# Robotics: Science and Systems VI

### A Non-invasive Real-Time Method for Measuring Variable Stiffness

*G. Grioli and A. Bicchi*

**Abstract:**

The need for adaptability to the environment, energy
conservation, and safety during physical interaction with
humans of many advanced robotic applications has prompted the
development of a number of Variable Stiffness Actuators (VSA).
These have been implemented in a variety of ways, using different
transduction technologies (electromechanical, pneumatic,
hydraulic, but also piezoelectric, active polymeric, etc. ) and
arrangements with elastic elements. All designs share a fundamentally
unavoidable nonlinear behavior. The control schemes
proposed for these actuators typically aim at independently
controlling the position (or force) of the link, and its stiffness with
respect to external disturbances. Although effective feedback control
schemes using position and force sensors are commonplace in
robotics, control of stiffness is at present completely openâ€“loop.
In practice, instead of measuring stiffness, it is inferred from
the mathematical model of the actuator. Being this in most cases
only roughly known, model mismatches affect severely stiffness
control, undermining its utility. It should be noticed that, while
for constant stiffness elements an accurate calibration of the
model is possible, the same approach is hardly viable for variable
stiffness systems.

We propose a method for estimating stiffness while it is varied,
either intentionally or not, hence without knowledge of the
command inputs. The method uses instantaneous measurements
of force and position at one of the ends of the compliant
elements in the system, and derives a measure that asymptotically
converges to the current value of stiffness, up to an error
which can be bounded by an arbitrarily small value. Simulation
and experimental results are provided, which illustrate the
performance of the proposed measurement method.

**Bibtex:**

@INPROCEEDINGS{ Grioli-RSS-10, AUTHOR = {G. Grioli AND A. Bicchi}, TITLE = {A Non-invasive Real-Time Method for Measuring Variable Stiffness }, BOOKTITLE = {Proceedings of Robotics: Science and Systems}, YEAR = {2010}, ADDRESS = {Zaragoza, Spain}, MONTH = {June}, DOI = {10.15607/RSS.2010.VI.012} }