Dynamic Modeling and Control of Variable Stiffness Actuators

A. Albu-Schäffer, O. Eiberger, M. Grebenstein, S. Haddadin, M. Nickl, F. Petit and S. Wolf

DLR – German Aeorospace CenterCenter of Robotics and Mechatronics

Skilful Manipulation with Variable Impedance Robots

Design and control of VIA hand/arm Safety and performance analysis of VIA devices

Size, force and dynamics of a human arm/handVariable stiffness 54 motors,108 position sensors

DLR - Anthropomorphic Hand-Arm-System

A Hand-Arm System for Space Assistance

Extension of the passivity based control approaches to the VIA robots:

Variable, nonlinear stiffnessStrongly coupled joints

Challenges for the Hand: DLR Hand IIb to the integrated hand arm system

Robot hand with size and force similar to the human one

Relocation of motors via tendons.Variable stiffness elements.

Critical tendon routingNonlinearity vs. Workspace/Friction.Joint coupling.

Challenges:Modeling and optimization of the mechanismElectronics integrationA controller to set joint position and stiffness independently.Stiffness trajectories for manipulation

Electronics Integration

Finger Prototype I

Tendon controlled finger with novel jointsHyperboloid joints.Hinge joints hold together by tendon force.

4 Joints.8 Tendons.Nonlinear tendon routing.

Finger Prototype II (STL)

Problem Formulation

Given the desired joint position and the desired mechanical joint stiffnessSolve for the desired motor position.Insert desired motor positions and desired tendon forces into a low-level motor controller → Active motor compliance in series with

mechanical (passive) compliance

Inverse

Simulation & Experimental Results

Step in desired joint positionof 0.2 rad joint positions Motor positions

Challenges for the VIA Arm and Leg Actuation

• Maximal peak power/weight ratio at reasonable stiffness adjusting rate

• Maximal efficiency in energy storage and release• High storable energy density

DLR Arm Joint PrototypesVS-Joint (Wolf & Hirzinger ICRA2008, TuF2.6) QA-Joint (Eiberger & al. ICRA2010) TuF2.6

New armjoint design

Testbed for Evaluation of the First Joint Prototypes

Motor

Encoder

TorqueSensor

VIA - Unit

QA- Prototype

Load

VS-Prototype

Joint Data Sheet: DLR VS-Joint

217°/sMax. Equilibrium Velocity

Variable StiffnessActuator Type

270 + 50 = 320 WNominal Power(not max./peak!)

16.8 JMax. Storable Energy

± 14° / ± 14°Max. Deflection Range (min./max Stiff.)

Ø97x106 / ~ Ø97x166 mmSize (w/wo Motors)

1.4 / ~ 2.0 kgWeight (w/wo Motors)

7.3%Torque Hysteresis at Max. Torque

0.2 sMin. Stiffness Adjusting Time(from 3% to 97% stiffness)

0 / 315 Nm/radMin./Max. Stiffness (no external load)

± 180 NmMaximum Joint Torque(repeatable, evaluated by measurement)

c : Radius of Cam DiskJoint Deflection cφφ

Common descriptionunder developmentby VIACTORS partners

Joint Data Sheet: DLR QA-Joint

217°/sMax. Equilibrium Velocity

Quasi AntagonisticActuator Type

270 + 50 = 320 WNominal Power(not max./peak!)

2.7 JMax. Storable Energy

± 15° / ± 3°Max. Deflection Range (min./max Stiff.)

Ø90x100 / ~ Ø90x160 mmSize (w/wo Motors)

1.4 / ~ 2.0 kgWeight (w/wo Motors)

+/-12.5%Torque Hysteresis at Max. Torque

0.15 sMin. Stiffness Adjusting Time(from 3% to 97% stiffness)

20 / 550 Nm/radMin./Max. Stiffness (no external load)

± 40 NmMaximum Joint Torque(repeatable, evaluated by measurement)

Control of VIA Joints

useful for cyclic movementsinvolving energy storage

(running or throwing)

damping of the arm for fast,fine positioning tasks has to be

realized by control.

The joints have very low intrinsic damping

Ensuring the achievement of the desired link position with motor position based control.Providing the desired stiffness property.

(Albu-Schäffer & al. ICRA 2010, WeA1.5 )

Active Vibration Damping for VIA Joints

No damping Active damping

External disturbance torque

Generic VS joint model – underactuated systemwith p.d.

Validation on 2dof Prototype

Performance Validation

VIA jointRigid joint

Optimal Control for Maximal Performance

Optimized stiffness and motion trajectory

Kicking Performance: Motivation

Kicking Experiments

Experimental Results

Impact joint torque

Kicking range

Speed

10 Nm85 Nm

4.05 m1.6 m

6.35 m/s3.06 m/s

VS-JointStiff Joint