DIRTREL

 DIRTREL

Direct Transcription with Ellipsoidal Disturbances and LQR Feedback - a new robust trajectory optimization algorithm presented at the 2017 Robotics: Science and Systems (RSS) conference at MIT.

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Zac Manchester

July 12, 2017
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Transcript

  1. DIRTREL: Robust Trajectory Optimization with Ellipsoidal Disturbances and LQR Feedback

    Zac Manchester and Scott Kuindersma Harvard Agile Robotics Lab
  2. Trajectory Optimization xgoal Trajectory optimization is a powerful tool for

    generating open-loop motion plans xstart ⇥ x0( t ) , u0( t ) ⇤ = argmin J ( x, u )
  3. Feedback Control The resulting open-loop plans are often tracked with

    time-varying linear feedback u ( t, x ) = u0( t ) K ( t ) x x0( t ) xgoal xstart
  4. The Problem Separating planning and feedback control design can lead

    to closed-loop systems that are “fragile” xgoal xstart ˙ x = f ( x, u, w ) disturbance `
  5. Approach • Design LQR feedback controller • Simulate closed-loop system

    with disturbance set • Evaluate robust cost function JW = ? W w 2
  6. Approach • Design LQR feedback controller • Simulate closed-loop system

    with disturbance set • Evaluate robust cost function w 2 JW = ? W
  7. Approach • Design LQR feedback controller • Simulate closed-loop system

    with disturbance set • Evaluate robust cost function JW = ? W w 2
  8. Approach JW = Z W ✓Z tf 0 L (

    x, u ) dt ◆ d W w 2 • Design LQR feedback controller • Simulate closed-loop system with disturbance set • Evaluate robust cost function
  9. Approach Ellipsoidal disturbance sets and linearization allow the robust cost

    term to be computed in closed form w 2 ˙ x ⇡ ( A BK ) x + Gw x 2 =)
  10. 10 DIRTRAN + LQR: DIRTREL: Nonlinear Friction

  11. 11 Fluid Slosh

  12. 12 Wind Gusts

  13. 13 Conclusions • DIRTREL optimizes dynamic motions while reasoning about

    feedback and bounded disturbances • Avoids disturbance sampling and outperforms heuristic techniques like constraint shrinking • Scales up to practical robotic systems and tasks • Computational cost is only marginally higher than standard direct methods http://agile.seas.harvard.edu