Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague 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 /CCR , ONR N , and College of Engineering at UIUC

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague Contributions 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 Teleoperator with Constant Time-Delays Slave Robot Slave Comm.& Control Slave Environ. T 2 (t) v 2 (t) F 2 (t) v 2 (t) Master Robot Master Comm.& Control Human Operator T 1 (t) v 1 (t) F 1 (t) v 1 (t)  

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague Outline 1. Energetic Passivity and Controller Passivity 2. Control Design and Analysis 3. Simulation 4. Conclusion

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague Passivity for Interaction Stability and Safety - 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 Energetic Passivity of the Closed-loop Teleoperator - maximum extractable energy from the closed-loop teleoperator is bounded - the closed-loop teleoperator does not generate energy by itself Mechanical power from closed-loop teleoperator finite constant (depending on initial condition) Closed-Loop Teleoperator as a Two-Port System Slave Robot Slave Comm.& Control Slave Environ. T 2 (t) v 2 (t) F 2 (t) v 2 (t) Master Robot Master Comm.& Control Human Operator T 1 (t) v 1 (t) F 1 (t) v 1 (t)   Closed-loop teleoperator

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

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague Outline 1. Energetic Passivity and Controller Passivity 2. Control Design and Analysis 3. Simulation 4. Conclusion

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague Control Design Closed-loop teleoperator is energetically passive if Slave Robot Slave Comm.& Control Slave Environ. T 2 (t) v 2 (t) F 2 (t) v 2 (t) Master Robot Master Comm.& Control Human Operator T 1 (t) v 1 (t) F 1 (t) v 1 (t)   local sensing Plant Dynamics Communication Structure PD-Based Control D-control action additional viscous damping (e.g. device damping) P-control action w/ passifying dissipation

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague Controller Passivity Controller Passivity Controller Power Decomposition (i.e. controller generates only bounded amount of energy) D-action power P-action power additional viscous damping (quadratic in velocity) - How to ensure that the energy generations by s d (t) and s p (t) be bounded?

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague D-action Passivity: Lyapunov-Krasovskii Functional D-action Passivity energy generation bounded by Lyapunov-Krasovskii as a storage function Lyapunov-Krasovskii (LK) functional sum of master and slave velocities

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague P-action Passivity: Parseval’s Identity P-action Passivity energy generation bounded by the spring energy Spring Energy :master-slave position error Parseval’s identity convert integral time-domain passivity condition into a solvable algebraic condition in frequency domain Passivity Condition positive-definite if dissipating energy

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague Energetic Structure Open-Loop Master + Slave Robots Human + Slave Environ. Closed-loop teleoperator + + s d (t) P(t) (dissipated) T 1 v 1 +T 2 v 2 F 1 v 1 +F 2 v 2 Communication+Control V d (t) Energy storage: kinetic energy s p (t) Dissipated via K d under passivity condition V p (t) Lyapunov -Krasovskii function Spring energy - 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 (d 1 2 ) and the slave environment (d 2 2 ) Control port Environ. port Energy inputs from huamn/environment

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague 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. 3. Bilateral force reflection: If master and slave velocity and acceleration are zero (i.e. static manipulation), F 1 (t)→ - F 2 (t). 1) 2. Master-slave position coordination: Suppose that M 1 (q 1 ), M 2 (q 2 ) and their first & second partial-derivatives w.r.t. q 1,q 2 are bounded for all q 1,q 2. Then, if F 1 (t)=F 2 (t)=0 (i.e. no human/environmental forcing), q 1 (t) →q 2 (t). 2) 3) Closed-loop dynamics : Barbalat’s lemma w/ boundedness assumption

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague Simulation Results - 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 slave contacts with a wall

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague 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

Dongjun Lee and Mark W. Spong, CSL, UIUCIFAC 2005 Prague Parseval’s Identity and L 2 -Stability quadratic in v 1,v 2 Suppose that the human and slave environment are passive and L  -stable impedance maps (i.e. F 1,F 2 are also bounded). Suppose further that the first partial derivatives of M 1 (q 1 ), M 2 (q 2 ) w.r.t. q 1,q 2 are bounded for all q 1,q 2. Then, if the v 1 (0),v 2 (0) and q E (0) are bounded, v 1 (t),v 2 (t)  L 2. Therefore, q E (t)=v 1 (t)-v 2 (t)  L 2 and the Parseval’s identity holds for all t  0..