Reduced order modeling and model order reduction for continuum manipulators: an overview

Soft robot's natural dynamics calls for the development of tailored modeling techniques for control. However, the high-dimensional configuration space of the geometrically exact modeling approaches for soft robots, i.e., Cosserat rod and Finite Element Methods (FEM), has been identified as a key obstacle in controller design. To address this challenge, Reduced Order Modeling (ROM), i.e., the approximation of the full-order models, and Model Order Reduction (MOR), i.e., reducing the state space dimension of a high fidelity FEM-based model, are enjoying extensive research. Although both techniques serve a similar purpose and their terms have been used interchangeably in the literature, they are different in their assumptions and implementation. This review paper provides the first in-depth survey of ROM and MOR techniques in the continuum and soft robotics landscape to aid Soft Robotics researchers in selecting computationally efficient models for their specific tasks.

Control-Oriented Models for Hyperelastic Soft Robots Through Differential Geometry of Curves

The motion complexity and use of exotic materials in soft robotics call for accurate and computationally efficient models intended for control. To reduce the gap between material and control-oriented research, we build upon the existing piece-wise constant curvature framework by incorporating hyperelastic and viscoelastic material behavior. In this work, the continuum dynamics of the soft robot are derived through the differential geometry of spatial curves, which are then related to finite-element data to capture the intrinsic geometric and material nonlinearities. To enable fast simulations, a reduced-order integration scheme is introduced to compute the dynamic Lagrangian matrices efficiently, which in turn allows for real-time (multilink) models with sufficient numerical precision. By exploring the passivity and using the parameterization of the hyperelastic model, we propose a passivity-based adaptive controller that enhances robustness toward material uncertainty and unmodeled dynamics-slowly improving their estimates online. As a study-case, a soft robot manipulator is developed through additive manufacturing, which shows good correspondence with the dynamic model under various conditions, for example, natural oscillations, forced inputs, and under tip-loads. The solidity of the approach is demonstrated through extensive simulations, numerical benchmarks, and experimental validations.

Learning 3D shape proprioception for continuum soft robots with multiple magnetic sensors

Sensing the shape of continuum soft robots without obstructing their movements and modifying their natural softness requires innovative solutions. This letter proposes to use magnetic sensors fully integrated into the robot to achieve proprioception. Magnetic sensors are compact, sensitive, and easy to integrate into a soft robot. We also propose a neural architecture to make sense of the highly nonlinear relationship between the perceived intensity of the magnetic field and the shape of the robot. By injecting a priori knowledge from the kinematic model, we obtain an effective yet data-efficient learning strategy. We first demonstrate in simulation the value of this kinematic prior by investigating the proprioception behavior when varying the sensor configuration, which does not require us to re-train the neural network. We validate our approach in experiments involving one soft segment containing a cylindrical magnet and three magnetoresistive sensors. During the experiments, we achieve mean relative errors of 4.5%.

Design, Modeling and Control of an Enhanced Soft Pneumatic Network Actuator

Inspired by nature, soft-bodied pneumatic network actuators (PNAs) composed of compliant materials have been successfully applied in the fields of industry and daily life because of large-amplitude motion and long life span. However, compliant materials simultaneously limit the output force, challenge the dynamic modeling and impede corresponding control. In this paper, we investigate the design, modeling and control of an enhanced PNA. First, an enhanced structure is proposed to improve the output force of PNAs with features of simplification of fabrication, lightweight and compliant material retentivity. Second, a dynamic model of the enhanced PNA is constructed based on the Euler–Lagrange (EL) method. Finally, an adaptive robust controller is addressed for PNAs in presence of system uncertainties without knowledge of its bounds in prior. Experiment results show that the output force of the enhanced PNA is four times greater than the actuator without enhanced structures, which affords to theoretical estimation. Moreover, the proposed controller is utilized and compared with previous works in humanoid finger experiments to illustrate the effectiveness.

How to Model Tendon-Driven Continuum Robots and Benchmark Modelling Performance

Tendon actuation is one of the most prominent actuation principles for continuum robots. To date, a wide variety of modelling approaches has been derived to describe the deformations of tendon-driven continuum robots. Motivated by the need for a comprehensive overview of existing methodologies, this work summarizes and outlines state-of-the-art modelling approaches. In particular, the most relevant models are classified based on backbone representations and kinematic as well as static assumptions. Numerical case studies are conducted to compare the performance of representative modelling approaches from the current state-of-the-art, considering varying robot parameters and scenarios. The approaches show different performances in terms of accuracy and computation time. Guidelines for the selection of the most suitable approach for given designs of tendon-driven continuum robots and applications are deduced from these results.

First-Order Dynamic Modeling and Control of Soft Robots

Modeling of soft robots is typically performed at the static level or at a second-order fully dynamic level. Controllers developed upon these models have several advantages and disadvantages. Static controllers, based on the kinematic relations tend to be the easiest to develop, but by sacrificing accuracy, efficiency and the natural dynamics. Controllers developed using second-order dynamic models tend to be computationally expensive, but allow optimal control. Here we propose that the dynamic model of a soft robot can be reduced to first-order dynamical equation owing to their high damping and low inertial properties, as typically observed in nature, with minimal loss in accuracy. This paper investigates the validity of this assumption and the advantages it provides to the modeling and control of soft robots. Our results demonstrate that this model approximation is a powerful tool for developing closed-loop task-space dynamic controllers for soft robots by simplifying the planning and sensory feedback process with minimal effects on the controller accuracy.

Reality-Assisted Evolution of Soft Robots through Large-Scale Physical Experimentation: A Review

We introduce the framework of reality-assisted evolution to summarize a growing trend towards combining model-based and model-free approaches to improve the design of physically embodied soft robots. In silico, data-driven models build, adapt, and improve representations of the target system using real-world experimental data. By simulating huge numbers of virtual robots using these data-driven models, optimization algorithms can illuminate multiple design candidates for transference to the real world. In reality, large-scale physical experimentation facilitates the fabrication, testing, and analysis of multiple candidate designs. Automated assembly and reconfigurable modular systems enable significantly higher numbers of real-world design evaluations than previously possible. Large volumes of ground-truth data gathered via physical experimentation can be returned to the virtual environment to improve data-driven models and guide optimization. Grounding the design process in physical experimentation ensures that the complexity of virtual robot designs does not outpace the model limitations or available fabrication technologies. We outline key developments in the design of physically embodied soft robots in the framework of reality-assisted evolution.

On the motion/stiffness decoupling property of articulated soft robots with application to model-free torque iterative learning control

This article tackles the problem of controlling articulated soft robots (ASRs), i.e., robots with either fixed or variable elasticity lumped at the joints. Classic control schemes rely on high-authority feedback actions, which have the drawback of altering the desired robot softness. The problem of accurate control of ASRs, without altering their inherent stiffness, is particularly challenging because of their complex and hard-to-model nonlinear dynamics. Leveraging a learned anticipatory action, iterative learning control (ILC) strategies do not suffer from these issues. Recently, ILC was adopted to perform position control of ASRs. However, the limitation of position-based ILC in controlling variable stiffness robots is that whenever the robot stiffness profile is changed, a different input action has to be learned. Our first contribution is to identify a wide class of ASRs, whose motion and stiffness adjusting dynamics can be proved to be decoupled. This class is described by two properties that we define: strong elastic coupling, relative to motors and links of the system and their connections; and homogeneity, relative to the characteristics of the motors. Furthermore, we design a torque-based ILC scheme that, starting from a rough estimation of the system parameters, refines the torque needed for the joint positions tracking. The resulting control scheme requires minimum knowledge of the system. Experiments on variable stiffness robots prove that the method effectively generalizes the iterative procedure with respect to the desired stiffness profile and allows good tracking performance. Finally, potential restrictions of the method, e.g., caused by friction phenomena, are discussed.