ICRA 2019 Tutorial on Dynamical System-based Learning from Demonstration
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Modulation: Stable non-contact/contact transitions.
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ICRA 2019 Tutorial on Dynamical System-based Learning from Demonstration
- 1. Modulation Strategies 0 Non-contact/Contact Transitions Obstacle avoidance Start with an estimate of ሶ𝑥 = 𝑓 𝑥 from a set of demonstrations We can change the behavior of the system by: ሶ𝒙 = 𝑴 𝒙 𝒇 𝒙
- 2. Modulation Strategies 1 Non-contact/Contact Transitions Obstacle avoidance Start with an estimate of ሶ𝑥 = 𝑓 𝑥 from a set of demonstrations We can change the behavior of the system by: ሶ𝒙 = 𝑴 𝒙 𝒇 𝒙
- 3. Non-contact/Contact Transitions 2 Intuition Method Experiments Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 4. Non-contact/Contact Transitions 2 Intuition Method Experiments Demonstration Learning Execution Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 5. Non-contact/Contact Transitions 2 Intuition Method Experiments Demonstration Learning Execution Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 6. Non-contact/Contact Transitions 2 Intuition Method Experiments Demonstration Learning Execution Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 7. Non-contact/Contact Transitions 2 Intuition Method Experiments Demonstration Learning Execution Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 8. Non-contact/Contact Transitions 2 Intuition Method Experiments Demonstration Learning Execution Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 9. Non-contact/Contact Transitions 2 Intuition Method Experiments Demonstration Learning Execution Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 10. Non-contact/Contact Transitions 2 Intuition Method Experiments Demonstration Learning Execution Expected Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 11. Non-contact/Contact Transitions 2 Intuition Method Experiments Demonstration Learning Execution Reality Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 12. Non-contact/Contact Transitions 11 Intuition Method Experiments Demonstration Learning Execution RealityExpected Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 13. Non-contact/Contact Transitions 12 Intuition Method Experiments Endow the robotic system with a controller such that: (I) Ensuring stable contact, (II) At a desired location, (III) Leaving on the surface at a desired point Task objectives ➢The impact happens only once ➢The contact and departure points Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L 𝑥 𝑐 𝑥 𝑙 Contact surface ➢ Non-penetrable, passive and convex.
- 17. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 𝑥 𝑙 0 < 𝛤 13 𝛤 = 0 𝛤 < 0
- 18. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 𝑥 𝑙 0 < 𝛤 13 𝛤 = 0 𝛤 < 0
- 19. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 𝑥 𝑙 13 𝛤 = 0 𝛤 < 0 Free-motion region: 𝛤 𝑥, 𝛼 ≥ 𝜌 Transition region: 0 < 𝛤 𝑥, 𝛼 < 𝜌 Contact region: 𝛤 𝑥, 𝛼 = 0 𝜌 < 𝛤 𝜌 > 0
- 20. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 𝑥 𝑙 13 𝛤 = 0 𝛤 < 0 Free-motion region: 𝛤 𝑥, 𝛼 ≥ 𝜌 Transition region: 0 < 𝛤 𝑥, 𝛼 < 𝜌 Contact region: 𝛤 𝑥, 𝛼 = 0 0 < 𝛤 < 𝜌 𝜌 < 𝛤 𝜌 > 0
- 21. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 𝑥 𝑙 13 𝛤 = 0 𝛤 < 0 Free-motion region: 𝛤 𝑥, 𝛼 ≥ 𝜌 Transition region: 0 < 𝛤 𝑥, 𝛼 < 𝜌 Contact region: 𝛤 𝑥, 𝛼 = 0 0 < 𝛤 < 𝜌 𝜌 < 𝛤 𝜌 > 0 𝛤 𝑥 𝑐 , 𝛼 = 0
- 22. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 𝑥 𝑙 14 𝛤 = 0 𝛤 < 0 𝜌 > 00 < 𝛤 < 𝜌 𝜌 < 𝛤 𝛤 𝑥 𝑐 , 𝛼 = 0 Free-motion region: 𝛤 𝑥, 𝛼 ≥ 𝜌 Transition region: 0 < 𝛤 𝑥, 𝛼 < 𝜌 Contact region: 𝛤 𝑥, 𝛼 = 0
- 23. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 𝑥 𝑙 14 𝛤 = 0 𝛤 < 0 𝜌 > 00 < 𝛤 < 𝜌 𝜌 < 𝛤 𝛤 𝑥 𝑐 , 𝛼 = 0 Free-motion region: 𝛤 𝑥, 𝛼 ≥ 𝜌 Transition region: 0 < 𝛤 𝑥, 𝛼 < 𝜌 Contact region: 𝛤 𝑥, 𝛼 = 0
- 24. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 𝑥 𝑙 14 𝛤 = 0 𝛤 < 0 𝜌 > 00 < 𝛤 < 𝜌 𝜌 < 𝛤 𝛤 𝑥 𝑙 , 𝛼 = 𝜌𝛤 𝑥 𝑐 , 𝛼 = 0 Free-motion region: 𝛤 𝑥, 𝛼 ≥ 𝜌 Transition region: 0 < 𝛤 𝑥, 𝛼 < 𝜌 Contact region: 𝛤 𝑥, 𝛼 = 0
- 25. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 𝑥 𝑙 14 𝛤 = 0 𝛤 < 0 𝜌 > 00 < 𝛤 < 𝜌 𝜌 < 𝛤 𝛤 𝑥 𝑙 , 𝛼 = 𝜌 0 < 𝛼 𝛤 𝑥 𝑐 , 𝛼 = 0 Free-motion region: 𝛤 𝑥, 𝛼 ≥ 𝜌 Transition region: 0 < 𝛤 𝑥, 𝛼 < 𝜌 Contact region: 𝛤 𝑥, 𝛼 = 0
- 26. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 18 𝑥 𝑙 𝑞1 𝑞2 Legend 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point Task objectives ➢The impact happens only once ➢The contact and stop/departure points
- 27. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 18 𝑥 𝑙 𝑞1 𝑞2 Legend 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point Task objectives ➢The impact happens only once ➢The contact and stop/departure points Elastic impact
- 28. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 18 𝑥 𝑙 𝑞1 𝑞2 Legend 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point Task objectives ➢The impact happens only once ➢The contact and stop/departure points Task objectives ➢The impact happens only once: 𝑞1 𝑇 ሶ𝑥 𝑡∗ = 0 Elastic impact
- 29. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 18 𝑥 𝑙 𝑞1 𝑞2 Legend 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point Task objectives ➢The impact happens only once ➢The contact and stop/departure points Task objectives ➢The impact happens only once: 𝑞1 𝑇 ሶ𝑥 𝑡∗ = 0 Elastic impact ሶ𝑥 = 𝑀 𝑥 𝑓 𝑥
- 30. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 18 𝑥 𝑙 𝑞1 𝑞2 Legend 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point Task objectives ➢The impact happens only once ➢The contact and stop/departure points Task objectives ➢The impact happens only once: 𝑞1 𝑇 ሶ𝑥 𝑡∗ = 0 Elastic impact ሶ𝑥 = 𝑀 𝑥 𝑓 𝑥 We must control for the robot’s velocity at contact.
- 31. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 18 𝑥 𝑙 𝑞1 𝑞2 Legend 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point Task objectives ➢The impact happens only once ➢The contact and stop/departure points Task objectives ➢The impact happens only once: 𝑞1 𝑇 ሶ𝑥 𝑡∗ = 0 Elastic impact ሷ𝑥 = 𝑀 𝑥, ሶ𝑥 𝑓 𝑥, ሶ𝑥, 𝑡 We must control for the robot’s velocity at contact.
- 32. Non-contact/Contact Transitions Intuition Method Experiments 31 ሷ𝑥 = 𝑓 𝑥, ሶ𝑥ሶ𝑥 = 𝑓 𝑥 ➢ Input: Position ➢ Output: Velocity ➢ Control variable is Position ➢ Demonstrations must cover position space. ➢ Input: Position and Velocity ➢ Output: Acceleration ➢ Control variable is Velocity and indirectly Position. ➢ Demonstrations must cover position and velocity space.
- 33. Non-contact/Contact Transitions Intuition Method Experiments 𝑥 𝑐 32 𝑀 𝑥, ሶ𝑥 = 𝑄Λ𝑄−1 𝑄 = 𝑞1 ⋯ 𝑞 𝑑 𝑇 ሷ𝑥 = 𝑀 𝑥, ሶ𝑥 𝑓 𝑥, ሶ𝑥, 𝑡 Locally activeDirectional Modulation 𝑥 𝑙 𝑞1 𝑞2 𝑥 𝑐 Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L Legend 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point
- 34. Legend Non-contact/Contact Transitions Intuition Method Experiments 𝑞1 33 𝑀 𝑥, ሶ𝑥 = 𝑄Λ𝑄−1 𝑄 = 𝑞1 ⋯ 𝑞 𝑑 𝑇 ሷ𝑥 = 𝑀 𝑥, ሶ𝑥 𝑓 𝑥, ሶ𝑥, 𝑡 Locally activeDirectional Modulation 𝑞2 𝑥 𝑐 𝑥 𝑙 Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L 33 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point
- 35. Non-contact/Contact Transitions Intuition Method Experiments 34 ሷ𝑥 = 𝑀 𝑥, ሶ𝑥 𝑓 𝑥, ሶ𝑥, 𝑡 Locally active 𝑥 𝑐 𝑥 𝑙 𝑞1 𝑞2 Free motion region: 𝜌 ≤ Γ 𝑥 Transition/contact regions: 0 ≤ Γ 𝑥 < 𝜌 Λ = I → M = 𝑄𝑄−1 ሷ𝑥 = 𝑓 𝑥, ሶ𝑥, 𝑡 Λ = 𝜆11 ⋯ 𝜆1𝑑 ⋮ ⋱ ⋮ 𝜆 𝑑1 ⋯ 𝜆 𝑑𝑑 Legend 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point 00:15.510 𝑀 𝐼 𝜌 Γ 𝑥 Λ Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 36. Legend Non-contact/Contact Transitions Intuition Method Experiments 35 𝑀 𝑥, ሶ𝑥 = 𝑄Λ𝑄−1 𝑄 = 𝑞1 ⋯ 𝑞 𝑑 𝑇 ሷ𝑥 = 𝑀 𝑥, ሶ𝑥 𝑓 𝑥, ሶ𝑥, 𝑡 Locally activeDirectional Modulation 𝑥 𝑐 𝑥 𝑙 Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L 35 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point Λ = 𝜆11 ⋯ 𝜆1𝑑 ⋮ ⋱ ⋮ 𝜆 𝑑1 ⋯ 𝜆 𝑑𝑑 lim 𝑡→∞ 𝑞𝑖 𝑇 𝑥 − 𝑞𝑖 𝑇 𝑥 𝑐 = 0 ∀𝑖 ∈ 2 … 𝑑 lim 𝑡→∞ 𝑞1 𝑇 𝑥 = 0 𝑞1 𝑇 ሶ𝑥 𝑡∗ = 0
- 37. Legend Non-contact/Contact Transitions Intuition Method Experiments 29 ሷ𝑥 = 𝑀 𝑥, ሶ𝑥 𝑓 𝑥, ሶ𝑥, 𝑡 Locally activeDirectional Modulation 𝑥 𝑐 𝑥 𝑙 Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L 36 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point lim 𝑡→∞ 𝑞𝑖 𝑇 𝑥 − 𝑞𝑖 𝑇 𝑥 𝑙 = 0 ∀𝑖 ∈ 2 … 𝑑 lim 𝑡→∞ 𝑞1 𝑇 𝑥 = 0 𝑞1 𝑇 ሶ𝑥 𝑡∗ = 0 𝑀 𝑥, ሶ𝑥 = 𝑄Λ𝑄−1 𝑄 = 𝑞1 ⋯ 𝑞 𝑑 𝑇 Λ = 𝜆11 ⋯ 𝜆1𝑑 ⋮ ⋱ ⋮ 𝜆 𝑑1 ⋯ 𝜆 𝑑𝑑
- 38. Legend Non-contact/Contact Transitions Intuition Method Experiments 29 ሷ𝑥 = 𝑀 𝑥, ሶ𝑥 𝑓 𝑥, ሶ𝑥, 𝑡 Locally activeDirectional Modulation 𝑥 𝑐 𝑥 𝑙 Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L 37 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point lim 𝑡→∞ 𝑞𝑖 𝑇 𝑥 − 𝑞𝑖 𝑇 𝑥 𝑙 = 0 ∀𝑖 ∈ 2 … 𝑑 lim 𝑡→∞ 𝑞1 𝑇 𝑥 = 0 𝑞1 𝑇 ሶ𝑥 𝑡∗ = 0 𝑀 𝑥, ሶ𝑥 = 𝑄Λ𝑄−1 𝑄 = 𝑞1 ⋯ 𝑞 𝑑 𝑇 Λ = 𝜆11 ⋯ 𝜆1𝑑 ⋮ ⋱ ⋮ 𝜆 𝑑1 ⋯ 𝜆 𝑑𝑑
- 39. Legend Non-contact/Contact Transitions Intuition Method Experiments 29 ሷ𝑥 = 𝑀 𝑥, ሶ𝑥 𝑓 𝑥, ሶ𝑥, 𝑡 Locally activeDirectional Modulation 𝑥 𝑐 𝑥 𝑙 Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L 38 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point lim 𝑡→∞ 𝑞𝑖 𝑇 𝑥 − 𝑞𝑖 𝑇 𝑥 𝑙 = 0 ∀𝑖 ∈ 2 … 𝑑 lim 𝑡→∞ 𝑞1 𝑇 𝑥 = 0 𝑞1 𝑇 ሶ𝑥 𝑡∗ = 0 𝑀 𝑥, ሶ𝑥 = 𝑄Λ𝑄−1 𝑄 = 𝑞1 ⋯ 𝑞 𝑑 𝑇 Λ = 𝜆11 ⋯ 𝜆1𝑑 ⋮ ⋱ ⋮ 𝜆 𝑑1 ⋯ 𝜆 𝑑𝑑
- 40. Legend Non-contact/Contact Transitions Intuition Method Experiments 29 ሷ𝑥 = 𝑀 𝑥, ሶ𝑥 𝑓 𝑥, ሶ𝑥, 𝑡 Locally activeDirectional Modulation 𝑥 𝑐 𝑥 𝑙 Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L 39 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point lim 𝑡→∞ 𝑞𝑖 𝑇 𝑥 − 𝑞𝑖 𝑇 𝑥 𝑙 = 0 ∀𝑖 ∈ 2 … 𝑑 lim 𝑡→∞ 𝑞1 𝑇 𝑥 = 0 𝑞1 𝑇 ሶ𝑥 𝑡∗ = 0 Free motion region: 𝜌 ≤ Γ 𝑥 Λ = I M = I ሷ𝑥 = 𝑓 𝑥, ሶ𝑥, 𝑡 𝑀 𝑥, ሶ𝑥 = 𝑄Λ𝑄−1 𝑄 = 𝑞1 ⋯ 𝑞 𝑑 𝑇 Λ = 𝜆11 ⋯ 𝜆1𝑑 ⋮ ⋱ ⋮ 𝜆 𝑑1 ⋯ 𝜆 𝑑𝑑
- 41. Legend Non-contact/Contact Transitions Intuition Method Experiments 29 ሷ𝑥 = 𝑀 𝑥, ሶ𝑥 𝑓 𝑥, ሶ𝑥, 𝑡 Locally activeDirectional Modulation 𝑥 𝑐 𝑥 𝑙 Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L 40 𝑥 Robot’s state Γ(x) The surface contact 𝑥 𝑐 Desired contact point 𝑥 𝑙 Desired departure point lim 𝑡→∞ 𝑞𝑖 𝑇 𝑥 − 𝑞𝑖 𝑇 𝑥 𝑙 = 0 ∀𝑖 ∈ 2 … 𝑑 lim 𝑡→∞ 𝑞1 𝑇 𝑥 = 0 𝑞1 𝑇 ሶ𝑥 𝑡∗ = 0 Free motion region: 𝜌 ≤ Γ 𝑥 Λ = I M = I ሷ𝑥 = 𝑓 𝑥, ሶ𝑥, 𝑡 𝑀 𝑥, ሶ𝑥 = 𝑄Λ𝑄−1 𝑄 = 𝑞1 ⋯ 𝑞 𝑑 𝑇 Λ = 𝜆11 ⋯ 𝜆1𝑑 ⋮ ⋱ ⋮ 𝜆 𝑑1 ⋯ 𝜆 𝑑𝑑
- 42. Non-contact/Contact Transitions Intuition Method Experiments 41 Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 43. Non-contact/Contact Transitions Intuition Method Experiments 42 Mirrazavi Salehian, S. S. and Billard, A. (2018) A Dynamical System Based Approach for Controlling Robotic Manipulators During Non-contact/Contact Transitions. RA-L
- 44. 43 Exercise Session 3 Non-contact/Contact transitions
- 45. 44 Download/Install Exercise Repository https://github.com/epfl-lasa/icra19-lfd-tutorial-exercises
- 46. 45 Download/Install Exercise Repository https://github.com/epfl-lasa/icra19-lfd-tutorial-exercises
- 48. 47
- 49. 48 Tasks 1. Robots reaches the surface at one point and leaves it at another point.
- 50. 49 Tasks 1. Robots reaches the surface at one point and leaves it at another point. 2. Automatically repeat the same task.