Wolfgang Pointner, Gabriele Kotsis,Peter Langthaler, and Michael Naderhirn

AeroSpySense & Avoid Technology GmbH

Safe autonomous landing maneuver

Consideration of aerodynamic capabilities

Accurate representation of flight state

Verification through formal methods

Example for development methodology

Wing Span 1.3 m

Weight 1.5 kg

Endurance 30 min

Applications� Aerial Photography

� Observation

� Search and Rescue

� Gas Detection

Application at limited landing areas

No landing equipment

Steep landing angle

Low velocity� vertically

� horizontally

Longitudinal point-mass model

Control input

� Thrust T

� Elevon �����������

Lateral forces not considered

Lift, Drag, Pitching Moment

Consider control surface

Cover post-stall conditions

Longitudinal DSL trajectories

Velocity

Angle of descent

1. V0 = 10.05 m/s �0 = -6.87° �0 = -16.62°2. V0 = 9.68 m/s �0 = 16.04° �0 = -10.88°3. V0 = 7.65 m/s �0 = -15.47° �0 = -38.96°

Discrete state dynamics = Operational modes

Continuous state dynamics = Aerodynamic model

Transitions� System-initiated

� Caused externally

Subsystems� State bounds

� Control inputs

Control inputs

State boundsHybrid automaton

Identification of hybrid subsystems (Hx)

System-initiated mode transitions ( x)

Calculation of backwards reachable sets (Wx)� Toolbox for Level Set Methods (Ian Mitchell, UBC)

� Time dependent Hamilton-Jacobi PDE

� Calculate safe flight envelopes

Regular flight requires certain hinit to complete DSL

High Vinit and positive �init� Overturn at initialization

Low Vinit and low hinit� Unsafe touchdown

Recovery only safe at altitudes above approx. 20 m

Higher �init exacerbates DSL

Safe states remain inherently safe

Only system-initiated transitions to unsafe regions

DSL is a practical landing maneuverReachability analysis show suggested shapesHigh computational costsMethodology applicable for similar problems

Implementation on an autopilotImprovements to calculate landing trajectoryDevelopment of a GA landing assistance system

R. F. Stengel, Flight Dynamics. Princeton University Press, 2004.C. J. Tomlin, I. M. Mitchell, A. M. Bayen, and M. Oishi, “Computational techniques for the verification of hybrid systems,” in Proceedings of the IEEE, pp. 986–1001, 2003.S. Osher and J. A. Sethian, “Fronts propagating with curvature dependent speed: Algorithms based on hamilton-jacobi formulations,” Journal of Computational Physics, vol. 79, no. 1, pp. 12–49, 1988.I. M. Mitchell, “Application of level set methods to control and reachability problems in continuous and hybrid systems,” Ph.D. dissertation, Stanford University, 2002.I.M. Mitchell, “The flexible, extensible and efficient toolbox of level set methods,” Journal of Scientific Computing, vol. 35, no. 2–3, 2008.M. Oishi, C. J. Tomlin, and A. Degani, “Discrete abstractions of hybrid systems: Verification of safety and application to user-interface design,” NASA, Ames Research Center, Tech. Rep., 2003.