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Iterative Learning of Feed Forward Corrections for High Performance - - PowerPoint PPT Presentation

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Iterative Learning of Feed Forward Corrections for High Performance Tracking Fabian L. Mueller, Angela P. Schoellig, Raffaello DAndrea Institute for Dynamic Systems and Control ETH Zrich, Switzerland 1 Iterative Learning of Feed

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Iterative Learning of Feed‐Forward Corrections for High‐Performance Tracking

Fabian L. Mueller, Angela P. Schoellig, Raffaello D’Andrea

Institute for Dynamic Systems and Control ETH Zürich, Switzerland

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Iterative Learning of Feed‐Forward Corrections for High‐Performance Tracking

Fabian L. Mueller, Angela P. Schoellig, Raffaello D’Andrea

Institute for Dynamic Systems and Control ETH Zürich, Switzerland

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GOAL – Precise tracking of a desired output trajectory

Angela Schoellig

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Example: Quadrotor vehicle

GOAL – Precise tracking of a desired output trajectory

Angela Schoellig

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Example: Quadrotor vehicle Typical setup: Feedback control Limitations of feedback control: Disturbances and unmodelled dynamics (non‐zero mean)

GOAL – Precise tracking of a desired output trajectory

Angela Schoellig CONTROL Desired position Measured position

Large repetitive error

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Potential: Acausal action, anticipating repetitive disturbances.

LEARNING APPROACH

SYSTEM

Input Disturbance Output

LEARNING

Angela Schoellig

Improve the performance over causal, feedback control by learning from a repeated operation.

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LEARNING APPROACH

1. Dynamics model (here: from numerical simulation) 2. Disturbance estimation* 3. Update of input trajectory*

* Angela P. Schoellig, Fabian L. Mueller, Raffaello D‘Andrea, “Optimization‐based iterative learning for precise quadrocopter trajectory tracking,” Autonomous Robots, 2012

SYSTEM

Input Output

DISTURBANCE ESTIMATION

Estimated disturbance Updated input

INPUT UPDATE

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Prerequisites:

  • Coarse model
  • Desired output trajectory

with corresponding nominal input

Input sequence

1 | DYNAMICS MODEL

Angela Schoellig

SYSTEM

Output sequence, constrained sequence

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1 | DYNAMICS MODEL

Define:

  • Linear mapping from input deviations to changes in output and

constrained variables: From numerical dynamics simulation:

  • Obtain by running identification runs
  • Apply
  • Obtain

Angela Schoellig

ith column

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For each trial Recurring disturbance .

  • Unknown. Only small changes between iterations:

Noise .

  • Unknown. Changing from iteration to iteration.

1 | ITERATION‐DOMAIN MODEL

From trial to trial our knowledge about improves.

trial‐uncorrelated, zero‐mean Gaussian noise

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UPDATE OF DISTURBANCE ESTIMATE

via Kalman filter in the iteration domain:

Prediction step: Measurement update step: Obtain .

ESTIMATION

EXECUTE ESTIMATE UPDATE

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EXECUTE UPDATE ESTIMATE

INPUT UPDATE

INPUT UPDATE via convex optimization:

minimizes the expected tracking error in the next trial:

subject to

Obtain .

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EXPERIMENTAL RESULTS

Angela Schoellig CONTROL Desired position Measured position

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VIDEO: https://youtu.be/zHTCsSkmADo?list=PLC12E387419CEAFF2

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  • Learning algorithm

combines model data with experimental data

  • Convergence in around

5‐10 iterations

CONCLUSIONS

Repetitive error components can be effectively compensated for by learning from past data. Result is an improved tracking performance.