DIRTREL

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