SuRFR: A fast recursive simulator for soft manipulators with discrete joints on SE(3) - Samei, Hossain; Chhabra, Robin (Mechanism and machine theory, 2024)
We develop a fast, recursive, and parameterization-free formulation for the dynamics of soft robots. Such systems are modelled as multi-body systems, composed of rigid and flexible bodies connected with discrete joints. We couple the recursive Newton–Euler equation for rigid bodies and the Partial Differential Equations (PDEs) on the Special Euclidean group SE(3) modelling dynamic Cosserat rods to capture the system’s dynamics. Our proposed inverse dynamics recursively determines the system’s response and the joint torques, given a joint-space trajectory; while subject to known joint torques and external forces, the forward dynamics determines the system’s motion. Unlike rigid systems, the inclusion of flexible bodies necessitates solving a coupled set of PDEs with separated Boundary Conditions (BCs). We develop a shooting-method-based BC solver to move BCs to one point and a numerical framework based on a finite difference method to spatially integrate these equations using a geometrically exact integrator on SE(3). We implement the proposed algorithms into a software library, named SimUlator for Rigid–Flexible Robots (SuRFR), and study the response of a manipulator with a soft gripper. •We develop fast recursive algorithms for forward and inverse dynamics of soft robots.•We model multi-body systems with rigid and flexible bodies on SE(3).•We develop a boundary condition solver for PDEs capturing dynamics of soft robots.•We develop a finite difference method to integrate PDEs on SE(3).•We develop a software library to simulate generic rigid–flexible multi-body systems.