Soft robots' ability to safely navigate complex environments motivates the development of algorithms for accurate environmental interaction assessment, enabling greater autonomy. Specifically, strain-based shape and force estimation of continuum robots with embedded soft sensors poses an open challenge mainly owing to continuous softness, anisotropic deformation, and non-linear properties. Mathematical description of deformable soft bodies and accurate estimation of external forces are crucial for achieving controllable and intelligent behaviors of these robots. In this paper, a kinetostatic strain-based modeling for rod-driven soft robots (RDSR) with embedded stretch sensors is proposed, which incorporates local strains, actuation variables, and external interactions. The strain model enables full shape estimation of the robot and prediction of strain variations in soft bodies. Building on this, we develop a force estimator based on predicted and measured sensor and actuator lengths to evaluate 3D external forces, accounting for both orthogonal and tangential components relative to the backbone. Moreover, we introduce a methodology using a novel ellipsoid representation to handle tangential forces that may become insensitive in certain singular configurations. This estimator allows us to either disregard such forces when they do not influence deformation or estimate them when they become observable. Our simulations and experiments demonstrate how this approach can be used to analyze the robot's configuration and successfully estimate external forces. Finally, it is demonstrated that when the continuum arm follows trajectories with higher strain sensitivity, tangential force estimation is significantly improved.

Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such systems, however, they tend to be high-dimensional and time-consuming. This article presents a novel model order reduction approach for soft and hybrid robots by combining strain-based modeling with proper orthogonal decomposition (POD). The method identifies optimal coupled strain basis functions—or mechanical synergies—from simulation data, enabling the description of soft robot configurations with a minimal number of generalized coordinates. The reduced order model (ROM) achieves substantial dimensionality reduction in the configuration space while preserving accuracy. Rigorous testing demonstrates the interpolation and extrapolation capabilities of the ROM for soft manipulators under static and dynamic conditions. The approach is further validated on a snake-like hyper-redundant rigid manipulator and a closed-chain system with soft and rigid components, illustrating its broad applicability. Moreover, the approach is leveraged for shape estimation of a real six-actuator soft manipulator using only two position markers, showcasing its practical utility. Finally, the ROM's dynamic and static behavior is validated experimentally against a parallel hybrid soft-rigid system, highlighting its effectiveness in representing the high-order model and the real system. This POD-based ROM offers significant computational speed-ups, paving the way for real-time simulation and control of complex soft and hybrid robots.

Model-based manipulation of deformable objects has traditionally dealt with objects while neglecting their dynamics, thus mostly focusing on very lightweight objects at steady state. At the same time, soft robotic research has made considerable strides toward general modeling and control, despite soft robots and deformable objects being very similar from a mechanical standpoint. In this work, we leverage these recent results to develop a control-oriented, fully dynamic framework of slender deformable objects grasped at one end by a robotic manipulator. We introduce a dynamic model of this system using functional strain parameterizations and describe the manipulation challenge as a regulation control problem. This enables us to define a fully model-based control architecture, for which we can prove analytically closed-loop stability and provide sufficient conditions for steady state convergence to the desired state. The nature of this work is intended to be markedly experimental. We provide an extensive experimental validation of the proposed ideas, tasking a robot arm with controlling the distal end of six different cables, in a given planar position and orientation in space.

Rod-driven soft robots (RDSR) with a well-balanced performance in terms of perception, precision, and intelligence have a great potential for application. Mathematical description and predicted sensing of deformable soft bodies are crucial to achieve controllable and intelligent behaviors of these robots. In this work, we propose a kinetostatic model for RDSR embedded with co-located sensors based on the Geometric Variable Strain (GVS) approach where local deformations, actuation lengths and external interactions are included. This approach allows us to estimate the shape of RDSR and predict the strain variation of soft bodies under internal and external interactions. Simulations and experimental results show that tip position errors are not greater than 1.8% with respect to the whole body length under different loads (0, 100, 200, 300 gf). The maximum error of predicted sensor length change is up to 2 mm and its percentage relative to the actual length does not exceed 4%. The results demonstrate the accuracy and effectiveness of the proposed model.

Sensing antenna devices, that mimic insect antennae or mammal whiskers, is an active field of research that still needs new developments in order to become efficient and reliable components of robotic systems. This work reports a new result in the area of signal processing of these devices that allows to detect the instant of the impact of a flexible antenna with an object faster than other reported methods. Previous methods require the use of filters that introduce delays in the impact detection. A method based on the Super-Twisting algorithm is proposed here that avoids the use of these filters and reduces such delays improving the impact instant estimation. Experiments show that these delays can be reduced in more than 50%, allowing reliable estimation of the impact instant with an error of less than 5 ms in many cases requiring a limited computational effort.

In this paper a fractional order model for an irrigation main canal is proposed. This system has two pools that present a strong interaction between them. Then a multivariable model with two inputs: the pump flow and the opening of an intermediate gate, and two outputs: the water levels in the two pools, is derived. The identification of the model parameters is based on the experiments developed in a laboratory prototype of a hydraulic canal and the application of a direct system identification methodology. The accuracy of the proposed fractional order models is compared with the standard integer-order models of the canal. The parameters of the mathematical models have been identified by minimizing the Integral Square Error Index (ISE) existing between the time responses of the models and the real-time experimental data obtained from the canal prototype. A comparison of the performances of the integer-order and fractional-order models shows that the fractional-order model has significantly lower error: about 30%, and, therefore, higher accuracy in capturing the canal dynamics.