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Design of controllers for a quad-rotor UAV using optical flow

Design of controllers for a quad-rotor UAV using optical flow. Bruno Hérissé CEA List Fontenay-Aux-Roses, France bruno.herisse@cea.fr. Introduction. Purpose : measurements of inertial data and visual optical flow for the design of controllers for a VTOL UAV. IMU

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Design of controllers for a quad-rotor UAV using optical flow

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

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

  3. T F=f(T,R) Translational dynamics Constant forces  Rotational Dynamics Already controlled Model of the UAV • 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 : High gain controller SRI-LIST

  4. 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. SRI-LIST

  5. Kinematics of an image point under spherical projection • Optical flow from an image plane to a spherical retina. Optical Flow SRI-LIST

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

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

  8. Stabilization of the hovering flight • For the stabilisation of the hovering flight define the error term, • The goal is the regulation of to zero : • The control law ensures the exponential convergence of to zero (PI-type controller) • The UAV does not collide the obstacle SRI-LIST

  9. Vertical landing control (1) • 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. Smooth vertical landing SRI-LIST

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

  11. Vertical landing control (3) • 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. SRI-LIST

  12. Drone: - Embeded attitude control from IMU data -running at 166Hz Camera: -Focus: 2.1mm 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 • Analogical transmission: • Transmission at 2.4GHz • Associate with an acquisition card, a new image is available each 50 ms Ground station: Treatment of vision algorithms at 60 ms Textured ground Experimental setup SRI-LIST

  13. Experiments SRI-LIST

  14. Terrain following (1) • 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. SRI-LIST

  15. Terrain following (2) • The control law ensures the asymptotic convergence of to • The UAV does not collide the obstacle SRI-LIST

  16. Terrain following (3) • Proof: SRI-LIST

  17. Terrain following (3) SRI-LIST

  18. Terrain following (3) SRI-LIST

  19. Experiments SRI-LIST

  20. 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. SRI-LIST

  21. 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 FlowIEEE/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 flowIEEE International Conference on Robotics and Automation, ICRA'09, 2009 François-Xavier Russotto Tarek Hamel Robert Mahony SRI-LIST

  22. Acknowledgments Projet Naviflow Assistance à la NAVIgation par FLux Optique SRI-LIST

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