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Passive Bilateral Control of Teleoperators under Constant Time-Delay

Passive Bilateral Control of Teleoperators under Constant Time-Delay. Dongjun Lee and Mark W. Spong Coordinated Science Laboratory University of Illinois at Urbana-Champaign Research support by NSF IIS 02-33314/CCR 02-09202, ONR N00014-02-1-0011, and College of Engineering at UIUC.

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Passive Bilateral Control of Teleoperators under Constant Time-Delay

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  1. Passive Bilateral Control of Teleoperators under Constant Time-Delay Dongjun Lee and Mark W. Spong Coordinated Science Laboratory University of Illinois at Urbana-Champaign Research support by NSF IIS 02-33314/CCR 02-09202, ONR N00014-02-1-0011, and College of Engineering at UIUC IFAC 2005 Prague

  2. T1 (t) T2 (t) F2 (t) F1 (t)  Slave Robot Slave Comm.& Control Slave Environ. Master Robot Human Operator Master Comm.& Control v2 (t) v2 (t) v1 (t) v1 (t)  Contributions Teleoperator with Constant Time-Delays 1. Novel PD- based control framework for passive bilateral teleoperation with constant time-delays without relying on scattering-based teleoperation 2. Passivity is established using the Parseval’s identity, Lyapunov-Krasovskii technique, and controller passivity concept 3. Master-slave position coordination with explicit position feedback 4. Bilateral force reflection in the static manipulation IFAC 2005 Prague

  3. Outline 1. Energetic Passivity and Controller Passivity 2. Control Design and Analysis 3. Simulation 4. Conclusion IFAC 2005 Prague

  4. T1 (t) T2 (t) F2 (t) F1 (t)  Slave Robot Slave Comm.& Control Slave Environ. Master Robot Human Operator Master Comm.& Control v2 (t) v2 (t) v1 (t) v1 (t)  Closed-loop teleoperator - maximum extractable energy from the closed-loop teleoperator is bounded - the closed-loop teleoperator does not generate energy by itself Passivity for Interaction Stability and Safety Closed-Loop Teleoperator as a Two-Port System Energetic Passivity of the Closed-loop Teleoperator Mechanical power from closed-loop teleoperator finite constant (depending on initial condition) -Interaction stability: the feedback-interconnection is stable with any passive humans [Hogan89] /environments without relying on their detailed models - Interaction safety: possible damage on human/environment is bounded IFAC 2005 Prague

  5. T1 (t) T2 (t) F2 (t) F1 (t)  Slave Robot Slave Comm.& Control Slave Environ. Master Robot Human Operator Master Comm.& Control v2 (t) v2 (t) v1 (t) v1 (t)  Communication + Control Controller Passivity[Lee&Li] does not rely on the open-loop dynamics but only on the controller structure Mechanical power generated by the controller combined communication+control block generates only limited amount of energy 1. Simpler passivity analysis 2. Passivity can be ensured regardless of model uncertainty (Robust passivity is achieved) maximum extractable energy from the closed-loop system is bounded Controller Passivity and Robust Passivity Closed-Loop Teleoperator as a Two-Port System finite constant imply Energetic Passivity IFAC 2005 Prague

  6. Outline 1. Energetic Passivity and Controller Passivity 2. Control Design and Analysis 3. Simulation 4. Conclusion IFAC 2005 Prague

  7. T1 (t) T2 (t) F2 (t) F1 (t)  Slave Robot Slave Comm.& Control Slave Environ. Master Robot Human Operator Master Comm.& Control v2 (t) v2 (t) v1 (t) v1 (t)  local sensing local sensing D-control action additional viscous damping (e.g. device damping) P-control action w/ passifying dissipation Control Design Plant Dynamics Communication Structure PD-Based Control Closed-loop teleoperator is energetically passive if IFAC 2005 Prague

  8. Controller Passivity Controller Passivity (i.e. controller generates only bounded amount of energy) Controller Power Decomposition additional viscous damping (quadratic in velocity) D-action power P-action power - How to ensure that the energy generations by sd(t) and sp(t) be bounded? IFAC 2005 Prague

  9. D-action Passivity: Lyapunov-Krasovskii Functional Lyapunov-Krasovskii (LK) functional sum of master and slave velocities D-action Passivity energy generation bounded by Lyapunov-Krasovskii as a storage function IFAC 2005 Prague

  10. dissipating energy Parseval’s identity convert integral time-domain passivity condition into a solvable algebraic condition in frequency domain Passivity Condition positive-definite if P-action Passivity: Parseval’s Identity :master-slave position error Spring Energy P-action Passivity energy generation bounded by the spring energy IFAC 2005 Prague

  11. Energetic Structure Closed-loop teleoperator Communication+Control Open-Loop Master + Slave Robots Human + Slave Environ. Vd(t) Lyapunov -Krasovskii function Control port Environ. port sd(t) + T1v1+T2v2 F1v1+F2v2 + Vp(t) Spring energy sp(t) Energy storage: kinetic energy Dissipated via Kd under passivity condition P(t) (dissipated) - Controller passivity: comm.+control blocks are passified altogether - Key relation:total energy in the three energy storages can not increase more than energy inputs from the passive human operator (d12) and the slave environment (d22) Energy inputs from huamn/environment IFAC 2005 Prague

  12. Position Coordination and Force Reflection 1. If the human and slave environment are passive. Then, master-slave velocity (i.e. coupled stability) and position coordination error are bounded. 2. Master-slave position coordination:Suppose that M1(q1), M2(q2) and their first & second partial-derivatives w.r.t. q1,q2 are bounded for all q1,q2. Then, if F1(t)=F2(t)=0 (i.e. no human/environmental forcing), q1(t) →q2(t). : Barbalat’s lemma w/ boundedness assumption 1) 2) 3) Closed-loop dynamics 3. Bilateral force reflection:If master and slave velocity and acceleration are zero (i.e. static manipulation), F1(t)→ - F2(t). IFAC 2005 Prague

  13. Simulation Results slave contacts with a wall - 2-DOF serial-link nonlinear planar master and slave robots - a wall installed in the slave environment with the reaction force only along the x-axis - human as a PD-type position controller - both the forward and backward delays = 2 sec (i.e. round-trip delay = 4sec) - free-motion and contact behavior are stable even with the large time-delay - contact force is faithfully reflected to the human when the slave contacts with the wall - master-slave position coordination achieved whenever the contact is removed IFAC 2005 Prague

  14. Conclusion 1. We propose a novel PD-based control framework for passive bilateral teleoperation with constant time-delays without relying on scattering-based teleoperation 2. Utilizing controller passivity concept, Lyapunov-Krasovskii technique, and the Parseval’s identity, the proposed framework passifies the combination of the control and communication blocks together 3. The proposed framework enforces master-slave position coordination and bilateral force reflection in the static manipulation 4. Simulation results validate the proposed framework 5. Explicit position feedback would be useful for such an application as Internet teleoperation with packet-loss 6. The proposed framework has also been extended to the cases where communication delays are asymmetric and unknown with less required-damping IFAC 2005 Prague

  15. Suppose that the human and slave environment are passive and L-stable impedance maps (i.e. F1,F2 are also bounded). Suppose further that the first partial derivatives of M1(q1), M2(q2) w.r.t. q1,q2 are bounded for all q1,q2. Then, if the v1(0),v2(0) and qE(0) are bounded, v1(t),v2(t)L2. Therefore, qE(t)=v1(t)-v2(t)  L2 and the Parseval’s identity holds for all t  0. . Parseval’s Identity and L2-Stability quadratic in v1,v2 IFAC 2005 Prague

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