Optimization Based Iterative Learning Control for Trajectory - PowerPoint PPT Presentation

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 1

CHALLENGING… [video] Angela Schoellig ‐ ETH Zürich 2

AUTOMATED SYSTEMS REPEATED OPERATION INPUT AND STATE CONSTRAINTS GOAL High performance trajectory tracking through iterative learning Taking constraints explicitly into account … Making full use of system‘s capabilities! Angela Schoellig ‐ ETH Zürich 3

ITERATIVE LEARNING CONTROL EXECUTE – ESTIMATE – CONTROL Angela Schoellig ‐ ETH Zürich 4

SYSTEM DYNAMICS Model of the real ‐ world system G I V Input and state constraints E N Desired trajectory LINEARIZE AND DISCRETIZE Small deviations from nominal trajectory Angela Schoellig ‐ ETH Zürich 5

LIFTED ‐ SYSTEM REPRESENTATION Linear, time ‐ varying difference equations ! LIFT IT with . cv and assuming that . Angela Schoellig ‐ ETH Zürich 6

ITERATION ‐ TIME DOMAIN For trial : • Model error along the trajectory ! DESIGN PARAMETER • Process and measurement noise trial uncorrelated LINEAR, TIME ‐ INVARIANT, DISCRETE ‐ TIME SYSTEM Angela Schoellig ‐ ETH Zürich 7

ESTIMATION EXECUTE NEW ITERATION ESTIMATE Error estimate CONTROL Minimizing Initial conditions KALMAN FILTER IN THE ITERATION DOMAIN Angela Schoellig ‐ ETH Zürich 8

CONTROL EXECUTE NEW ITERATION ESTIMATE subject to CONTROL Different norms Weighting ! DESIGN PARAMETER CONVEX PROGRAMMING PROBLEM Angela Schoellig ‐ ETH Zürich 9

EXPERIMENT GOAL Open ‐ loop swing up CHARACTERISTICS • Nonlinear, unstable dynamics Coarse model • • State and input constraints • Very sensitive to error SWING IT UP! Angela Schoellig ‐ ETH Zürich 10

MOVIE https://youtu.be/W2gCn6aAwz4?list=PLC12E387419CEAFF2 SWING IT UP! Angela Schoellig ‐ ETH Zürich 11

MORE RESULTS AND FEATURES (1) ROBUSTNESS DOUBLE THE MASS KEEP SAME MODEL & UPDATE RULE Angela Schoellig ‐ ETH Zürich 12

MORE RESULTS AND FEATURES (2) WEIGHTING Weight on angle rate Swing up in… 0.006 ‐‐‐ INFLUENCES 0.012 4th iteration LEARNING BEHAVIOR 0.05 6th iteration 0.1 7th iteration SPEED OF LEARNING Epsilon Swing up in… 0.01 6th iteration 0.1 5th iteration 10 4th iteration 100 4th iteration NORM Angela Schoellig ‐ ETH Zürich 13

SUMMARY Repetitive process EXECUTE Trajectory to be followed Input and state constraints NEW ITERATION ESTIMATE OPTIMAL FILTERING: Kalman Filter CONTROL CONVEX OPTIMIZATION: Cplex Fast learning taking constraints explicitly into account. High tracking performance tapping the system‘s full potential. Angela Schoellig ‐ ETH Zürich 14

FINALLY… [video] Angela Schoellig ‐ ETH Zürich 15