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Jan 14, 2016

ADAPTIVE AUGMENTED CONTROL OF UNMANNED ROTORCRAFT VEHICLES C.L. Bottasso , R. Nicastro , L. Riviello , B. Savini Politecnico di Milano AHS International Specialists' Meeting on Unmanned Rotorcraft Chandler, AZ, January 23-25, 2007. Rotorcraft UAVs at PoliMI. - PowerPoint PPT Presentation

ADAPTIVE AUGMENTED CONTROL OF UNMANNED ROTORCRAFT VEHICLESC.L. Bottasso, R. Nicastro, L. Riviello, B. Savini

Politecnico di Milano

Unmanned Rotorcraft

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Rotorcraft UAVs at PoliMI

Low-cost platform for development and testing of navigation and control strategies (including vision, flight envelope protection, etc.);

Vehicles: off-the-shelf hobby helicopters;

Bottom-up approach: everything is in-house developed (Inertial Navigation System, Guidance and Control algorithms, Linux-based real-time OS, flight simulators, etc. etc.)

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Reference Augmented Model Identification;

Reference Augmented Neural Control;

Vision/sensor range

Strategic layer: assign mission objectives (typically relegated to a human operator);

Tactical layer: generate vehicle guidance information, based on input from strategic layer and sensor information;

Reflexive layer: track trajectory generated by tactical layer, control, stabilize and regulate vehicle.

In this paper: Adaptive Non-linear Model Predictive Control.

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Non-Linear Model Predictive Control

Non-linear Model Predictive Control (NMPC):

Find the control action which minimizes an index of performance, by predicting the future behavior of the plant using a non-linear reduced model.

- Reduced model:

- Initial conditions:

- Output definition:

Stability results: Findeisen et al. 2003, Grimm et al. 2005.

L

Motivation

For any given problem: wealth of knowledge and legacy methods which perform reasonably well;

Quest for better performance/improved capabilities: undesirable and wasteful to neglect valuable existing knowledge;

Reference Augmented Predictive Control (RAPC): exploit available legacy methods, embedding them in a non-linear model predictive control framework.

Specifically:

Model: augment flight mechanics rotorcraft models (BEM+inflow theories) to account for unresolved or unmodeled physics;

Control: design a non-linear controller augmenting linear ones (LQR) which are known to provide a minimum level of performance about certain linearized operating conditions.

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Reference Augmented Predictive Control

- Augment the reference using an adaptive parametric function;

- Adjust the function parameters to ensure good approximation of the actual system / optimal control law (parameter identification).

Reasons for using a reference model / control:

- Reasonable predictions / controls even before any learning has taken place (otherwise would need extensive pre-training);

Easier and faster adaption: the defect is typically a small quantity, if the reference solution is well chosen.

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Plant

29.unknown

26.unknown

Reference Augmented Model Identification;

Reference Augmented Neural Control;

Goal:

Develop reduced model capable of predicting the behavior of the plant with minimum error (same outputs when subjected to same inputs);

Reduced model must be self-adaptive (capable of learning) to adjust to varying operating conditions.

Predictive solutions

Reference Augmented Model Identification

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Neural augmented reference model:

reference (problem dependent) analytical model,

Remark: reference model will not, in general, ensure adequate predictions, i.e.

when = system states/controls,

when

Hence, if we knew , we would have perfect prediction capabilities.

Reference Augmented Model Identification

where

and

= sigmoid activation functions;

Reference Augmented Model Identification

Pitch rate for plant, reference, and neural-augmented reference with same prescribed inputs.

Short transient =

fast adaption

Black: plant

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Reference Augmented Model Identification;

Reference Augmented Neural Control;

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Non-Linear Model Predictive Control

It can be shown that minimizing control is See paper for details.

F

u

t

u

r

e

P

a

s

t

P

r

e

d

i

c

t

i

o

n

w

i

n

d

o

w

x

0

t

0

t

0

t

0

where is the unknown control defect.

Remark: if one knew , the optimal control would be available without having to solve the open-loop optimal control problem.

Idea:

Identify on-line, i.e. find the parameters which minimize the reconstruction error .

Reference Augmented Predictive Control

Iterative procedure to solve the problem in real-time:

Integrate reduced model equations forward in time over the prediction window, using and the latest available parameters (state prediction):

Integrate adjoint equations backward in time (co-state prediction):

Correct control law parameters , e.g. using steepest descent:

On-line Identification of Control Parameters

p

c

u

r

e

f

p

c

seeks to enforce the transversality condition

Once this is satisfied, the control is optimal, since the state and co-state equations and the boundary conditions are satisfied.

On-line Identification of Control Parameters

_

Advance plant

Past

_

Approximate temporal dependence using shape functions:

Associate each nodal value with the output of a single-hidden-layer feed-forward neural network, one for each component:

where

Output:

Input:

Reference Augmented Model Identification;

Reference Augmented Neural Control;

Vehicle model:

Quasi-steady flapping dynamics, aerodynamic damping correction;

Look-up tables for aerodynamic coefficients of lifting surfaces;

Effects of compressibility and downwash at the tail due to main rotor;

Process and measurement noise, delays.

Reflexive controller:

Reference controller: output-feedback LQR at 50 Hz;

Goal trajectory planned as in Bottasso et al. 2007.

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Significant improvement over LQR

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

RAPC without model adaption

RAPC with model adaption

Significant improvement over LQR

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Initial transient

Linear controller promoted to non-linear;

Hard real-time capable (fixed number of ops, no iterations);

Adaption of control action can be performed independently from adaption of reduced model;

Reference model and reference control ensure good predictions even before adaption, avoid need for pre-training, simplify adaption since defect is small;

Conceptually possible (but not investigated here) to do adaption diagnostics by monitoring defects;

Theoretically non-linearly stable (if identification of , successful);

Basic concept demonstrated in a high-fidelity virtual environment.

p

c

p

m

Outlook

Real-time implementation and integration in a rotorcraft UAV (in progress) at the Autonomous Flight Lab at PoliMI;

Testing and extensive experimentation;

Politecnico di Milano

Unmanned Rotorcraft

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Rotorcraft UAVs at PoliMI

Low-cost platform for development and testing of navigation and control strategies (including vision, flight envelope protection, etc.);

Vehicles: off-the-shelf hobby helicopters;

Bottom-up approach: everything is in-house developed (Inertial Navigation System, Guidance and Control algorithms, Linux-based real-time OS, flight simulators, etc. etc.)

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Reference Augmented Model Identification;

Reference Augmented Neural Control;

Vision/sensor range

Strategic layer: assign mission objectives (typically relegated to a human operator);

Tactical layer: generate vehicle guidance information, based on input from strategic layer and sensor information;

Reflexive layer: track trajectory generated by tactical layer, control, stabilize and regulate vehicle.

In this paper: Adaptive Non-linear Model Predictive Control.

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Non-Linear Model Predictive Control

Non-linear Model Predictive Control (NMPC):

Find the control action which minimizes an index of performance, by predicting the future behavior of the plant using a non-linear reduced model.

- Reduced model:

- Initial conditions:

- Output definition:

Stability results: Findeisen et al. 2003, Grimm et al. 2005.

L

Motivation

For any given problem: wealth of knowledge and legacy methods which perform reasonably well;

Quest for better performance/improved capabilities: undesirable and wasteful to neglect valuable existing knowledge;

Reference Augmented Predictive Control (RAPC): exploit available legacy methods, embedding them in a non-linear model predictive control framework.

Specifically:

Model: augment flight mechanics rotorcraft models (BEM+inflow theories) to account for unresolved or unmodeled physics;

Control: design a non-linear controller augmenting linear ones (LQR) which are known to provide a minimum level of performance about certain linearized operating conditions.

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Reference Augmented Predictive Control

- Augment the reference using an adaptive parametric function;

- Adjust the function parameters to ensure good approximation of the actual system / optimal control law (parameter identification).

Reasons for using a reference model / control:

- Reasonable predictions / controls even before any learning has taken place (otherwise would need extensive pre-training);

Easier and faster adaption: the defect is typically a small quantity, if the reference solution is well chosen.

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Plant

29.unknown

26.unknown

Reference Augmented Model Identification;

Reference Augmented Neural Control;

Goal:

Develop reduced model capable of predicting the behavior of the plant with minimum error (same outputs when subjected to same inputs);

Reduced model must be self-adaptive (capable of learning) to adjust to varying operating conditions.

Predictive solutions

Reference Augmented Model Identification

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Neural augmented reference model:

reference (problem dependent) analytical model,

Remark: reference model will not, in general, ensure adequate predictions, i.e.

when = system states/controls,

when

Hence, if we knew , we would have perfect prediction capabilities.

Reference Augmented Model Identification

where

and

= sigmoid activation functions;

Reference Augmented Model Identification

Pitch rate for plant, reference, and neural-augmented reference with same prescribed inputs.

Short transient =

fast adaption

Black: plant

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Reference Augmented Model Identification;

Reference Augmented Neural Control;

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Non-Linear Model Predictive Control

It can be shown that minimizing control is See paper for details.

F

u

t

u

r

e

P

a

s

t

P

r

e

d

i

c

t

i

o

n

w

i

n

d

o

w

x

0

t

0

t

0

t

0

where is the unknown control defect.

Remark: if one knew , the optimal control would be available without having to solve the open-loop optimal control problem.

Idea:

Identify on-line, i.e. find the parameters which minimize the reconstruction error .

Reference Augmented Predictive Control

Iterative procedure to solve the problem in real-time:

Integrate reduced model equations forward in time over the prediction window, using and the latest available parameters (state prediction):

Integrate adjoint equations backward in time (co-state prediction):

Correct control law parameters , e.g. using steepest descent:

On-line Identification of Control Parameters

p

c

u

r

e

f

p

c

seeks to enforce the transversality condition

Once this is satisfied, the control is optimal, since the state and co-state equations and the boundary conditions are satisfied.

On-line Identification of Control Parameters

_

Advance plant

Past

_

Approximate temporal dependence using shape functions:

Associate each nodal value with the output of a single-hidden-layer feed-forward neural network, one for each component:

where

Output:

Input:

Reference Augmented Model Identification;

Reference Augmented Neural Control;

Vehicle model:

Quasi-steady flapping dynamics, aerodynamic damping correction;

Look-up tables for aerodynamic coefficients of lifting surfaces;

Effects of compressibility and downwash at the tail due to main rotor;

Process and measurement noise, delays.

Reflexive controller:

Reference controller: output-feedback LQR at 50 Hz;

Goal trajectory planned as in Bottasso et al. 2007.

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Significant improvement over LQR

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

RAPC without model adaption

RAPC with model adaption

Significant improvement over LQR

Reference Augmented Predictive Control

POLITECNICO di MILANO DIA

Initial transient

Linear controller promoted to non-linear;

Hard real-time capable (fixed number of ops, no iterations);

Adaption of control action can be performed independently from adaption of reduced model;

Reference model and reference control ensure good predictions even before adaption, avoid need for pre-training, simplify adaption since defect is small;

Conceptually possible (but not investigated here) to do adaption diagnostics by monitoring defects;

Theoretically non-linearly stable (if identification of , successful);

Basic concept demonstrated in a high-fidelity virtual environment.

p

c

p

m

Outlook

Real-time implementation and integration in a rotorcraft UAV (in progress) at the Autonomous Flight Lab at PoliMI;

Testing and extensive experimentation;

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