1. 1 26/03/09 LIST – DTSI Design of controllers for a quad-rotor UAV using optical flow Bruno Hérissé CEA List Fontenay-Aux-Roses, France bruno.herisse@cea.fr

2. 2 26th March 2009 DTSI SRI-LIST Introduction  Purpose : measurements of inertial data and visual optical flow for the design of controllers for a VTOL UAV. Camera IMU (inertial measurments unit)

3. 3 26th March 2009 DTSI SRI-LIST Model of the UAV T   The system is nonlinear and under actuated.  Definition of used frames. I : Inertial frame attached to the earth B : body-fixed frame attached to the vehicle’s center of mass.  Vehicle state: : position of the center of mass in I : speed of the center of mass in I : orientation matrix from B to I : rotational velocity in B  Inputs: : Global thrust in B : Control torque in B  Dynamic Model used : Translational dynamics Rotational Dynamics Already controlled F=f(T,R) Constant forces High gain controller

4. 4 26th March 2009 DTSI SRI-LIST Plan  The main object : elaboration of controllers for hovering flight, vertical landing and terrain following of a VTOL UAV above a textured target.  Optical flow computation Computation of the translational optical flow  A non-linear controller for the stabilization of the hovering flight.  A non-linear controller for a smooth vertical landing.  A non-linear controller for terrain following.

5. 5 26th March 2009 DTSI SRI-LIST Kinematics of an image point under spherical projection  Optical flow from an image plane to a spherical retina. Optical Flow

6. 6 26th March 2009 DTSI SRI-LIST  I T d Translational optical flow computation Known data : η Measured data :,  Rotational term Translational term

7. 7 26th March 2009 DTSI SRI-LIST Schema of control UAV dynamics Controller Camera + - Environment configuration State : (ξ, v) Optical flow : w Set point : w c (P, PI) (0 ou ω*) Perturbations

8. 8 26th March 2009 DTSI SRI-LIST  For the stabilisation of the hovering flight define the error term,  The goal is the regulation of to zero :  The control lawensures the exponential convergence of to zero (PI-type controller)  The UAV does not collide the obstacle Stabilization of the hovering flight

9. 9 26th March 2009 DTSI SRI-LIST  Consider that, that is is the distance of the vehicle to the ground  Define for the control of the third component of the dynamics the error term,  Goal: and for all time  Proposition 1: Consider the control law, then for all, one can ensure the exponential convergence of to zero while keeping for all time. Vertical landing control (1) Smooth vertical landing

10. 10 26th March 2009 DTSI SRI-LIST  Proof: Define, and, and The third component of the dynamics is: Integrating this equation, it yields Differentiating L, it yields Chosing k lim such that and It ensures that is bounded. Consequently, converges to zero with as exponential decay constant. Vertical landing control (2)

11. 11 26th March 2009 DTSI SRI-LIST  Proposition 2: Consider the following control law, then for all it ensures the exponential convergence of to zero with as exponential decay constant while keeping for all time. Vertical landing control (3)

12. 12 26th March 2009 DTSI SRI-LIST Experimental setup Drone: - Embeded attitude control from IMU data -running at 166Hz Numerical transmission: - Transmision of the desired attitude to the drone - Transmission of IMU data to the ground station - 70 ms are required for the data transmission Textured ground Ground station: Treatment of vision algorithms at 60 ms Camera: -Focus: 2.1mm Analogical transmission: -Transmission at 2.4GHz - Associate with an acquisition card, a new image is available each 50 ms

13. 13 26th March 2009 DTSI SRI-LIST Experiments

14. 14 26th March 2009 DTSI SRI-LIST  Consider that  The goal is, or has to be set to a constant :  Control on the z axis and on the x axis Control on the x axis and on the z axis  Maintaining a constant forward thrust, the drag force opposite to the vehicle's direction of flight ensures that the forward velocity converges to a constant. Then, one can consider that is constant. Terrain following (1)

15. 15 26th March 2009 DTSI SRI-LIST  The control lawensures the asymptotic convergence of to  The UAV does not collide the obstacle Terrain following (2)

16. 16 26th March 2009 DTSI SRI-LIST  Proof: Terrain following (3)

17. 17 26th March 2009 DTSI SRI-LIST Terrain following (3)

18. 18 26th March 2009 DTSI SRI-LIST Terrain following (3)

19. 19 26th March 2009 DTSI SRI-LIST Experiments

20. 20 26th March 2009 DTSI SRI-LIST Conclusion  Computation of the translational optical flow over a textured flat target plane.  Rigorous non-linear controllers for hovering flight, vertical landing and terrain (or wall) following.  The UAV remains free from collision.  The control approach has been experimented on a quad-rotor UAV to demonstrate the performance of controllers.

21. 21 26th March 2009 DTSI SRI-LIST Publications [1]Herisse, B.; Russotto, F-X.; Hamel, T. & Mahony, R. Hovering flight and vertical landing control of a VTOL Unmanned Aerial Vehicle using Optical Flow IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS'08, 2008 [2]Herisse, B.; Hamel, T.; Mahony, R. & Russotto, F-X. A nonlinear terrain-following controller for a VTOL Unmanned Aerial Vehicle using translational optical flow IEEE International Conference on Robotics and Automation, ICRA'09, 2009 Tarek Hamel Robert Mahony François-Xavier Russotto

22. 22 26th March 2009 DTSI SRI-LIST Acknowledgments Projet Naviflow Assistance à la NAVIgation par FLux Optique