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Optimization Based Iterative Learning Control for Trajectory - - PowerPoint PPT Presentation

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Optimization Based Iterative Learning Control for Trajectory Tracking Angela Schoellig and Raffaello DAndrea Institute for Dynamic Systems and Control ETH Zrich, Switzerland European Control Conference 2009 Budapest, Hungary 1

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Optimization‐Based Iterative Learning Control for Trajectory Tracking

Angela Schoellig and Raffaello D‘Andrea

Institute for Dynamic Systems and Control ETH Zürich, Switzerland European Control Conference 2009  Budapest, Hungary

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CHALLENGING… [video]

Angela Schoellig ‐ ETH Zürich

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AUTOMATED SYSTEMS REPEATED OPERATION

Angela Schoellig ‐ ETH Zürich

INPUT AND STATE CONSTRAINTS

GOAL

High performance trajectory tracking through iterative learning Taking constraints explicitly into account … Making full use of system‘s capabilities!

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ITERATIVE LEARNING CONTROL

EXECUTE – ESTIMATE – CONTROL

Angela Schoellig ‐ ETH Zürich

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SYSTEM DYNAMICS

Model of the real‐world system Input and state constraints Desired trajectory

LINEARIZE AND DISCRETIZE

Small deviations from nominal trajectory

G V N

Angela Schoellig ‐ ETH Zürich

I E

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LIFTED‐SYSTEM REPRESENTATION

Linear, time‐varying difference equations

! LIFT IT

with .

cv

and assuming that .

Angela Schoellig ‐ ETH Zürich

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For trial :

  • Model error along the trajectory
  • Process and measurement noise

trial uncorrelated

LINEAR, TIME‐INVARIANT, DISCRETE‐TIME SYSTEM

ITERATION‐TIME DOMAIN

! DESIGN PARAMETER Angela Schoellig ‐ ETH Zürich

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ESTIMATION

KALMAN FILTER IN THE ITERATION DOMAIN

NEW ITERATION

EXECUTE ESTIMATE CONTROL

Error estimate Minimizing Initial conditions Angela Schoellig ‐ ETH Zürich

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CONVEX PROGRAMMING PROBLEM

Different norms Weighting

CONTROL

NEW ITERATION

EXECUTE ESTIMATE CONTROL

subject to

! DESIGN PARAMETER Angela Schoellig ‐ ETH Zürich

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GOAL Open‐loop swing up CHARACTERISTICS

  • Nonlinear, unstable dynamics
  • Coarse model
  • State and input constraints
  • Very sensitive to error

SWING IT UP! EXPERIMENT

Angela Schoellig ‐ ETH Zürich

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MOVIE https://youtu.be/W2gCn6aAwz4?list=PLC12E387419CEAFF2

SWING IT UP!

Angela Schoellig ‐ ETH Zürich

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MORE RESULTS AND FEATURES (1)

Angela Schoellig ‐ ETH Zürich

ROBUSTNESS

DOUBLE THE MASS KEEP SAME MODEL & UPDATE RULE

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MORE RESULTS AND FEATURES (2)

Angela Schoellig ‐ ETH Zürich

WEIGHTING

INFLUENCES LEARNING BEHAVIOR

SPEED OF LEARNING NORM

Weight on angle rate Swing up in… 0.006 ‐‐‐ 0.012 4th iteration 0.05 6th iteration 0.1 7th iteration Epsilon Swing up in… 0.01 6th iteration 0.1 5th iteration 10 4th iteration 100 4th iteration

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Fast learning taking constraints explicitly into account. High tracking performance tapping the system‘s full potential.

SUMMARY

NEW ITERATION

EXECUTE ESTIMATE CONTROL

Repetitive process Trajectory to be followed Input and state constraints

OPTIMAL FILTERING: Kalman Filter CONVEX OPTIMIZATION: Cplex

Angela Schoellig ‐ ETH Zürich

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FINALLY… [video]

Angela Schoellig ‐ ETH Zürich