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Improving tracking performance by learning from past data Angela P. - - PowerPoint PPT Presentation

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Improving tracking performance by learning from past data Angela P. Schoellig Doctoral examina on July 30, 2012 Advisor: Prof. Raffaello DAndrea // Co advisor: Prof. Andrew Alleyne 1 Improving tracking performance by learning from

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Improving tracking performance by learning from past data

Angela P. Schoellig

Doctoral examinaon − July 30, 2012 Advisor: Prof. Raffaello D’Andrea // Co‐advisor: Prof. Andrew Alleyne

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Improving tracking performance by learning from past data

Angela P. Schoellig

Doctoral examinaon − July 30, 2012 Advisor: Prof. Raffaello D’Andrea // Co‐advisor: Prof. Andrew Alleyne

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MOTIVATION

HUMANS learn from experience.

We constantly adapt to changing environments. We learn from mistakes and get better through practice.

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MOTIVATION

AUTOMATED SYSTEMS typically make the same mistakes over

and over again when performing a task repeatedly.

Robots of a car assembly line.

Why?

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AUTOMATED SYSTEMS are typically operated using feedback

control:

Performance limitations:

  • Causality of disturbance correction: “first detect error, then react”.
  • Model‐based controller design; model ≠ real system.

Disturbance

MOTIVATION

Output

PLANT CONTROLLER

Input

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GOAL

Improve the performance over causal, feedback control by learning from previous experiments. SYSTEM

Input Disturbance Output

LEARNING

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Learning task: Following a predefined trajectory. Approach:

  • Model‐based learning based on a priori knowledge of the system

dynamics.

  • Adaptation of the input.

Potential:

Acausal action, anticipating repetitive disturbances.

SCOPE OF WORK

Input Output LEARNING

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OVERVIEW

I. Introduction

a. Testbed: The Flying Machine Arena b. Motivation for learning

II. Project A. Iterative learning for precise trajectory following: single‐agent and multi‐agent results. III. Project B. Learning of feed‐forward parameters for rhythmic flight performances

  • IV. Summary
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TESTBED, see www.flyingmachinearena.org

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THE TEAM

Sergei Lupashin Markus Hehn Mark Müller Federico Augugliaro

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THE FLYING MACHINE ARENA

Vehicle position and attitude

Control Algorithms

Collective thrust and turn rates (wireless) wireless

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OPERATION

Trajectory‐following controller (TFC)

Measured position and attitude Collective thrust and turn rates Desired position

Output Input

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MOTIVATION: PROJECT A

Desired motion.

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MOTIVATION: PROJECT A

Performance with trajectory‐following controller.

Large repetitive error Different trials

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OVERVIEW

I. Introduction II. Project A. Iterative learning for precise trajectory following

a. Learning approach b. Results

III. Project B. Learning of feed‐forward parameters for rhythmic flight performances

  • IV. Summary
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A | PUBLICATIONS

Peer‐reviewed publications

Schoellig, A. P. and R. D’Andrea (2009): “Optimization‐based iterative learning control for trajectory tracking.” In Proceedings of the European Control Conference (ECC). Schoellig, A. P., F. L. Mueller, and R. D’Andrea (2012): “Optimization‐based iterative learning for precise quadrocopter trajectory tracking.” Auton‐

  • mous Robots.

Mueller, F.L., A. P. Schoellig, and R. D’Andrea (2012): “Iterative learning of feed‐forward corrections for high‐performance tracking.” To appear in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

Joint work with Fabian L. Mueller (Master student).

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A | LEARNING APPROACH

Features: Learning through a repeated operation, updating full input trajectory after each trial.

SYSTEM

Input trajectory Output trajectory

DISTURBANCE ESTIMATION

Estimated disturbance Updated input

INPUT UPDATE

LEARNING

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PREREQUISITES

  • Dynamics model of system

(i) in analytical form or (ii) in form of a numerical dynamics simulation

  • Desired output trajectory

and corresponding nominal input trajectory  must satisfy the model equations.

RESULT

  • Learned input
  • Estimated disturbance vector

A | LEARNING APPROACH

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A | LIFTED‐DOMAIN REPRESENTATION

Dynamics model of the physical system: Consider small deviations from nominal trajectory. Linearize and discretize. Linear, time‐varying difference equation. Static mapping. Representing one trial.

With , and .

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For each trial Recurring disturbance .

  • Unknown. Only small changes between iterations:

Noise .

  • Unknown. Changing from iteration to iteration.

A | 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:

estimates the repetitve disturbance by taking into account all past measurements. Prediction step: Measurement update step: Obtain .

A | STEP 1: ESTIMATION

EXECUTE ESTIMATE UPDATE

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EXECUTE UPDATE ESTIMATE

A | STEP 2: UPDATE

INPUT UPDATE via convex optimization:

minimizes the tracking error in the next trial:

subject to

Obtain .

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A | TWO EXPERIMENTAL SCENARIOS

SCENARIO 1 SCENARIO 2

  • No feedback from motion capture

cameras during task execution

  • Camera information is used.
  • Analytical model
  • Model via numerical simulation
  • 2D quadrocopter model
  • 3D quadrocopter model
  • Constraints on single motor thrusts and turn rates.

Collective thrust and turn rates Position, attitude Position Position, attitude

TFC

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S‐shaped trajectory.

A | SCENARIO 1: state trajectories

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S‐shaped trajectory.

A | SCENARIO 1: input trajectories

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S‐shaped trajectory.

A | SCENARIO 1: state trajectories

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A | TWO EXPERIMENTAL SCENARIOS

SCENARIO 1 SCENARIO 2

  • No feedback from motion capture

cameras during task execution

  • Camera information is used.
  • Analytical model
  • Model via numerical simulation
  • 2D quadrocopter model
  • 3D quadrocopter model
  • Constraints on single motor thrusts and turn rates.

Collective thrust and turn rates Position, attitude Position Position, attitude

TFC

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S‐shaped trajectory.

A | SCENARIO 2: state trajectories

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S‐shaped trajectory.

A | SCENARIO 2: state trajectories

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S‐shaped trajectory.

A | SCENARIO 2: state trajectories

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S‐shaped trajectory.

A | SCENARIO 2: state trajectories

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A | SCENARIO 2: error convergence

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  • Prerequisites: approximate model of system dynamics.
  • Efficient learning algorithm: convergence in around 5‐10 iterations.
  • Acausal compensation: outperforms pure feedback control.

Scenario 2: without learning with learning

A | SUMMARY

Powerful combination Learning applied to feedback‐control systems: compensation for repetitive and non‐repetitive disturbances.

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VIDEO: http://tiny.cc/SlalomLearning

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OVERVIEW

I. Introduction II. Project A. Iterative learning for precise trajectory following III. Project B. Learning of feed‐forward parameters for rhythmic flight performances

a. Learning approach b. Results

I. Summary

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B | PUBLICATIONS

Peer‐reviewed publications

Schoellig, A. P., F. Augugliaro, and R. D’Andrea (2009): “Synchronizing the motion of a quadrocopter to music.” In Proceedings of IEEE International Conference on Robotics and Automation (ICRA). Schoellig, A. P., F. Augugliaro, and R. D’Andrea (2010): “A platform for dance performances with multiple quadrocopters.” In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)–Workshop on Robots and Musical Expressions. Schoellig, A. P., M. Hehn, S. Lupashin, and R. D’Andrea (2011): “Feasibility of motion primitives for choreographed quadrocopter flight.” In Proceedings of the American Control Conference (ACC). Schoellig, A. P., C. Wiltsche, and R. D’Andrea (2012): “Feed‐forward parameter identification for precise periodic quadrocopter motions.” In Proceedings of the American Control Conference (ACC).

Joint work with Federico Augugliaro (Bachelor/Master student) and Clemens Wiltsche (semester project).

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VIDEO: http://tiny.cc/DanceWith3

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Task: Precise tracking of periodic motions. Features:

  • Learning through a dedicated identification routine performed prior to

flight performance.

  • Adaptation of only a few input parameters.

B | LEARNING APPROACH

Position Position, attitude

TFC

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Amplitude and phase error

For each directional motion component and frequency, we learn: (1) amplitude correction factor, (2) additive phase correction.

B | LEARNING APPROACH

PURE FEEDBACK WITH LEARNED CORRECTION FACTORS

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VIDEO: http://tiny.cc/Armageddon

Angela Schoellig ‐ ETH Zurich

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OVERVIEW

I. Introduction II. Project A. Iterative learning for precise trajectory following III. Project B. Learning of feed‐forward parameters for rhythmic flight performances

  • IV. Summary
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SUMMARY

SYSTEM

Input Disturbance Output

LEARNING

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

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Carolina Flores Igor Thommen Marc Corzillius Hans Ulrich Honegger

RESEARCH SUPPORT STAFF

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IT FOLLOWS...

Live demonstration in the Flying Machine Arena

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Improving tracking performance by learning from past data

Angela P. Schoellig

Doctoral examinaon − July 30, 2012 Advisor: Prof. Raffaello D’Andrea // Co‐advisor: Prof. Andrew Alleyne