Force Generation by Parallel Combinations of Fiber-Reinforced Fluid-Driven Actuators

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 letter, we explore the potential of combining multiple differently configured FREEs in parallel to achieve fully controllable multidimensional 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 test platform. The force predictions matched measured values with a root-mean-square error of less than 1.5 N force and $\mathbf {8 \times 10^{-3}}$ Nm moment, demonstrating the utility of the presented methodology.