1. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB, An Improved Line-of- Sight Guidance Law for UAVs R. Curry, M. Lizarraga, B. Mairs, and G.H. Elkaim University of California, Santa Cruz

2. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Accelerating UAV Demand Military Civilian Forestry Marine Fisheries Photography Border surveilance New Missions  New Autopilot Designs

3. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB SLUGS GABE INSERT YOUR SLIDE HERE

4. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Talk Outline Review of a simple but effective UAV guidance law Examine the impact of roll dynamics Extend the concept to Improve stability All operational situations Compare the two in 6 DOF simulations

5. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Line-of-Sight Guidance Originally proposed by Amidi (1991) for robots Park, Deyst, How (2007) made significant contributions Theory Linear Analysis Asymptotic stability Flight demonstrations A form of pursuit guidance originally used in air- to-air missiles, but range doesn’t change

6. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Line-of-Sight Guidance

7. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Commanded Acceleration Geometry Kinematics Combined constant UAV Bank angle

8. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Stability We noticed that became less stable in downwind conditions Simulations Flight experiments Also mentioned by Niculescu (2001) ignores roll dynamics We used the Park/Deyst/How linear model to explore this

9. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Linear Model (Park, Deyst, How)

10. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Linear Model (cont) System Response where Note: Let

11. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Linear Model with Roll Dynamics

12. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Root Locus with Roll Dynamics

13. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Summary of Guidance Asymptotically stable assuming instantaneous acceleration response (Park/Deyst/How) Accurate tracking for circles (Park/Deyst/How) Reduced stability with increasing ground speed due to roll dynamics not defined in some operational situations

14. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Guidance is a notational change to distinguish from Use a different look-ahead distance is constant Now system poles independent of ground speed Command independent of look ahead distance

15. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Operational Scenarios Neither nor account for important operational conditions Intercepting the desired path Overshoot due to large intercept angles Switching waypoints Desired path not defined Return to Base from anywhere Fly to first waypoint from any initial conditions

16. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Intercepting Desired Path Cross track errors can be larger than Initial path acquisition Errors in path following Create a new aim point On the desired path Defined by a specified down-path distance But it leads to overshoot due to large intercept angles

17. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Overshoot Large intercept angles lead to excessive overshoot (roll lag, bank angle limits) Limit the intercept angle within of the path A common practice in aviation (ATC controllers) Final down-path aim point distance smaller of Distance determined by max intercept angle Distance used for path acquisition

18. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Guidance

19. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Tracking During Waypoint Transition For any look-ahead guidance law Tracking a path during a waypoint transition leads to path errors starts tracking the transition path when vehicle’s projection (not aim point) is on the transition Also need more lead time for roll angle lag

20. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Tracking During Waypoint Transition (cont)

21. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Guidance With No Path There are several scenarios where there is no defined path Returning to base (RTB) from anywhere Flying to first waypoint in an array Homing—steer to line of sight uses one guidance law in all conditions

22. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Simulations 6 DOF rigid body nonlinear model of Rascal UAV Hobby aircraft, wing span of 1.2m Inputs: throttle, elevator, aileron, rudder Outputs: 12 state variables Dryden model winds Constant wind Gust levels depend on height above ground and mean wind

23. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB and on Waypoints

24. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB and Circle Tracking

25. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Homing Mode—Return To Base

26. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Moving “Base” The homing mode only requires a line of sight to the objective There is no requirement that the objective be stationary On a whim, we tried tracking a moving objective We used the homing mode without any modification Results were very encouraging

27. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB RTB with Moving “Base”

28. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Summary Amidi/Park/Deyst/How is a very simple and efficient pursuit guidance law But roll dynamics and increased groundspeed lead to more instability scales look-ahead distance with ground speed System response time determined by System poles independent of groundspeed

29. UC SANTA CRUZ, AUTONOMOUS SYSTEMS LAB Summary (cont) always has an aim point  extends the operational envelope always uses the same guidance law 6 DOF simulations show Improved response, no impact of groundspeed Extended operational envelope RTB works with a moving base