With the explosive growth of rigid-body simulators, policy learning in simulation has become the de facto standard for most rigid morphologies. In contrast, soft robotic simulation frameworks remain scarce and are seldom adopted by the soft robotics community. This gap stems partly from the lack of easy-to-use, general-purpose frameworks and partly from the high computational cost of accurately simulating continuum mechanics, which often renders policy learning infeasible. In this work, we demonstrate that rapid soft robot policy learning is indeed achievable via implicit time-stepping. Our simulator of choice, DisMech, is a general-purpose, fully implicit soft-body simulator capable of handling both soft dynamics and frictional contact. We further introduce delta natural curvature control, a method analogous to delta joint position control in rigid manipulators, providing an intuitive and effective means of enacting control for soft robot learning. To highlight the benefits of implicit time-stepping and delta curvature control, we conduct extensive comparisons across four diverse soft manipulator tasks against one of the most widely used soft-body frameworks, Elastica. With implicit time-stepping, parallel stepping of 500 environments achieves up to 6x faster speeds for non-contact cases and up to 40x faster for contact-rich scenarios. Finally, a comprehensive sim-to-sim gap evaluation--training policies in one simulator and evaluating them in another--demonstrates that implicit time-stepping provides a rare free lunch: dramatic speedups achieved without sacrificing accuracy.

The intrinsic compliance and high degree of freedom (DoF) of redundant soft manipulators facilitate safe interaction and flexible task execution. However, effective kinematic control remains highly challenging, as it must handle deformations caused by unknown external loads and avoid actuator saturation due to improper null-space regulation - particularly in confined environments. In this paper, we propose a Sensor-Space Imitation Learning Kinematic Control (SS-ILKC) framework to enable robust kinematic control under actuator saturation and restrictive environmental constraints. We employ a dual-learning strategy: a multi-goal sensor-space control framework based on reinforcement learning principle is trained in simulation to develop robust control policies for open spaces, while a generative adversarial imitation learning approach enables effective policy learning from sparse expert demonstrations for confined spaces. To enable zero-shot real-world deployment, a pre-processed sim-to-real transfer mechanism is proposed to mitigate the simulation-to-reality gap and accurately characterize actuator saturation limits. Experimental results demonstrate that our method can effectively control a pneumatically actuated soft manipulator, achieving precise path-following and object manipulation in confined environments under unknown loading conditions.

Inspired by the embodied intelligence of biological creatures like the octopus, the soft robotic arm utilizes its highly flexible structure to perform various tasks in the complex environment. While the classic Cosserat rod theory investigates the bending, twisting, shearing, and stretching of the soft arm, it fails to capture the in-plane deformation that occurs during certain tasks, particularly those involving active lateral traction. This paper introduces an extended Cosserat rod theory addressing these limitations by incorporating an extra strain variable reflecting the in-plane inflation ratio. To accurately describe the viscoelasticity effect of the soft body in dynamics, the proposed model enhances the constitutive law by integrating the Saint-Venant Kirchhoff hyperelastic and Kelvin-Voigt viscous models. The active and environmental loads are accounted for the equations of motion, which are numerically solved by adapting the Geometric Variable Strain (GVS) approach to balance the accuracy and computational efficiency. Our contributions include the derivation of the extended Cosserat rod theory in dynamic context, and the development of a reduced-order numerical method that enables rapid and precise solutions. We demonstrate applications of the model in stiffness tuning of a soft robotic arm and the study of complex octopus' arm motions.

A neural network-based framework is developed and experimentally demonstrated for the problem of estimating the shape of a soft continuum arm (SCA) from noisy measurements of the pose at a finite number of locations along the length of the arm. The neural network takes as input these measurements and produces as output a finite-dimensional approximation of the strain, which is further used to reconstruct the infinite-dimensional smooth posture. This problem is important for various soft robotic applications. It is challenging due to the flexible aspects that lead to the infinite-dimensional reconstruction problem for the continuous posture and strains. Because of this, past solutions to this problem are computationally intensive. The proposed fast smooth reconstruction method is shown to be five orders of magnitude faster while having comparable accuracy. The framework is evaluated on two testbeds: a simulated octopus muscular arm and a physical BR2 pneumatic soft manipulator.

This paper presents a novel framework to realize proprioception and closed-loop control for soft manipulators. Deformations with large elongation and large bending can be precisely predicted using geometry-based sensor signals obtained from the inductive springs and the inertial measurement units (IMUs) with the help of machine learning techniques. Multiple geometric signals are fused into robust pose estimations, and a data-efficient training process is achieved after applying the strategy of sim-to-real transfer. As a result, we can achieve proprioception that is robust to the variation of external loading and has an average error of 0.7% across the workspace on a pneumatic-driven soft manipulator. The realized proprioception on soft manipulator is then contributed to building a sensor-space based algorithm for closed-loop control. A gradient descent solver is developed to drive the end-effector to achieve the required poses by iteratively computing a sequence of reference sensor signals. A conventional controller is employed in the inner loop of our algorithm to update actuators (i.e., the pressures in chambers) for approaching a reference signal in the sensor-space. The systematic function of closed-loop control has been demonstrated in tasks like path following and pick-and-place under different external loads.

This work concerns the application of physics-informed neural networks to the modeling and control of complex robotic systems. Achieving this goal required extending Physics Informed Neural Networks to handle non-conservative effects. We propose to combine these learned models with model-based controllers originally developed with first-principle models in mind. By combining standard and new techniques, we can achieve precise control performance while proving theoretical stability bounds. These validations include real-world experiments of motion prediction with a soft robot and of trajectory tracking with a Franka Emika manipulator.

Soft actuators offer compliant and safe interaction with an unstructured environment compared to their rigid counterparts. However, control of these systems is often challenging because they are inherently under-actuated, have infinite degrees of freedom (DoF), and their mechanical properties can change by unknown external loads. Existing works mainly relied on discretization and reduction, suffering from either low accuracy or high computational cost for real-time control purposes. Recently, we presented an infinite-dimensional feedback controller for soft manipulators modeled by partial differential equations (PDEs) based on the Cosserat rod theory. In this study, we examine how to implement this controller in real-time using only a limited number of actuators. To do so, we formulate a convex quadratic programming problem that tunes the feedback gains of the controller in real time such that it becomes realizable by the actuators. We evaluated the controller's performance through experiments on a physical soft robot capable of planar motions and show that the actual controller implemented by the finite-dimensional actuators still preserves the stabilizing property of the desired infinite-dimensional controller. This research fills the gap between the infinite-dimensional control design and finite-dimensional actuation in practice and suggests a promising direction for exploring PDE-based control design for soft robots.

Abstract: Across various species and different scales, certain organisms use their appendages to grasp objects not through clamping but through wrapping. This pattern of movement is found in octopus tentacles, elephant trunks, and chameleon prehensile tails, demonstrating a great versatility to grasp a wide range of objects of various sizes and weights as well as dynamically manipulate them in the 3D space. We observed that the structures of these appendages follow a common pattern - a logarithmic spiral - which is especially challenging for existing robot designs to reproduce. This paper reports the design, fabrication, and operation of a class of cable-driven soft robots that morphologically replicate spiral-shaped wrapping. This amounts to substantially curling in length while actively controlling the curling direction as enabled by two principles: a) the parametric design based on the logarithmic spiral makes it possible to tightly pack to grasp objects that vary in size by more than two orders of magnitude and up to 260 times self-weight and b) asymmetric cable forces allow the swift control of the curling direction for conducting object manipulation. We demonstrate the ability to dynamically operate objects at a sub-second level by exploiting passive compliance. We believe that our study constitutes a step towards engineered systems that wrap to grasp and manipulate, and further sheds some insights into understanding the efficacy of biological spiral-shaped appendages. One-Sentence Summary: Design, fabrication, and operation of spiral soft robots at variable scales that can manipulate objects through wrapping. Main Text: INTRODUCTION Wrapping as a paradigm for grasping and manipulation (1), which are two key objectives in robotics (2, 3), is found in the prehensile tail of chameleons and seahorses with length scales as small as a few millimeters (4), as well as in the tentacles of octopuses and the trunks of elephants as large as a meter (Figure 1A) (5, 6).

In this study, an inhomogeneous Cosserat rod theory is introduced and compared to the conventional homogeneous rod for modeling soft manipulators. The inhomogeneity is addressed by considering the pressure actuation as part of the rod's constitutive laws, resulting in shifting the neutral axis. This shift is investigated for a soft manipulator with three parallel fiber-reinforced actuators. Furthermore, a fiber-reinforced actuator is modeled using nonlinear continuum mechanics to extract the effect of radial pressure on axial deformation and is combined with Cosserat model. Finally, several numerical methods are employed to solve the proposed model and validated by a series of experiments.

In this paper, we propose a novel variable-length estimation approach for shape sensing of extensible soft robots utilizing fiber Bragg gratings (FBGs). Shape reconstruction from FBG sensors has been increasingly developed for soft robots, while the narrow stretching range of FBG fiber makes it difficult to acquire accurate sensing results for extensible robots. Towards this limitation, we newly introduce an FBG-based length sensor by leveraging a rigid curved channel, through which FBGs are allowed to slide within the robot following its body extension/compression, hence we can search and match the FBGs with specific constant curvature in the fiber to determine the effective length. From the fusion with the above measurements, a model-free filtering technique is accordingly presented for simultaneous calibration of a variable-length model and temporally continuous length estimation of the robot, enabling its accurate shape sensing using solely FBGs. The performances of the proposed method have been experimentally evaluated on an extensible soft robot equipped with an FBG fiber in both free and unstructured environments. The results concerning dynamic accuracy and robustness of length estimation and shape sensing demonstrate the effectiveness of our approach.