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Biomimetic Sensing for Robotic Manipulation Neil Petroff, Ph. D. Candidate University of Notre Dame Lerner Research Institute Cleveland, OH December 8, 2005

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Outline Me on Me Grasping –biology as motivation for current work Robotic Manipulation –Nonholonomic motion planning –Motion planning for stratified systems Open-Chain Manipulators –Forward kinematics –Inverse kinematics Biomimetic Robot Sensors –Vision, touch Control Perspective on Deep Brain Stimulation The Rest of the Story

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Hand Orthosis Target Group: C5 - C7 SCI 3 Grasps –Fingertip, key, cylindrical Increase Autonomy Mercury Orthotics –Rehabilitation technology therapeutic quality of life

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Grasping Interaction Creation Task Execution Grasping Hand Orthosis Robotic Manipulation Fuzzy Logic Open-Chain Manipulators Biomimetic Robot Sensors Work to Date

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Grasping Can we improve robotic manipulation by imbuing robots with useful human characteristics? RobotsHumans Poor at fine motiongood at fine motion No feedback vision, proprioception structured adaptive precise robust rapid slow strong variable stamina need to rest Grasping Hand Orthosis Robotic Manipulation Fuzzy Logic Open-Chain Manipulators Biomimetic Robot Sensors Work to Date

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Biological Motivation Haptic Recognition –Force feedback Compliance is Useful for Manipulation Brain Model –Fuzzy logic Hierarchical Control Grasping Hand Orthosis Robotic Manipulation Fuzzy Logic Open-Chain Manipulators Biomimetic Robot Sensors Work to Date

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Biological Control Loop desired task motion planning algorithm inverse kinematics encoder counts PIDRobot current configuration encoder counts sensor readings trajectory adjustment fuzzy supervisor

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Testbed

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Robotic Motion Planning Steering Using Piecewise Constant Inputs –This is a geometric analysis –Provides a systematic approach for establishing controllability –Applicable to underactuated systems with nonholonomic constraints –Exact for nilpotent systems of the form Driftless Not all g i ’s may exist a system is nilpotent if all Lie brackets greater than a certain order are zero –Lie bracket motions allows the system to move in a new direction

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Lie Bracket Motions Flow along g 3 can be approximated by flowing along g 1 and g 2 Higher order brackets can be generated, e.g.

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Example Parallel parking a car

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Example Car equations g1g1 g2g2 Extended System l

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Car Simulation

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Why Didn’t it Work? The Car Model is not Nilpotent –g 5 points in the same direction as g 3 –Motion along lower order brackets induces motion along higher order brackets Solution –Iterate –Feedback nilpotentization Other Drawbacks –Small Time or Small Inputs obstacle avoidance –Open Loop highly susceptible to modeling errors no error correction

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Stratified Systems Extends motion planning algorithm to systems with discontinuities –Intermittent contact locomotion manipulation S 12 S1S1 S2S2 g 1,1 g 1,2 -g 1,1 -g 2,1 g 2,2 g 2,1 M=S 0 Neither finger in contact finger 2 in contact finger 1 in contact Both fingers in contact stratum

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Control Architecture Desired task motion planning algorithm

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Open-Chain Manipulators Forward kinematics Product-of-exponentials formula A configuration is of the form s P T

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Inverse Kinematics The inverse kinematics solution is not unique 1 1 1 1

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Inverse Kinematics PUMA geometry makes an analytical solution tractable p w - p b

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Inverse Kinematics 14” diameter circle

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Control Architecture Desired task motion planning algorithm inverse kinematics encoder counts PIDRobot current configuration current counts fuzzy supervisor

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Biomimetic Sensing

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Force Sensors Feedback at Finger/Object Junction Piezoelectric –Used in biomedical testing –Compliant –Tend to drift under static load Flexiforce Sensor

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Finding an Object

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Control Architecture desired task motion planning algorithm inverse kinematics encoder counts PIDRobot current configuration encoder counts sensor readings fuzzy supervisor trajectory adjustment

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Summary So Far –Built a closed loop system to perform robotic manipulation stratified motion planning inverse kinematics solution force feedback To Do –Manipulation Currently working on simulation apply to robots

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Control Perspective on DBS (or “What the heck am I doing here?”) Underlying manipulation technique is a geometric approach to nonlinear controls Nonlinear control lies at the forefront of modern control methods One of the most intriguing aspects of nonlinearity is that of chaos Nonlinear control techniques have been used to suppress cardiac arrythmia, a chaotic process Is neuron transmission chaotic? –at the heart of successful treatments using deep brain stimulation is the ability to control chaos Robust and nonlinear control techniques provide an analytical foundation on which to study such systems Soft computing techniques provide an additional approach that while not at rigorous may yield equal or better results

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Open Questions on DBS By approaching DBS from a control Theory Standpoint, Can We –Control with external stimulation locally? Filter the signals? –Characterize which signals cause which disruptions stimulation can suppress dyskinesia tremors tend to lessen during movement Keep symptoms from returning with fatique? –Muscle spasticity Completely eliminate meds?

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The Rest of the Story 54,000 SCI –Additional 2,800 / yr at C5 – C6 level Parkinson’s affects 750,000 – 1 million people in the U.S. Other Pathologies –Hemiplegic stroke –Multiple sclerosis –Muscular dystrophy Rehab Funding –Competition for startup money Who Can Pay? –Hand Mentor from KMI $3,950 Coverage from private insurance companies in only 2 states Currently no medicare coverage –State of Indiana Home and Community Based Care Act Provides funding for community and home-based care 2002: 84 / 16 Medicaid savings of $1,300 per client per month Savings on the order of 3:1 when compared with institutional care

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My Plea As researchers, I believe we have a responsibility to pursue noble goals Obligation of the Engineer –“… conscious always that my skill caries with it the obligation to serve humanity …” Hippocratic Oath –“I will remember that I do not treat a fever chart, a cancerous growth, but a sick human being, whose illness may affect the person's family and economic stability. My responsibility includes these related problems, if I am to care adequately for the sick.” –“will remember that I remain a member of society, with special obligations to all my fellow human beings, those sound of mind and body as well as the infirm.”

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On a Lighter Note

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Motion planning algorithm Solve for v’s from desired trajectory Expand vector exponentials and equate coefficients Solve for h’s by equating B’s of above

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3 rd order bracket

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Fictitious Input Flow

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Revolute Joint Lemmas Position Preservation Distance Preservation

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Stratified Motion Planning If t 4 = t 6 and t 1 = t 3, on S 12 Motion planning performed on S 12 with projected vector fields interchanged

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Contact Coordinates Mapping from R 3 R 2 Shows evolution of finger on object EOMs on the sheets

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Grasp Constraints End effector motion is limited due to contact with object Present control system such that it is in “standard” form Relative contact velocities are control inputs –Defines joint torques

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Extended System Motion planning for smooth systems (extended) Lie bracket directions The v i s are fictitious inputs for extended system, pick trajectory, Can write any flow:

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Lie Bracket Given two vector fields, g 1 and g 2, we can generate a third which points in a new direction This is an approximation by TSE Higher order brackets can be generated, e.g.

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Inverse Kinematics Finding

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Two twists

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Orthosis Design and Feedback Requires joint angle feedback - difficult Change in DIP Angle of the Second Metacarpal of the Right Hand for Three Subjects During Flexion (Both Angles are Relative to the MCP)

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Measuring the MCP Angle

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Mercury Orthotics 2004-2005 Notre Dame Business Plan Competition Semi-Finalist Mission: Provide state-of-the art rehabilitation technology for therapeutic and quality-of-life aid Problem I: Rehabilitation of Hand Injuries –Current structure of therapy is restrictive facility based requires dedicated therapist Problem II: Assistive Aid for Long-Term Care –Current techniques are invasive or incomplete Solution: HandStand System –Provides a method to automate certain therapy functions facility or home based Automatic storage of relevant information and progress assessment therapist is freed to focus on patient care while treating more patients –Provides a noninvasive method for restoring basic hand function responds to user commands

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Phillip Hall Basis Forms a basis for a Lie algebra –A basis is like spice? –Vector fields are elements of the algebra Some of the vector fields created by Lie bracket operations are in this basis –These generate new directions in which a system can move –Once we have enough to span the space, any point is reachable from any other point

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Determine the kinematic equations of motion, velocity constraints Determine the vector fields which annihilate the constraints –Directions in which the system is able to move Determine the Phillip Hall basis Eliminate additional, linearly dependent vector fields Describe the “extended” system comprised of actual inputs and fictitious inputs generated by Lie bracket motions Define a nominal steering trajectory Determine the inputs The span of the set of remaining linearly independent vector fields determines the involutive closure, –The dimension of equals the dimension of the configuration space meaning the system is small time, locally controllable Since the distribution is involutive it can be integrated General Solution Approach

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Configuration Space S 12 S 1 2 S g 1,1 g 1,2 g 1,1 - g 2,1 - g 2,2 g 2,1 M=S 0 Neither Finger in Contact Finger 1 in Contact Finger 2 in Contact Both Fingers in Contact stratum Partition of M into submanifolds Different EOMs on each stratum Restricted to each stratum - equations are smooth Cyclic strata switches –manipulation Consider the sequence

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Fuzzy Logic Mamdani Inference System

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