Whisker sensing by force and moment measurements at the
whisker base
E.L. Starostin, V.G.A. Goss & G.H.M. van der Heijden
We address the theoretical question which forces and moments measured at
the base of a whisker (tactile sensor) allow for the prediction of the
location in space of the point at which a whisker makes contact with an
object. We deal with the general case of three-dimensional deformations as
well as with the special case of planar configurations. All deformations
are treated as quasi-static and contact is assumed to be frictionless. We
show that the minimum number of independent forces or moments required is
three but that conserved quantities of the governing elastic equilibrium
equations prevent certain triples from giving a unique solution in the case
of contact at any point along the whisker except the tip. The existence of
these conserved quantities depends on the material and geometrical
properties of the whisker. For whiskers that are tapered and intrinsically
curved there is no obstruction to the prediction of the contact point. We
show that the choice of coordinate system (Cartesian or cylindrical) affects
the number of suitable triples. Tip and multiple point contact are also
briefly discussed. Our results explain recent numerical observations in the
literature and offer guidance for the design of robotic tactile sensory
devices.
keywords: whisker, tactile sensor, multiple point contact, elastic rod,
boundary-value problem, conserved quantity
Soft Robotics 10, 326-335 (2023)