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Deformable linear objects (DLOs), such as rods, cables, and ropes, play important roles in daily life. However, manipulation of DLOs is challenging as large geometrically nonlinear deformations may occur during the manipulation process. This problem is made even more difficult as the different deformation modes (e.g., stretching, bending, and twisting) may result in elastic instabilities during manipulation. In this paper, we formulate a physics-guided data-driven method to solve a challenging manipulation task—accurately deploying a DLO (an elastic rod) onto a rigid substrate along various prescribed patterns. Our framework combines machine learning, scaling analysis, and physical simulations to develop a physics-based neural controller for deployment. We explore the complex interplay between the gravitational and elastic energies of the manipulated DLO and obtain a control method for DLO deployment that is robust against friction and material properties. Out of the numerous geometrical and material properties of the rod and substrate, we show that only three non-dimensional parameters are needed to describe the deployment process with physical analysis. Therefore, the essence of the controlling law for the manipulation task can be constructed with a low-dimensional model, drastically increasing the computation speed. The effectiveness of our optimal control scheme is shown through a comprehensive robotic case study comparing against a heuristic control method for deploying rods for a wide variety of patterns. In addition to this, we also showcase the practicality of our control scheme by having a robot accomplish challenging high-level tasks such as mimicking human handwriting, cable placement, and tying knots. 

Abstract Elastic gridshell is a class of net-like structure formed by an ensemble of elastically deforming rods coupled through joints, such that the structure can cover large areas with low self-weight and allow for a variety of aesthetic configurations. Gridshells, also known as X-shells or Cosserat Nets, are a planar grid of elastic rods in its undeformed configuration. The end points of the rods are constrained and positioned on a closed curve—the final boundary—to actuate the structure into a 3D shape. Here, we report a discrete differential geometry-based numerical framework to study the geometrically nonlinear deformation of gridshell structures, accounting for non-trivial bending-twisting coupling at the joints. The form-finding problem of obtaining the undeformed planar configuration given the target convex 3D topology is then investigated. For the forward (2D to 3D) physically based simulation, we decompose the gridshell structure into multiple one-dimensional elastic rods and simulate their deformation by the well-established discrete elastic rods (DER) algorithm. A simple penalty energy between rods and linkages is used to simulate the coupling between two rods at the joints. For the inverse problem associated with form-finding (3D to 2D), we introduce a contact-based algorithm between the elastic gridshell and a rigid 3D surface, where the rigid surface describes the target shape of the gridshell upon actuation. This technique removes the need of several forward simulations associated with conventional optimization algorithms and provides a direct solution to the inverse problem. Several examples—hemispherical cap, paraboloid, and hemi-ellipsoid—are used to show the effectiveness of the inverse design process. 

Despite tremendous progress in the development of untethered soft robots in recent years, existing systems lack the mobility, model‐based control, and motion planning capabilities of their piecewise rigid counterparts. As in conventional robotic systems, the development of versatile locomotion of soft robots is aided by the integration of hardware design and control with modeling tools that account for their unique mechanics and environmental interactions. Here, a framework for physics‐based modeling, motion planning, and control of a fully untethered swimming soft robot is introduced. This framework enables offline co‐design in the simulation of robot parameters and gaits to produce effective open‐loop behaviors and enables closed‐loop planning over motion primitives for feedback control of a frog‐inspired soft robot testbed. This pipeline uses a discrete elastic rods (DERs) physics engine that discretizes the soft robot as many stretchable and bendable rods. On hardware, an untethered aquatic soft robot that performs frog‐like rowing behaviors is engineered. Hardware validation verifies that the simulation has sufficient accuracy to find the best candidates for sets of parameters offline. The simulator is then used to generate a trajectory library of the robot's motion in simulation that is used in real‐time closed‐loop path following experiments on hardware.