Optimizing Compliant, Model-Based Robotic Assistance to Promote Neurorehabilitation Eric Wolbrecht, PhD Assistant Professor, Department of Mechanical Engineering University of Idaho This majority of this work was completed at the Department of Mechanical and Aerospace Engineering University of California, Irvine Supported by NIH N01-HD-3-3352 and NCRR M01RR00827 Motivation for Robotic Movement Training • A stroke is suffered by over 700,000 people in the U.S. each year, making it a leading cause of severe, long term disability. • 80 percent of stroke victims experience upper extremity movement impairment. • The estimated direct and indirect cost of stroke for 2007 is $62.7 billion. • Stoke rate to increase as population ages. Can Robotic Devices Help? • Evidence suggests that intensive, repetitive sensory motor training can improve functional recovery. • Traditional hands-on therapy is expensive and labor intensive, and therefore patients receive limited amounts of it. • One possible solution to this problem is to develop robotic devices to automate functional motor training. Robotic movement training with Pneu-WREX • It was previously believed that movement recovery was possible only for acute patients (< 6 months post-stroke). Research has shown that recovery is possible for people with chronic stoke as well (>6 months post-stroke). 1st Generation Devices for Movement Training after Stroke MIT-Manus Impedance control Impedance channel toward target ARM Guide (UCI) Proportional derivative control, Active Constrained MIME (Stanford) Proportional derivative control, Active constrained and bilateral modes 2nd Generation Devices for Movement Training after Stroke ARMin (Zurich) PD control & gravity compensation Vertical Module for MIT-Manus Impedance control & gravity compensation RUPERT (Arizona State) Open loop control Pneu-WREX: Development History • An offspring of WREX (Wilmington Robotic Exoskeleton), a passive gravity balancing orthosis (Rahman et al, 2000.) WREX • WREX was modified to create T-WREX (Training-WREX), a sensorized, passive gravity balancing orthosis (Sanchez et al, 2004.) • Pneu-WREX (Pneumatic-WREX) was created by adding pneumatic actuators to TWREX (Sanchez, Wolbrecht et al, 2005.) T-WREX • Current research focuses on promoting recovery through advanced control (Wolbrecht et al, 2006, 2007.) Pneu-WREX Why Choose Pneumatics? • Advantage of Pneumatics – Large power to weight ratio – Clean, and inexpensive. – Force controllable. – Backdrivable and compliant. – Inherent compliance increases safety. • Disadvantages of Pneumatics – Non-linear friction – Require advanced control – Not all facilities have compressed air and in-room compressors can be expensive and noisy. Design Features • 4 degrees-of-freedom, lightweight, compliant. • Strong (can apply > 50 N of force at hand). • Grip handle with grip sensor. • Two servovalves per cylinder, keeping air consumption and friction low. Servovalves (2 per cylinder) • Uses a spring to counterbalances the weight of the orthosis, expanding the vertical force range. Spring Counterbalance Mechanism Safety Features • Spring counterbalance provides a safe transition during an e-stop. • Normally exhausting main valve controls system air supply and is vented during emergency-stop or a detected failure. • Pneumatics are inherently compliant and maximum force is limited. • Workspace of device is less than the workspace of the arm. • Numerous software checks, including a check of redundant position sensors. Pneu-WREX Sensing 4 cylinders with LTR potentiometers, Bimba PFC 4 angular potentiometers, Midori CP-2fb 2, 2-axes MEMS accelerometers, Analog Devices ADXL320EB 8 pressure sensors, Honeywell ASCX100AM Data Acquisition and Control • Controller developed in The Mathworks Simulink® and executed using the xPC Target real-time operating system. • Data input and output using four Measurement Computing PCI cards – (3) PCIM-DAS1602/16, 8 Differential A/D, 2 D/A, 16 bit – (1) PCI-DDA08/16, 8 channel D/A, 16 bit A/D, D/A PCI Card, Measurement Computing PCIM-DAS1602/16 • 1 kHz sampling rate • Target Execution Time (TET) ≈ 650 μs D/A PCI Card, Measurement Computing PCIM-DDA08/16 State Estimation • State Estimation using MEMS accelerometers in a Kalman Filter • Estimated velocity and position signals have reduced noise and phase lag compared to a conventional low-pass filter. State Estimation: Advantages • Signals have less noise and less phase lag • Improved stability • Quieter operation • Reduced air consumption Servovalve Characterization for Improved Force Control • Experimentally determined flow map equation to linearize airflow through the servovalves. • Separate maps for both inflow and outflow. u f md , pc u control signal (volts) md desired flow rate (SLPM) pc chamber pressure (kPA) Hypothesis: An “Optimal” Movement Training Controller Should: 1. Help Complete Movements. Stimulate afferent signals from the arm by assisting patients in making spatial movements with small errors, overcoming gravity, tone, and weakness. 2. Be Mechanically Compliant. Allow patients to influence movements, maintaining the effort and error connection essential for motor learning. 3. Assist Only As Needed. Stimulate efferent signals from the brain by encouraging subjects to contribute as much as possible to the movements. Selecting a Controller for “Optimal” Movement Training Controller Type Stiff Proportional Derivative Impedance Control Impedance Control w/ Gravity Offset Adaptive Adaptive, Assist-As-Needed Help Complete Movements Mechanically Compliant Assist As Needed Adaptive, Assist-As-Needed Controller • “Adaptive, Assist-As-Needed Controller” builds on the passivity based adaptive controller developed by Slotine and Li. Γ,Λ, K D , K P = symmetric, positive definite matrices n n Y matrix of known functions m n a aˆ a Fr forces applied by the actuators n 1 a, aˆ parameter & parameter estimates m 1 Fh forces applied by the human subject n 1 x, x d actual & desired arm coordinates n 1 M generalized inertia matrix of the robot/arm n n x x xd C Coriollis matrix of the robot/arm n n "forgetting rate" time constant N external forces (gravity,friction, etc.) n 1 f 1 robot "forgetting rate" r Neuromuscular Weakness Model • For a standard adaptive controller: ˆ N ˆ Cw ˆ Y x, x, w, w aˆ Mw • For movement training following stoke, however, N̂ must include a general representation of neuromuscular weakness, which is implemented using a grid of radial basis functions in task space: g g1 g2 g n exp x μ n T g n 2 2 2 Y1203 Radial basis functions 1 D.O.F. example gT 0 gT T g 0 • There are 120 radial basis functions, spaced 10 cm apart in a 3-D grid -8 points left to right (-x to +x) -5 points in and out (-y to +y) -3 points down and up (-z to +z) 3-D grid Pneu-WREX • Yes, but, does it work? Testing the Adaptive Controller • Testing Goal: Evaluate controller with and without forgetting to determine how well the controller “assists-as-needed”. • We have tested the adaptive controller with 8 subjects with movement impairment due to stroke. • 1st Test: The subjects tracked a cursor from a central home position to seven targets located in the frontal plane. The cursor (displayed on the computer screen) moved between targets and the home position with a peek velocity of 0.12 m/s. • 2nd Test: Subjects tracked a curser between two targets spaced 30 cm apart in the frontal plane (peek velocity 0.12 m/s). Controller Helps Complete Movements Controller Learns Assistance Force for Different Arm Weights With “Forgetting”, Controller Reduces Force when Errors are Small Without “Forgetting”, Subject Allows Robot to “Take-Over” With “Forgetting”, Subject Contribution Increases With “Forgetting”, Assistance is Proportional to Impairment Therapy Games Shopping Egg Cracking Window Cleaning Basketball Driving Therapy with Robotic Assistance • Point to point reaching “Shopping” game, with robotic orthosis assistance. Playing without Robotic Assistance • Point to point reaching “Shopping” game, without robotic orthosis assistance. Adaptive, Assist-As-Needed Controller • Forces applied during point to point reaching “Shopping” game. Robotic Assessments: Game Time Robotic Assessments: Reaching Speeds Summary • Pneu-WREX is a lightweight, compliant, 4 degree-of-freedom upper extremity robotic orthosis. • The adaptive, assist-as-needed controller encourages patient effort while helping the patient to complete movements with small errors. • Subjects feel in control of movements because of compliance, adaptation, and forgetting rate. • We have shown human motor control effort minimization for a real movement trajectory. • Initial pilot therapy study results are promising. Acknowledgements • SUPPORT NIH N01-HD-3-3352 and NCRR M01RR0082 • LABORATORIES Robotics & Automation Laboratory, UCI MAE Biomechatronics Laboratory, UCI MAE Human Performance Laboratory, UCI GCRC • COLLABORATORS (UCI) James Bobrow, Ph.D. Dave J. Reinkensmeyer, Ph.D. Steven Cramer, M.D., Ph.D. Robert Sanchez, Ph.D. John Leavitt, Ph.D. Robert Smith, Eng. Tech. Vicki Chan, PT Vu Le, M.S. Julius Klein, M.S. Koyiro Minakata, B.S. Appendix Appendix: System Dynamics • The system dynamics are Mx Cx N Fr Fh x position of the hand n 1 M generalized inertia matrix n n C Coriolis matrix n n N forces acting on the orthosis (gravity,friction, etc.) n 1 Fr forces applied by the pneumatic actuators, mapped by the Jacobian to the hand position. n 1 Fh forces applied by the human subject at the location of the hand, representing subject effort. n 1 • The sliding surface and reference trajectories are defined s x Λx x x d x x d sliding surface w xd Λx xd Λ x Λx d reference trajectory x x x d position error x position of the hand n 1 x d desired position of the hand n 1 Appendix: System Dynamics • Using x s w the system dynamics are Ms Mw Cs Cw N Fr Fh Ms Cs Mw Cw N Fh Fr • Now define Ya Mw Cw N Fh a actual system parameters m n Y matrix of know functions of x, x, w, & w m n • To get Ms Cs Ya Fr • Now substitute for the estimate error and force error a aˆ a system parameter estimate error Fr Fr Fr ,d force error • To get Ms Cs Yaˆ Fr ,d Ya Fr Appendix: Force Dynamics • The force dynamics for the base side chambers are fb kVb1 pa Ab mb lb Vb fb fb base side chamber forces n 1 mb base side mass flow rates n 1 l b base side mass flow due to leakage rates n 1 pa atmospheric pressure k 1.4 ratio of specific heats of air ab,1 ab,2 Ab = 0 vb,1 vb,2 Vb = 0 0 base side piston areas ab,n 0 base side chamber volumes vb, n • Now substitute for the leakage estimate error lb ˆlb lb base side leakage error n 1 • To get ˆl = base side leakage estimate b fb kVb1 pa Ab mb ˆlb Vbfb kVb1 pa Ab lb n 1 Appendix: Lyapunov Function Candidate • Lyapunov function candidate V t = 12 sT Ms 12 xT K P + ΛK D x 12 aT Γa 12 fbT Ψfb 12 frT Ψfr 12 lbT Φlb 12 lrT Φlr parameter base side rod side base side rod side estimate force force leakage leakage error error error estimate estimate error error trajectory error x position of the hand n 1 s x Λx sliding surface x x x d position error a aˆ a system parameter estimate error x d desired position of the hand n 1 aˆ estimated system parameters m 1 a actual system parameters m 1 fb fb fb, d base side force error f r f r f r ,d rod side force error ˆl , ˆl estimated base, rod side valve leakages n 1 b r lb ˆlb l b base side leakage estimate error lr ˆl r l r rod side leakage estimate error fb , f r base, rod side cylinder forces n 1 l b , l r actual base, rod side valve leakages n 1 fb, d , fr ,d desired base, rod side cylinder forces n 1 K P , K D , Λ, Γ, Ψ, Φ = symmetric, constant, positive definite matrices n n Force Dynamics and Chamber Force Selection • Cylinder Force Output • Force Dynamics a1,1 a1,2 A1 0 f f1 f 2 f atm f1 V11k RTA1 m1 l1 V1f1 0 v1,1 v1,2 V 1 c1,n 0 0 v1,n • Chamber force selection with smoothing function d 1 f d f 0 f atm f 2 e d f1 1 fd e f 0 f atm 2 fd 0 fd 0 1 f d f0 2 e d f2 f d 1 e f d f 0 2 fd 0 fd 0 Force Controller • Passivity based force controller 1 1 1 m1 ˆl1 A1 V1f1 V1 f1d Ψ 1J c J e1s Ωf1 RT k 1 1 1 m 2 ˆl 2 A 2 V2f 2 V2 f 2d Ψ 1J c J e1s Ωf 2 RT k • Adaptive leakage estimation ˆl kRTΦ 1A V 1Ψf 1 1 1 1 ˆl kRTΦ 1A V 1Ψf 2 2 2 2 Single Cylinder Force Tracking to 40 Hz Position Tracking to 2 Hz Position Testing Results Controller Modification: Assist-As-Needed • When errors are small, the controller should decay force according to: Yaˆ f r Yaˆ where f r is the forgetting rate • The minimum solution for â is found by solving a constrained minimization problem: min : f 12 aˆ T aˆ : g Yaˆ f r Yaˆ 0 • The solution is: aˆ f r Y T YY T 1 Yaˆ