Control synthesis and verification for a perching UAV using LQR-Trees

We consider the problem of designing a feedback controller for a fixed-wing unmanned aerial vehicle (UAV) to execute a dynamic post-stall maneuver and land accurately on a perch. This controller must deal with the nonlinearity of the post-stall dynamics and inherently limited control authority of the actuators. Using a recently proposed algorithm called “LQR-Trees”, here we demonstrate that we can generate formal guarantees (using time-varying Lyapunov functions) which verify that a controller generated with trajectory optimization and local linear feedback can achieve the desired perching tolerance from a range of initial conditions. These locally valid controllers are then combined into an library of controllers which cover a space of initial conditions with verified controllers. We describe some of the details of the implementation, which requires formulating and solving large semidefinite programs, and compare the verified regions with numerical samples of the system's true performance. This perching problem represents the most high-dimensional and numerically challenging application of the LQR Trees algorithm reported to date.