Design of Advanced Control Techniques for an Underwater Vehicle Divine Maalouf Advisors: Vincent Creuze Ahmed Chemori René Zapata 5 juillet 2012
OUTLINE I. Introduction: Problems/Challenges II. Modeling and State of the Art III. Proposed Solutions IV. Experimental Platform V. Experimental Results VI. Summary 2 1
Objective Make the robot follow a desired trajectory in presence of parameter uncertainties and variations in the model. 3 2
Design and implementation of control approaches for trajectory following on a small underwater vehicle Inherent Problems o o o o o o Highly nonlinear dynamics Strong uncertainties Variation of the model parameters Immeasurable coordinates: Strong coupling in dynamics High hysteresis in the thrusters AC-ROV (Acces Ltd) Actuation: 6 DOF 6 Thrusters 5 actuated DOF Sensors: Camera Depth sensor IMU 4 3
Motion Variables for a Marine Vessel [SNAME1950] Dynamic Modeling [Fossen2002] M C( ) J( ) D( ) G( ) ν [ u v w p q r] Vector of velocities in the body frame Τ η [ x y z Vector of coordinates Φ θ ψ] position and angular Τ in the earth frame Forces produced by the thrusters M,C,D G τ J M odel matrices (M ass,coriolis, Damping) Vector of gravitation/buoyancy forces Vector of control inputs Transformation matrix 5 4
5 Main control schemes used in underwater robotics Classical schemes Robust schemes Adaptive schemes Hybrid schemes Other schemes PID and acceleration feedback [Fossen2002] Nonlinear State Feedback [Fossen2002] Nonlinear Output Feeback [Adhami2011] H_inf approaches [Roche2011] Sliding Mode [Akakaya2009] Higher Order Sliding Mode [Salgado2004] Regressor based Methods [Antonelli2001] Nonregressor Based methods [Zhao2005] Jacobian Transpose based Controller [Sun2009] Fuzzy Sliding Mode [Marzbanrad 2011] Adaptive Fuzzy Sliding Mode [Bessa2008] Backstepping/ Adaptive [Lapierre2006] Reinforcement learning [ElFakdi2008] Fuzzy logic [Chang2003] Predictive control [Steenson 2012]
Goal Trajectory following in presence of uncertainties and parameters changes Proposed Solutions Adaptive Control Law Estimation of z Robustness towards disturbances 2 nd Validation Real time experimental results 1 st Validation Matlab Simulations 7 6
designed control schemes Solution 1 classical PID Solution 2 nonlinear adaptive state feedback Solution 3 nonlinear L1 adaptive state feedback Scenario1 nominal conditions Scenario 2 robustness towards uncertainties added buoyancy added damping Scenario 3 external disturbances rejection waves mechanical shock 8 7
SOLUTION 1 : PROPORTIONAL INTEGRAL DERIVATIVE P K P e( t ) r( t ) e ( t ) t u( t ) y( t ) I K e( t ) dt I 0 D K D de( t dt ) 9 8
Solution 1: PID Tuning Method We can describe our system by the integrator plus dead time (IPDT) model : G( s ) a sl e sl Coefficient of the controller for IPDT models to minimize a chosen criterion [Visioli2001]: Integral of Squared Time Multiplied by Square Error with a a1 K, KP, Ti a4l,td a5l L KL 10 9
SOLUTION 2: NONLINEAR ADAPTIVE STATE FEEDBACK [FOSSEN2002] parameter update T ( a b,, )J 1 y ˆ ˆ ( a b,, ) ˆ control law ROV commanded acceleration in the body frame b a J 1 ( a n a J ) n K ~ K ~ K ~ dt d D commanded acceleration in the earth frame P ( t ), (t I t 0 ) ~ ~ d d y c ~ 0 c ~ 1 ( c0 and c1 regressor matrix constants) Nonlinear Adaptive State Feedback Controller 11 10
SOLUTION 3: L1 ADAPTIVE CONTROL [HOVAKIMYAN2010] 12 11
SOLUTION 3: L1 ADAPTIVE CONTROL [HOVAKIMYAN2010] L1 Adaptive Controller Control architecture 1 Controlled system 2 Prediction phase 3 Parameter update 4-5 Control input, with feedback gain k, pre-filter kg and filter D(s). 13 12
13 MATLAB SIMULATOR Based on Fossen s toolbox [Fossen2002]. Simulation and comparison of control laws. Trajectory Generator ROV Controller Inverse Motor Characteristic Motor Dynamics & ROV s dynamics estimated states State observer measured states
AC-ROV industrial Platform View of the modified AC-ROV Prototype Experimental Platform Controlled with a joystick Proportional controller integrated Control PC, Power Input, Emergency stop button, Video in, Tether plug, Ethernet Plug Video capture, Tether, AC-ROV 15 14
Control Inputs Depth Response Scenario 1 Nominal Conditions PID Controller Adaptive Controller 16 15
Depth Response Control Inputs nominal case floatability increase 16 Scenario 2 Buoyancy Increase 32% Parameter (W-B) PID Controller Adaptive Controller
Depth Response Control Inputs 18 17 Scenario 2 Damping Change PID Controller Adaptive Controller
Control Inputs Depth Response Scenario 3 Mechanical Shock mechanical shock PID Controller Adaptive Controller 19 18
Control Inputs Depth Response Scenario 3 Disturbing Waves PID Controller Adaptive Controller 20 19
Pitch angle (deg) Depth (m) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Measured Depth -0.1 Desired Trajectory -0.2 0 20 40 60 80 100 120 140 160 Time (s) 20 15 10 Depth (z) Pitch ϑ L1 Adaptive Control Scenario 1 Nominal Conditions 5 Measured Pitch 0 Desired Trajectory -5 0 20 40 60 80 100 120 140 160 Time (s) Control inputs Estimated parameters and disturbances 21 20
Pitch angle (deg) Depth (m) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Measured Depth -0.1 Desired Trajectory -0.2 0 20 40 60 80 100 120 140 160 Time (s) 20 15 10 Depth (z) Pitch (ϑ) 5 Measured Pitch 0 Desired Trajectory -5 0 20 40 60 80 100 120 140 160 Time (s) L1 Adaptive Control Scenario 2 Buoyancy Increase 32% Control inputs Estimated parameters and disturbances 21
Pitch angle (deg) Depth (m) Depth (z) L1 Adaptive Control 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Measured Depth -0.1 Desired Trajectory -0.2 0 20 40 60 80 100 120 140 160 Time (s) Scenario 3 Disturbing Waves Control inputs Pitch (ϑ) 20 15 10 5 Measured Pitch 0 Desired Trajectory -5 0 20 40 60 80 100 120 140 160 Time (s) Estimated parameters and disturbances 23 22
Scenario 3 Presence of Waves Scenario 2 Buoyancy Increase 32% Scenario 1 Nominal Conditions L1 ADAPTIVE CONTROL SUMMARY System output: z and ϑ Control input Estimated parameters and disturbances 24 23
Depth(m) Depth (m) Control Input (Newton) Depth (m) 24 SUMMARY OF DEPTH CONTROL Scenario 1 Nominal Conditions 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 PID Adaptive Control L1 Adaptive Control 0.1 Noisy Response 0 Filtered Response -0.1 Desired Trajectory -0.2 0 20 40 60 80 100 120 140 Time(s) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Noisy Response 0 Filtered Response -0.1 Desired Trajectory -0.2 0 20 40 60 Time (s) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0-0.1-0.2 Noisy Response Filtered Response Desired Trajectory 0 20 40 60 80 Time (s) 1.5 1 0.5 Motor 5 0-0.5-1 Motor 6-1.5 0 20 40 60 80 Time(s)
Problem: Trajectory following in presence of uncertainties, parameters changes and external disturbances Proposed Solutions designed control laws classical PID nonlinear adaptive state feedback nonlinear L1 adaptive state feedback Easy to implement Model independent Gains hard to tune Fails in presence of strong uncertainties Fails in presence of strong disturbances Robustness towards parameters change Robustness towards uncertainties External disturbances rejection Good parameter initialization is needed Large adaptive gains can lead to instability Robustness towards parameter change Robustness towards uncertainties External disturbances rejection Good initialization of parameters not needed Slight increase in computational cost 26 25