Alessandro Bettini, Panadda Marayong,
Samuel Lang, Allison M. Okamura, Gregory D. Hager
IEEE Transactions on Robotics, Vol.
20, NO.6 December 2004
Summary
The paper illustrated a control technique for
robot tele-operation, using the concept of “virtual
fixture”. A virtual fixture is defined as a restriction to a mechanism to a
certain subspace or volume o motion, doing exactly what a real fixture is capable and obtained
through a control system.
The approach is used in
the concept of tele-operation (where the usage of this technique has been
demonstrated to increase its performance by 70%), autonomous robotic execution
and free-hand procedures.
The result of vision-based
virtual fixtures (which are assisted by vision sensors) is that positioning
errors and execution time are reduced significantly in a macroscale task.
Through the linear viscous law (for which v=1/k*f, where v is the velocity,
seen also as the control output, f the force and 1/k is a constant).
If we consider the force
as based on two component fδ and fτ, we can
then consider having and admittance on the latter, which indicated the
stiffness on the direction orthogonal to δ (when equal to
0 we have not possible movement in any direction and 1 with isotropic
admittance, which means that we have equally stiffness in all direction.
Virtual fixtures are mainly used in two areas of application: reference target
and reference curve, the first one consist of a path, which is a segment in a
3D environment and in this case the motion ends when the target is reached,
while the latter is a fixed 3D Cartesian space curve. The two different cases
define two different approaches, in the case of reference target we define a
reference direction δt(xa)=xt-xa
, where xt is the target position and xa is
the manipulator position; for the reference curve instead the approach is different,
the curve is kept into account according to 3 variables: x(s), y(s) and z(s),
with s assuming values between 0 and 1, and δp is defined as
the normalized tangent direction to the curve, in this consideration though we
can’t affirm that δ=δp as δ=δt, in fact first the Cartesian error must be
calculated (as difference between the curve and the manipulators position. In
the calculation of the final δc, which
must be considered in the case of reference curve computation, a new factor,
influencing the Cartesian Error, appears: kd, which, in its positive
sign is the scalar gain and for which, in the case of an increase in value,
tracking performance appears to be improved and stability margin decreases. In
approaching the target point a convenient way indicated by the authors is by
using a spherical switching surface of radius ρ, about the target point. With further implementation
the calculations are introduced for volumes (tubes and cones, the latter for
the approaching point, as a “virtual
chamfer”).
Basically along the path
the manipulator is pushed towards a certain direction inside the volume,
influenced by the admittance value which is imputed inside the control system,
it will tend for instance to be inside the cone, where there is an isotropic
admittance.
Key Concepts
Virtual Fixtures,
Tele-Operation, Working in an environment which required high precision.
Key Results
The team has done
experiments and made a statistical analysis on the different situations (hard
fixturing or soft fixturing) The tests done demonstrate how cooperation
environment is performing better and how hard fixturing is to be considered the
best performance improvement, although it limits considerably the control of
direction of the motion, but still soft virtual fixturing can statistically be
considered improving user performance and keeping great user control. The
system has to improved under the aspect of robotic vision, having a better
resolution, which may enhance the control results and reduce the error
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