A novel tracking paradigm for flying geometric shapes using tethered kites is
presented. Because of the one-to-one correspondence between turning angles and
images of curves on a sphere it is possible to fly a given shape by tracking
the associated turning angle. Based on this principle a Lyapunov-based
nonlinear adaptive control loop is developed that needs control derivatives of
the kite aerodynamic model only. The resulting controller is found to be robust
when simulating against the Leuven-Heidelberg rigid body kite model, even under
severe initial model mismatch.