Department of Applied Mechanics – Budapest University of Technology and Economics Dynamics of rehabilitation robots – shake hands or hold hands? Dynamics of rehabilitation robots – shake hands or hold hands? G. Stépán, L. Kovács Department of Applied Mechanics Budapest University of Technology and Economics

Department of Applied Mechanics – Budapest University of Technology and Economics Contents -Introduction: force control -Motivation -Turbine blade polishing -Human force control -Rehabilitation robotics -1 DoF model of force control -Digital effect: sampling -Theoretical and experimental stability charts -Conclusion: bifurcations

Department of Applied Mechanics – Budapest University of Technology and Economics Position control 1 DoF models  x Blue trajectories: Q = 0 Pink trajectories: Q = – Px – Dx

Department of Applied Mechanics – Budapest University of Technology and Economics Force control Desired contact force: F d = ky d ; Sensed force: F s = ky Control force: Q = – P(F d – F s ) – DF s + F s or d

Department of Applied Mechanics – Budapest University of Technology and Economics Stabilization (balancing) Control force: Q = – Px – Dx Special case of force control: with k < 0

Department of Applied Mechanics – Budapest University of Technology and Economics Modelling digital control Special cases of force control: - position control with zero stiffness (k = 0) - stabilization with negative stiffness (k < 0) Digital effects: - quantization in time: sampling – linear - quantization in space: round-off errors at ADA converters – non-linear

Department of Applied Mechanics – Budapest University of Technology and Economics Alice’s Adventures in Wonderland Lewis Carroll (1899)

Department of Applied Mechanics – Budapest University of Technology and Economics Contents -Introduction: force control -Motivation -Turbine blade polishing -Human force control -Rehabilitation robotics -1 DoF model of force control -Digital effect: sampling -Theoretical and experimental stability charts -Conclusion: bifurcations

Department of Applied Mechanics – Budapest University of Technology and Economics Motivation -Polishing turbine blade (Newcastle/Parsons robot) -Rehabilitation robotics (human/machine contact) -Coupling force control (CFC) (between truck and trailer)* -Electronic brake force control (added to ABS systems)* *  Knorr-Bremse

Department of Applied Mechanics – Budapest University of Technology and Economics Motivation -Polishing turbine blade (Newcastle/Parsons robot) -Rehabilitation robotics (human/machine contact) -Coupling force control (CFC) (between truck and trailer)* -Electronic brake force control (added to ABS systems)* *  Knorr-Bremse

Department of Applied Mechanics – Budapest University of Technology and Economics Motivation -Polishing turbine blade (Newcastle/Parsons robot) -Rehabilitation robotics (human/machine contact) -Coupling force control (CFC) (between truck and trailer)* -Electronic brake force control (added to ABS systems)* *  Knorr-Bremse

Department of Applied Mechanics – Budapest University of Technology and Economics Motivation -Polishing turbine blade (Newcastle/Parsons robot) -Rehabilitation robotics (human/machine contact) -Coupling force control (CFC) (between truck and trailer)* -Electronic brake force control (added to ABS systems)* *  Knorr-Bremse

Department of Applied Mechanics – Budapest University of Technology and Economics Contents -Introduction: force control -Motivation -Turbine blade polishing -Human force control -Rehabilitation robotics -1 DoF model of force control -Digital effect: sampling -Theoretical and experimental stability charts -Conclusion: bifurcations

Department of Applied Mechanics – Budapest University of Technology and Economics Turbine blade polishing

Department of Applied Mechanics – Budapest University of Technology and Economics Mechanical model of polishing m r = 2500 [kg] b r = 32 [Ns/mm] C = 150 [N] m s = 0.95 [kg] b s = 2 [Ns/m(!)] k s = 45 [Ns/mm] m e = 4.43 [kg] b e = 3 [Ns/m(!)] k s = 13 [Ns/mm] F d = 50 [N]

Department of Applied Mechanics – Budapest University of Technology and Economics Experimental stability chart

Department of Applied Mechanics – Budapest University of Technology and Economics Self-excited oscillation – Hopf bifurcation

Department of Applied Mechanics – Budapest University of Technology and Economics Time-history and spectrum

Department of Applied Mechanics – Budapest University of Technology and Economics Contents -Introduction: force control -Motivation -Turbine blade polishing -Human force control -Rehabilitation robotics -1 DoF model of force control -Digital effect: sampling -Theoretical and experimental stability charts -Conclusion: bifurcations

Department of Applied Mechanics – Budapest University of Technology and Economics Human force control “Good memory causes trouble” Meeting others on narrow corridors  oscillations caused by the delay of our reflexes Why do we “shake” hands?

Department of Applied Mechanics – Budapest University of Technology and Economics Hemingway, E., The Old Man and the Sea (1952) Santiago plays arm-wrestling in a pub of Casablanca

Department of Applied Mechanics – Budapest University of Technology and Economics Human-robotic force control Dexter cartoon

Department of Applied Mechanics – Budapest University of Technology and Economics Contents -Introduction: force control -Motivation -Turbine blade polishing -Human force control -Rehabilitation robotics -1 DoF model of force control -Digital effect: sampling -Theoretical and experimental stability charts -Conclusion: bifurcations

Department of Applied Mechanics – Budapest University of Technology and Economics Rehabilitation robotics IRB 1400 H IRB 140 Couch Touch screen Control panel Operation mode selector Safety switch Etc. Instrumented orthosis Frame Stack lights Start pedal

Department of Applied Mechanics – Budapest University of Technology and Economics The safety relaxer

Department of Applied Mechanics – Budapest University of Technology and Economics The instrumented orthosis Robot Safety relaxer mechanism (SRM) 6 DOF force/torque transducer #1 Quick changer #1 6 DOF force/torque transducer #2 Quick changer #2 Orthosis shell Handle (the so-called safeball) Teaching-in device

Department of Applied Mechanics – Budapest University of Technology and Economics Mechanical model of relaxer

Department of Applied Mechanics – Budapest University of Technology and Economics Force control during teaching-in Sampling time at outer loop with   60 [ms] Sampling time at force sensor with  t  4 [ms] F d  0 F e,n  x d,n x n-1 x d,n  DSP (or PC) x n-L Fm,nFm,n force control robot - controller robot arm + teaching-in device force / torque acquisition deadtime 400ms !

Department of Applied Mechanics – Budapest University of Technology and Economics Delay and vibrations

Department of Applied Mechanics – Budapest University of Technology and Economics Delay and vibrations

Department of Applied Mechanics – Budapest University of Technology and Economics Delay and vibrations

Department of Applied Mechanics – Budapest University of Technology and Economics Contents -Introduction: force control -Motivation -Turbine blade polishing -Human force control -Rehabilitation robotics -1 DoF model of force control -Digital effect: sampling -Theoretical and experimental stability charts -Conclusion: bifurcations

Department of Applied Mechanics – Budapest University of Technology and Economics 1 DoF model of force control Equation of motion: Equilibrium: Force error: (Craig ’86) Stability for, 

Department of Applied Mechanics – Budapest University of Technology and Economics Contents -Introduction: force control -Motivation -Turbine blade polishing -Human force control -Rehabilitation robotics -1 DoF model of force control -Digital effect: sampling -Theoretical and experimental stability charts -Conclusion: bifurcations

Department of Applied Mechanics – Budapest University of Technology and Economics Modelling sampling Time delay  and zero-order-holder (ZOH) Dimensionless time

Department of Applied Mechanics – Budapest University of Technology and Economics Modelling sampling Sampling time is , the j th sampling instant is t j = j  Natural frequency: Sampling frequency: dim.less time: T = t/  Dimensionless equations of motion: x(j), x’(j)  B 1,B 2

Department of Applied Mechanics – Budapest University of Technology and Economics Contents -Introduction: force control -Motivation -Turbine blade polishing -Human force control -Rehabilitation robotics -1 DoF model of force control -Digital effect: sampling -Theoretical and experimental stability charts -Conclusion: bifurcations

Department of Applied Mechanics – Budapest University of Technology and Economics Stability of digital force control   stability Parameters: and

Department of Applied Mechanics – Budapest University of Technology and Economics Checking |  1,2,3 |<1 algebraically Routh-Hurwitz

Department of Applied Mechanics – Budapest University of Technology and Economics Stability chart of force control Vibration frequency: 0 < f < f s /2 Maximum gain: Minimum force error:

Department of Applied Mechanics – Budapest University of Technology and Economics Effect of viscous damping Damping ratio  : 0.04 and 0.5

Department of Applied Mechanics – Budapest University of Technology and Economics Experimental verification

Department of Applied Mechanics – Budapest University of Technology and Economics Experimental verification Damping ratio  = 0.04 P  [ms]

Department of Applied Mechanics – Budapest University of Technology and Economics Differential gain D in force control Sampling at the force sensor with  t = q  :

Department of Applied Mechanics – Budapest University of Technology and Economics Stability chart and bifurcations Dimensionless differential gain D  n = 0.1

Department of Applied Mechanics – Budapest University of Technology and Economics Stability chart and bifurcations Dimensionless differential gain D  n = 1.0

Department of Applied Mechanics – Budapest University of Technology and Economics Conclusions -All the 3 kinds of co-dimension 1 bifurcations arise in digital force control (Neimark-Sacker, flip, fold) -Application of differential gain leads to loss of stable parameter regions -Force derivative signal can be filtered with the help of sampling, but stability properties do not improve -Do not use differential gain in force control

Department of Applied Mechanics – Budapest University of Technology and Economics