Active Tremor Compensation in Handheld Instrument for Microsurgery Wei Tech Ang School of Mechanical & Aerospace Engineering Nanyang Technological University Singapore wtang@ntu.edu.sg 1
Contributors � Cameron N. Riviere � Wei Tech Ang Associate Research Professor Assistant Professor � David Y. Choi � Mounir Krichane Ph.D. Student Exchange Student (EPFL) � Si Yi Khoo Research Engineer Medical Robotics Technology Center Robotics Research Centre & The Robotics Institute Sch. of Mechanical & Aerospace Eng. Carnegie Mellon University Nanyang Technological University Pittsburgh, PA, USA Singapore 2
Microsurgery with Active Handheld Instrument Visual Feedback Engineering Motion Solutions Sensing Micron Visuomotor Control System Technical Task Definition Details Problem Vitreoretinal Analysis Microsurgery Tip manipulation for active error compensation Estimation of Noisy, Tremulous erroneous motion Motion 3
Vitreoretinal Microsurgery � Removal of membranes ≤ 20 µ m thick from front or back of retina 4
Vitreoretinal Microsurgery � Injection of anticoagulant using intraocular cannulation to treat retinal vein (~ ∅ 100 µm) occlusion 5
Vitreoretinal Microsurgery � Tremor: under microscope 6
Involuntary Hand Movement and Microsurgery 7
Involuntary Hand Movement and Microsurgery � Complicate microsurgical procedures and makes certain delicate interventions impossible � Impact on microsurgeons � 2 of 10 surgeons become microsurgeons � Factors affecting tremor � Fatigue – strenuous exercise etc. � Caffeine/alcohol consumption � Lack of practice – long vacation etc. � Age – experience vs hand stability � Microsurgeons’ consensus: � 10 µ m positioning accuracy 8
Involuntary Hand Movement of Healthy Human � Physiological Tremor � Roughly sinusoidal motion, 8-12 Hz � ≤ 50 µm rms in each principal axis � Non-tremulous Errors � Myoclonic jerk, drift etc. � Aperiodic, may be in the same frequency band as voluntary motion � Larger amplitude: > 100 µm 9
Microsurgery with Active Handheld Instrument Visual Feedback Motion Sensing Micron Visuomotor Control System Vitreoretinal Microsurgery Manipulation of tip for active error compensation Estimation of Noisy, Tremulous erroneous motion Motion 10
Robotic Error Compensation Approaches � Telerobotic systems: Zeus (Computer Motion) & Da Vinci (Intuitive Surgical) � Master-Slave manipulators � Erroneous motion filtered by motion scaling 11
Robotic Error Compensation Approaches � ‘Steady-hand’ robot: Russell Taylor et al., Johns Hopkins University � Surgeon and compliant robot hold tool simultaneously � Force feedback � ‘Third hand’ operation � Erroneous motion damped by rigidity of robot 12
Robotic Error Compensation Approaches � Active Handheld Instrument: Paolo Dario, Scuola Superiore Sant’Anna, Pisa, Italy � Same concept 13
Comparison of Robotic Solutions Obtrusive > US$1M � Telerobotics � ‘Steady Hand’ robot > US$150K � Active Handheld < US$15K Instrument Unobtrusive � Cheap � Unobtrusive � Safer � Limited workspace � No motion scaling � No ‘third hand’ 14
Micron Current Prototype � Length: 180 mm long Disposable � Diameter: Ø20(16) mm surgical needle � Weight <100 g Manipulator System � 9 DOF inertial and magnetic sensing system at the back end Ø16 mm Sensing � 3 DOF piezoelectric driven System parallel manipulator at front Ø20 mm end with disposable surgical needle 180 mm (w/ o needle) 15
System Overview Magnetometer- Motion of B A (6 × 1) , aided all- instrument B M (3 × 1) accelerometer IMU Sensing W D B (3 × 1) , Forward Sensor ADC W Θ B (3 × 1) kinematics fusion Erroneous tip W D tip (3 × 1) displacement Filtering Estimation of W D tremor (3 × 1) Host PC erroneous motion Manipulation Inverse Inverse feedforward DAC kinematics controller Joint variables λ 1 , λ 2 , λ 3 V 1 , V 2 , V 3 Piezoelectric Power Motion of -driven Amplifier instrument tip parallel W D voluntary (3 × 1) manipulator 16
Microsurgery with Active Handheld Instrument Visual Feedback Motion Sensing Visuomotor Micron Control System • Resolution Vitreoretinal • Accuracy Microsurgery Manipulation of tip for active error compensation Estimation of Noisy, Tremulous erroneous motion Motion 17
Sensing System Design Z B Sensing direction � Magnetometer-aided all- accelerometer inertial measurement unit (IMU): Manipulator System � 3 dual-axis miniature Dual-axis MEMS accelerometers accelerometer Front Sensor Analog Devices ADXL-203: Suite 5mm x 5mm x 2mm, < 1g Tri-axial � Three-axis magnetometer Back Sensor Magnetometer Suite Honeywell HMC-2003: 26mm x 19mm x 12mm, <10g X B � Housed in 2 locations Y B Dual-axis accelerometers 18
Sensing Modality � Internally referenced sensors because: � Less obtrusive Externally referenced sensors require a line of sight � Resolution: Inertial sensor < 1 µm Externally referenced (e.g. Optotrak): ~ 0.1 mm � All accelerometers because: � Low cost, miniature gyros too noisy → Poor sensing resolution � Navigation/tactical grade gyros - too expensive and bulky 19
Differential Sensing Kinematics � Body acceleration sensed by accelerometer at location { i }: {3} Tangential Acceleration � = + + Ω × Ω × + Ω × A A g P P P 13 i CG Bi Bi � � � � � � � � � P 23 Rotation − induced Accelerati ons Measurement P 3 Centripetal Acceleration {1} Z 2 � Differential Sensing P 12 P 1 P 2 ( ) � = − = Ω × Ω × + Ω × = A A A [ ][ ] [ ] P , i , j 1, 2, 3 {2} {B} ij j i ij Y 2 • • ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ a Z w 13 x ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = • = = • A , A a , A ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 13 23 23 y 12 Y w ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ • • a ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 12 z X w {W} 20
Differential Sensing Kinematics � 3 unknowns: {3} Ω = [ ω x ω y ω z ] T 3 differential acceleration P 13 measurements: P 23 P 3 A D = [ a 13 x a 23 y a 12 z ] T {1} � Solve system of nonlinear Z 2 P 12 P 1 equations by Gauss-Newton or P 2 {2} {B} Levenberg-Marquart method Y 2 � Numerical instability Z w � Assume Ω 2 ≈ 0, solve for � Ω Y w analytically X w {W} 21
Sensing Kinematics Updating quaternions: � Ω × Ω ⎡ ⎤ [ ] ~ ~ 1 × × = Ω Ω = 3 3 3 1 � q ( t ) ( t ) q ( t ), ⎢ ⎥ − Ω T 0 2 ⎣ ⎦ × 1 3 Directional Cosines matrix � ⎡ ⎤ + − − − + 2 2 2 2 q q q q 2 ( q q q q ) 2 ( q q q q ) 0 1 2 3 1 2 0 3 1 3 0 2 ⎢ ⎥ = + − + − − W 2 2 2 2 C B 2 ( q q q q ) q q q q 2 ( q q q q ) ⎢ ⎥ 1 2 0 3 0 1 2 3 2 3 0 1 ⎢ ⎥ − + − − + 2 2 2 2 2 ( q q q q ) 2 ( q q q q ) q q q q ⎣ ⎦ 1 3 0 2 2 3 0 1 0 1 2 3 Gravity Removal: W A E = W C B B A – W g � Tip Displacement: � t ∫ ∫ W = W − + W τ τ τ + W B Ω × B P ( t ) P ( t T ) A ( ) d d C ( t )[ ] P tip tip E B tip − t T 22
Sensing Resolution (Error Variance) Analysis Front sensor � Sensing resolution dependent σ Ax suite 2 on sensor noise floor σ Ay 2 � Angular Sensing σ ω x 2 or σ ω y 2 � Sensing equation: � A ij = f ( Ω )= ([ Ω× ] [ Ω× ] + [ × ]) P ij Ω P ij � Covariance: C( A ij ) = C( Ω ) P ij P ij ↑ , C( Ω ) ↓ � σ Ay 2 σ Ax 2 Back sensor suite 23
Proposed All-Accelerometer vs Conventional Inertial Measurement Unit � All-accelerometer IMU � Maximized P ij , with physical constraint of a slender handheld instrument � Conventional IMU (3A-3G) � Tokin CG-L43D rate gyros x 3 Noise reduction / 3G-3A 6A resolution Error std. dev. Error std. dev. improvement (deg/s) (deg/s) ω x & ω y 1.08 × 10 -2 1.41 99.3% / 130x ω z 4.42 × 10 -2 1.41 96.9% / 32x 24
Angular Sensing Resolution Comparison All-accelerometer IMU 8 � Small angular velocity 6 ω x , ω y (deg/s) & sensor noise floor 4 2 0 -2 0 50 100 150 200 250 300 350 400 450 500 Tokin Gyroscope 8 8 6 6 ω G (deg/s) ω z (deg/s) 4 4 2 2 0 0 -2 -2 0 50 100 150 200 250 300 350 400 450 500 0 50 100 150 200 250 300 350 400 450 500 Time (ms) Time (ms) 25
Sensing Resolution (Error Variance) Analysis � Translational Sensing � 2 accelerometers in each sensing direction: σ 1 1 1 = + → σ = Ai A σ σ σ 2 2 2 2 A Ai Aj � Sensing resolution improves by a factor of 2 ½ � Better orientation estimation → more complete removal of gravity → better translation estimation 26
Microsurgery with Active Handheld Instrument Visual Feedback Motion Sensing Visuomotor Micron Control System • Resolution Vitreoretinal • Accuracy Microsurgery Manipulation of tip for active error compensation Estimation of Noisy, Tremulous erroneous motion Motion 27
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