial speeds. These results suggest that, at least in the absence of significant disturbances like wind gusts, complex wing morphology and sensing are not strictly required to achieve accurate and robust perching even in the post-stall flow regime.

Unsteady dynamics of rapid perching manoeuvres

“…Mimicking the manoeuvrability of birds, particularly the ability to land safely on narrow platforms, would allow them to complete these tasks effectively and efficiently. Though recent advances have been made in designing MAVs that can land on a perch (Doyle et al 2011;Moore et al 2014;Reich et al 2009), existing MAVs still fall short in achieving the control, speed and precision of natural flyers in landing manoeuvres.…”

Funnel libraries for real-time robust feedback motion planning

“…The flat-plate model was also used as a baseline for the lift and drag coefficients of the wings, but an angle-of-attack dependent correction term was added. This correction term was fit from experimental data obtained from passive (i.e., unactuated) flights in a manner similar to [74]. Since lift and drag forces are dependent on the airspeed over the aerodynamic surface, we need to take into account the effect of "propwash" (i.e.…”

“…This simple strategy is a common one and has previously been found to be effective in a wide range of applications [47,75,94]. 97 …”

DIRTREL: Robust Trajectory Optimization with Ellipsoidal Disturbances and LQR Feedback

“…Moore et al extended the LQR-Trees framework to include uncertainty in funnel estimates using a Common Lyapunov formulation of a sums-of-squares (SOS) program [25]. A related line of work led to the development of robust adaptive tracking controllers with guaranteed finite-time performance [24].…”