A generalizable equilibrium model for bending soft arms with longitudinal actuators

Current models of bending in soft arms are formulated in terms of experimentally determined, arm-specific parameters, which cannot evaluate fundamental differences in soft robot arm design. Existing models are successful at improving control of individual arms but do not give insight into how the structure of the arm affects the arm’s capabilities. For example, omnidirectional soft robot arms most frequently have three parallel actuators, but may have four or more, while common biological arms, including octopuses, have tens of distinct longitudinal muscle bundles. This article presents a quasi-static analytical model of soft arms bent with longitudinal actuators, based on equilibrium principles and assuming an unknown neutral axis location. The model is presented as a generalizable framework and specifically implemented for an arm with N fluid-driven actuators, a subset of which are pressurized to induce a bend with a certain curvature and direction. The presented implementation is validated experimentally using planar (2D) and spatial (3D) bends. The planar model is used to initially estimate pressure for a closed-loop curvature control system and to bound the accessible configurations for a rapidly-exploring random trees (RRT) motion planner. A three-segment planar arm is demonstrated to navigate along a planned trajectory through a gap in a wall. Finally, the model is used to explore how the arm morphology affects maximum curvature and directional resolution. This research analytically connects soft arm structure and actuator behavior to unloaded arm performance, and the results may be used to methodically design soft robot arms.