  The compliant structure of soft robotic systems enables a variety of novel
capabilities in comparison to traditional rigid-bodied robots. A subclass of
soft fluid-driven actuators known as fiber reinforced elastomeric enclosures
(FREEs) is particularly well suited as actuators for these types of systems.
FREEs are inherently soft and can impart spatial forces without imposing a
rigid structure. Furthermore, they can be configured to produce a large variety
of force and moment combinations. In this paper we explore the potential of
combining multiple differently configured FREEs in parallel to achieve fully
controllable multi-dimensional soft actuation. To this end, we propose a novel
methodology to represent and calculate the generalized forces generated by soft
actuators as a function of their internal pressure. This methodology relies on
the notion of a state dependent fluid Jacobian that yields a linear expression
for force. We employ this concept to construct the set of all possible forces
that can be generated by a soft system in a given state. This force zonotope
can be used to inform the design and control of parallel combinations of soft
actuators. The approach is verified experimentally with the parallel
combination of three carefully designed actuators constrained to a 2DOF testing
rig. The force predictions matched measured values with a root-mean-square
error of less than 1.5 N force and 8 x 10^(-3)Nm moment, demonstrating the
utility of the presented methodology.
