Post on 30-Jun-2021
Giorgio Grioli* Alessandro Serio^ Antonio Bicchi*^
*Center for Robotics and Bioengineering “E. Piaggio”
^ IIT - Istituto Italiano di Tecnologia
Variable Stiffness Actuators have limitations: ◦ two motors per joint ◦ more complexity, weight ◦ less max stiffness than conventional joints
VSA and Safety ◦ may not be useful if heavy links are used ◦ may not be economically justified by added performance
Common sense on Robots and VSA: ◦ It’s hard to think of a stiff future for Robotics ◦ Variable impedance is important in nature ◦ Dynamic adaptability to tasks is a major advantage
Conclusions
Variable Stiffness Actuators (aka Robotic Muscles) @ Pisa
13-09-2010
The VSA HD
Hammering Drumming
The VSA Cube
13-09-2010
The VSA Cube
The VSA Cube
The VSA Cube
Casting Grasping
13-09-2010
• Simplestno,onofmechanicalimpedance:Linears,ffness(Hooke’sLaw)
• Generaliza,ontoNon‐LinearSprings:– Par,alderiva,ve
• Generaliza,ontoDynamicSystems:– LaplaceTransform:Impedance
Impedance for Non-Linear Mechanical Systems
13-09-2010
Impedance for Non-Linear Mechanical Systems
• GeneralizingImpedance:– Graph
• Analy,calDescrip,on
– AtaRegularpoint:Locallythereexists
•
Fréchetdifferen,al
Admittance View
13-09-2010
• Antagonist“muscle”system– Dynamics:
where
– Gen.S,ffness:– Gen.Damping:
An example
13-09-2010
13-09-2010
An example
13-09-2010
• Measurementsareatthebasisofscience
• Feedbackneedsmeasuring– MeasuringimpedanceisneededforcontrolofVIAactuators
• Impedanceisadifferen,aloperatornotaphysicalquan-tyinastrictsense
Measuring Impedance
“Physical Quantity: a property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference”
International Vocabulary of Metrology (VIM). Basic and General Concepts and Associated Terms.
“Misura ciò che e misurabile, e rendi misurabile ciò che non lo è” (Measure what is measurable, and make measurable what is not )
Galileo
13-09-2010
ImpedanceMeasurementsStateoftheArt• InME
• InBiomechanics
• InRobo,cs,etc.
CommonCharacteris,cs– Typically:repeatedexperimentswithprobingperturba,ons
– Mostly:notapplicableinreal,me– Always*:linear,,meinvariantimpedance
Measuring Impedance
• Simplecase
– Buildanon‐linearequivalentsystem
– ObservabilityCo‐distribu,on
13-09-2010
Measuring Linear Impedance
OBSERVABLE!
Buildaregression,ornon‐linearobservere.g.anExtendedKalmanFilter
13-09-2010
Measuring Linear Impedance
13-09-2010
Thesameapproachisnolongerpossible(atleast,nottrivially)
Measuring Nonlinear Impedance
13-09-2010
UsingEKFwithanonlinearimpedance…
Measuring Nonlinear Impedance
13-09-2010
– given
– differen,a,onyields
– buildanes,mate
The Variable Stiffness Observers
Th.:Theupdatelaw
convergestowithinanUniformlyUl@matelyBoundederrorregionaroundthereals@ffnessvalue
13-09-2010
“A Non-Invasive, Real-Time Method for Measuring Variable Stiffness”
G. Grioli, A. Bicchi Robotic Science and Systems 2010,
Zaragoza, Spain. Submitted paper
The Variable Stiffness Observer
13-09-2010
The Variable Stiffness Observer
• The steeper stiffness changes with position and input, the larger is the error
• Large co-contraction velocity with slow limb displacement may cause large errors
13-09-2010
VSO - Simulations
13-09-2010
– Whenthelimbstops…
– Errorsinm,b
propor,onalerror
More interesting Simulations
13-09-2010
The Variable Stiffness Observer
• The steeper stiffness changes with position and input, the larger is the error
• Large co-contraction velocity with slow limb displacement may cause large errors
Canweobserves,ffnesswithoutknowingmandb?
NO,ifwemeasureonlytheappliedtorque– e.g.humanmeasurements
YESifwemeasuretheelas,cforce(“inside”thejoint)– e.g.robots
VSO – Mass and Damping
13-09-2010
Experimental Results
Spring Calibration
13-09-2010
Experimental Results
Raw data
Position and Force
13-09-2010
Experimental Results
Observed Stiffness
Relative Error
13-09-2010
• Adiscussionofnonlinearimpedancedefini,ons
• Areal‐,me,non‐invasivealgorithmtoes,mates,ffness
• Useof“dirty”deriva,vesincreaseserror,donotposethreatstofilterstability(butitmightifclosedloop)
• Openissues– Extendton‐dof’s– Observe(nl,tv)generalizedmassanddamping
– Controlimpedanceinclosedloop– Applybeyondrobo,cs
Conclusions
13-09-2010
• VariableS,ffnessActuatorshavelimita,ons:– twomotorsperjoint– morecomplexity,weight
– lessmaxs,ffnessthanconven,onaljoints• VSAandSafety
– maynotbeusefulifheavylinksareused– maynotbeeconomicallyjus,fiedbyaddedperformance
• CommonsenseonRobotsandVSA:– It’shardtothinkofas,fffutureforRobo,cs– Variableimpedanceisimportantinnature– Dynamicadaptabilitytotasksisamajoradvantage
Conclusions
Questions
13-09-2010
• Aren’t “Variable Impedance Actuators” simply “Robot Muscles”?
• Whenwillsoarobotsbeanindustrialreality?
Safety and Compliance - on the market soon?
13-09-2010