Nonlinear Attitude and Position Control of a Micro Quadrotor using
Different control strategies for Attitude Stabilization. - Quaternion based linear feedback controller [Tayebi2006]. - Non-linear backstepping controller ...
Nonlinear Attitude and Position Control of a Micro Quadrotor using Sliding Mode and Backstepping Techniques Patrick Adigbli(1), Ch. Grand(2), J-B. Mouret (2), S. Doncieux (2) (1) Technical University of München - Germany (2) Institute of Intelligent Systems and Robotics University Paris 6 - France
Topics of this presentation Objectives
➡
Compare different control strategies for the stabilization of a micro quadri-rotor UAV
➡
Design and implement the most suitable control law
Outline 1. System modeling 2. Attitude controller 3. Position controller 4. Experimental results 5. Conclusion
micro Quadri-rotor UAV
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
2
System modeling
• Configuration vectors
• Velocity decoupling matrix
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
3
System modeling
• Forces distribution:
• Actuation model:
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
4
System modeling
• Dynamic equations (Euler-Lagrange): • Analytical model (with small angles simplification):
• Model abstraction: 21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
5
Control strategies
• Two sub-controllers: -
Attitude stabilization Position stabilization
• Different control strategies for Attitude Stabilization -
•
Quaternion based linear feedback controller [Tayebi2006] Non-linear backstepping controller [Bouabdallah2005] Non-linear sliding-mode controller
Backstepping controller for Position Stabilization
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
6
Control strategies Attitude control architecture
Cascaded control architecture
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
7
Attitude control: Linear feedback controller
• Quaternion based controller -
Reduced quaternion vector:
-
Linear feedback law:
➡Controller globally asymptotically stable [Tayebi2005] 21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
8
Attitude control: Backstepping controller Define non-linear control law based on Lyapunov fonctions State vector: Transform dynamic state vector:
Choose Lyapunov candidate function: Control law :
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
9
Attitude control: Sliding mode controller State vector: System dynamic model: Switching or sliding manifold:
Sliding-mode control law:
➡ Proof of control law stability (Lyapunov approach): see paper 21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
10
Attitude control: analysis and comparison
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
11
Attitude control: analysis and comparison
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
12
Position control: Backstepping controller
Using same approach based on Lyapunov function:
Dynamic model based position controller:
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
13
Position control: Backstepping controller
• Simulation results
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
14
First experiments: attitude stabilization
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
15
Conclusions
• Developed a simplified dynamic model for a quadri-rotor • Analyzed different control strategies for the attitude control -
Linear feedback law, backstepping, sliding-mode controller
• Proposed a backstepping controller for position stabilization • Evaluated and tuned the controller using numerical simulations
• First test on a real prototype of quadri-rotor UAV
21/09/07 - EMAV2007 - European Micro Air Vehicle Conference and Flight Competition
Sep 21, 2007 - By taking into account the equations (1) and (2), the ..... the UAV tracks well the desired quadratic path (left), it's actual position ξ is plotted ...
troller framework in order to obtain a nonlinear controller to control river flow. Simulations ... subject of numerous publications since the 1950's. Weinman.
In the past two years, the Department of Control Engineering at Aalborg Uni- ... mathematical model of the helicopter dynamics had been initiated, but no well ..... problems, described in Section 3.3, the PC-104 was replaced by a standard laptop ....
Polar speed diagram of a sailboat. The set of feasible chosen input vectors is. W D í b2[ ó9 ° >báî[áì[.ì[.î9. Ñ D áî í-\.îPáì í-\.ìP+á ó é. Ñ D. bÅPìî rií.î9áîPìì rií.ìáì.
A.) protection ring. B.) brushless motor. C.) contra-rotating propellers. D.) LIPO battery. E.) high-speed motor controller. F.) flight computer. G.) infrared sensors ...
â¢Embedded sensors : â Inertial Measurement Unit provides angles, angular velocity and accelerations. â 4 ultra sonic range finders - distances to obstacles.
device like a Fabry-Perot or a Michelson interferometer, although in the latter cases the assumption of Lorentzian filter response is clearly an approximation, ...
a control law which utilizes the inherent nonlinearities and hysteresis. To illustrate ... rod axis, moments align in the sense depicted in Fig- ure 2c and signi cant ...
This approach carries out an interpolation of the control laws but not of the ... control applied to the system results from a weighted average of the various control ...
main wall movement is reversible which leads to anhys- teretic (hysteresis free) .... the nonnegative matrix G penalizes large terminal val- ues of the state.
Apr 2, 2014 - angular rate sensors measuring both static and dynamic orientations. ... Of course, intrinsic limitations of these sensors do not allow a good ...
Aug 23, 2000 - scribes their 'activation' into design tools and constructive procedures. Structural ... For a long time a serious drawback of Lyapunov theory was the lack of pro- cedures for ...... recursive nonlinear designs includes the books by Kr
individual muscle forces in human movement. One of the .... The theoretical musculoskeletal model that was used for all calculations in this study. is shown ..... become less severe, the cost decreases until it reaches the minimal value when the ...
The authors are grateful to City University of Hong Kong for financial support via ... Deadzone compensation in motion control systems using neural networks, ...
INTRODUCTION. Crystallization is prominent ... cesses for control Engineering project) - Large Collaborative Project ..... Computers & chemical engineering, 31.
The passive control of vibration is a key problem in numerous engineering applications, ranging ... In the past, numerous methods have been developped, from.
g = 9.81m/s2. (λ0,λ1, λ2, λ3),(λ4, λ5) ... Ap = 0.8; Aq = 1; Ar = 0.8; the following results are ... Wind parameters estimation for Ap=0.8; Aq=0.5; Ar=1. 0. 10. 20. 30.
the âCAROLOâ programme towards an adaptive flight control system for micro ... When using artificial intelligence for flight control purposes of fully automatic micro planes, it makes sense to .... where âW marks the change in the weight matrix
[13] [10], and sliding mode control [14] are not directly applicable to underactuated ... Ap + u2d. Aq + u3d. Ar + u4.. in which. ⢠col(Ax,Ay,Az) and col(Ap,Aq,Ar) are the result- ..... [18] L. M. Milne-Thomson, âTheoretical Aerodynamicsâ, Dove
The first method, called partial state representation, emphasizes the control of ... over, many recent and traditional methods of nonlinear control design including ...
order derivative of the position and attitude (yaw, pitch and roll) of the vehicle. ... estimate the vehicle orientation and position in the current frame. Knowing the ..... 365â368. [10] R. Toledo-Moreo, D. Betaille, F. Peyret, and J. Laneurit, â
Feb 15, 2006 - estimation has to be continuous as well, or if not, at least that such the sampling .... In a discrete form the state vector is defined as. [. ] k n. T.
Feb 15, 2006 - that âa 3D solid rotation is equivalent to only one, along an eigen axis, ... filter is to adjust a prior estimation based on an attitude model, via measurements ...... The Kalman filter float diagram for airborne attitude control. .
