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.

We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical parameters. The iMODE method learns meta-knowledge, the functional variations of the force field of dynamical system instances without knowing the physical parameters, by adopting a bi-level optimization framework: an outer level capturing the common force field form among studied dynamical system instances and an inner level adapting to individual system instances. A priori physical knowledge can be conveniently embedded in the neural network architecture as inductive bias, such as conservative force field and Euclidean symmetry. With the learned meta-knowledge, iMODE can model an unseen system within seconds, and inversely reveal knowledge on the physical parameters of a system, or as a Neural Gauge to "measure" the physical parameters of an unseen system with observed trajectories. We test the validity of the iMODE method on bistable, double pendulum, Van der Pol, Slinky, and reaction-diffusion systems.

Robotic manipulation of slender objects is challenging, especially when the induced deformations are large and nonlinear. Traditionally, learning-based control approaches, such as imitation learning, have been used to address deformable material manipulation. These approaches lack generality and often suffer critical failure from a simple switch of material, geometric, and/or environmental (e.g., friction) properties. This article tackles a fundamental but difficult deformable manipulation task: forming a predefined fold in paper with only a single manipulator. A data-driven framework combining physically-accurate simulation and machine learning is used to train a deep neural network capable of predicting the external forces induced on the manipulated paper given a grasp position. We frame the problem using scaling analysis, resulting in a control framework robust against material and geometric changes. Path planning is then carried out over the generated "neural force manifold" to produce robot manipulation trajectories optimized to prevent sliding, with offline trajectory generation finishing 15$\times$ faster than previous physics-based folding methods. The inference speed of the trained model enables the incorporation of real-time visual feedback to achieve closed-loop sensorimotor control. Real-world experiments demonstrate that our framework can greatly improve robotic manipulation performance compared to state-of-the-art folding strategies, even when manipulating paper objects of various materials and shapes.

Multi-flagellated bacteria utilize the hydrodynamic interaction between their filamentary tails, known as flagella, to swim and change their swimming direction in low Reynolds number flow. This interaction, referred to as bundling and tumbling, is often overlooked in simplified hydrodynamic models such as Resistive Force Theories (RFT). However, for the development of efficient and steerable robots inspired by bacteria, it becomes crucial to exploit this interaction. In this paper, we present the construction of a macroscopic bio-inspired robot featuring two rigid flagella arranged as right-handed helices, along with a cylindrical head. By rotating the flagella in opposite directions, the robot's body can reorient itself through repeatable and controllable tumbling. To accurately model this bi-flagellated mechanism in low Reynolds flow, we employ a coupling of rigid body dynamics and the method of Regularized Stokeslet Segments (RSS). Unlike RFT, RSS takes into account the hydrodynamic interaction between distant filamentary structures. Furthermore, we delve into the exploration of the parameter space to optimize the propulsion and torque of the system. To achieve the desired reorientation of the robot, we propose a tumble control scheme that involves modulating the rotation direction and speed of the two flagella. By implementing this scheme, the robot can effectively reorient itself to attain the desired attitude. Notably, the overall scheme boasts a simplified design and control as it only requires two control inputs. With our macroscopic framework serving as a foundation, we envision the eventual miniaturization of this technology to construct mobile and controllable micro-scale bacterial robots.

Soft deployable structures - unlike conventional piecewise rigid deployables based on hinges and springs - can assume intricate 3-D shapes, thereby enabling transformative technologies in soft robotics, shape-morphing architecture, and pop-up manufacturing. Their virtually infinite degrees of freedom allow precise control over the final shape. The same enabling high dimensionality, however, poses a challenge for solving the inverse design problem involving this class of structures: to achieve desired 3D structures it typically requires manufacturing technologies with extensive local actuation and control during fabrication, and a trial and error search over a large design space. We address both of these shortcomings by first developing a simplified planar fabrication approach that combines two ingredients: strain mismatch between two layers of a composite shell and kirigami cuts that relieves localized stress. In principle, it is possible to generate targeted 3-D shapes by designing the appropriate kirigami cuts and selecting the right amount of prestretch, thereby eliminating the need for local control. Second, we formulate a data-driven physics-guided framework that reduces the dimensionality of the inverse design problem using autoencoders and efficiently searches through the ``latent" parameter space in an active learning approach. We demonstrate the effectiveness of the rapid design procedure via a range of target shapes, such as peanuts, pringles, flowers, and pyramids. Tabletop experiments are conducted to fabricate the target shapes. Experimental results and numerical predictions from our framework are found to be in good agreement.

Fully soft bistable mechanisms have shown extensive applications ranging from soft robotics, wearable devices, and medical tools, to energy harvesting. However, the lack of design and fabrication methods that are easy and potentially scalable limits their further adoption into mainstream applications. Here a top-down planar approach is presented by introducing Kirigami-inspired engineering combined with a pre-stretching process. Using this method, Kirigami-Pre-stretched Substrate-Kirigami trilayered precursors are created in a planar manner; upon release, the strain mismatch -- due to the pre-stretching of substrate -- between layers would induce an out-of-plane buckling to achieve targeted three dimensional (3D) bistable structures. By combining experimental characterization, analytical modeling, and finite element simulation, the effect of the pattern size of Kirigami layers and pre-stretching on the geometry and stability of resulting 3D composites is explored. In addition, methods to realize soft bistable structures with arbitrary shapes and soft composites with multistable configurations are investigated, which could encourage further applications. Our method is demonstrated by using bistable soft Kirigami composites to construct two soft machines: (i) a bistable soft gripper that can gently grasp delicate objects with different shapes and sizes and (ii) a flytrap-inspired robot that can autonomously detect and capture objects.