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.

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