ZodiAq: An Isotropic Flagella-Inspired Soft Underwater Drone for Safe Marine Exploration

The inherent challenges of robotic underwater exploration, such as hydrodynamic effects, the complexity of dynamic coupling, and the necessity for sensitive interaction with marine life, call for the adoption of soft robotic approaches in marine exploration. To address this, we present a novel prototype, ZodiAq, a soft underwater drone inspired by prokaryotic bacterial flagella. ZodiAq's unique dodecahedral structure, equipped with 12 flagella-like arms, ensures design redundancy and compliance, ideal for navigating complex underwater terrains. The prototype features a central unit based on a Raspberry Pi, connected to a sensory system for inertial, depth, and vision detection, and an acoustic modem for communication. Combined with the implemented control law, it renders ZodiAq an intelligent system. This article details the design and fabrication process of ZodiAq, highlighting design choices and prototype capabilities. Based on the strain-based modeling of Cosserat rods, we have developed a digital twin of the prototype within a simulation toolbox to simplify analysis and control. To optimize its operation in dynamic aquatic conditions, a simplified model-based controller has been developed and implemented, facilitating intelligent and adaptive movement in the hydrodynamic environment. Extensive experimental demonstrations highlight the drone's potential, showcasing its design redundancy, embodied intelligence, crawling gait, and practical applications in diverse underwater settings. This research contributes significantly to the field of underwater soft robotics, offering a promising new avenue for safe, efficient, and environmentally conscious underwater exploration.

Cosserat Rod-Based Tendon Friction Modeling, Simulation, and Experiments for Tendon-Driven Continuum Robots

Traditional tendon-driven continuum robot (TDCR) models based on Cosserat rod theory often assume that tendon tension is a continuous wrench along the backbone. However, this assumption overlooks critical factors, including the discrete arrangement of disks, the segmented configuration of tensioned tendons, and the friction between tendons and guide holes. Additionally, tendon forces are not continuous but discrete, concentrated wrenches, with the frictional force magnitude and direction varying based on the TDCR's bending configuration. We propose a TDCR modeling method that integrates Cosserat rod theory with a finite element approach to address these limitations. We construct a Cosserat rod model for the robot's backbone, discretize the tendon geometry using the finite element method (FEM), and incorporate friction modeling between tendons and guide holes. Furthermore, we introduce an algorithm to determine the direction of friction forces, enhancing modeling accuracy. This approach results in a more realistic and comprehensive mathematical representation of TDCR behavior. Numerical simulations under various tendon-routing scenarios are conducted and compared with classical TDCR models. The results indicate that our friction-inclusive model improves accuracy, yielding an average configuration deviation of only 0.3% across different tendon routings. Experimental validation further confirms the model's accuracy and robustness.

Advancing Soft Robot Proprioception Through 6D Strain Sensors Embedding

Soft robots and bioinspired systems have revolutionized robot design by incorporating flexibility and deformable materials inspired by nature's ingenious designs. Similar to many robotic applications, sensing and perception are paramount to enable soft robots to adeptly navigate the unpredictable real world, ensuring safe interactions with both humans and the environment. Despite recent progress, soft robot sensorization still faces significant challenges due to the virtual infinite degrees of freedom of the system and the need for efficient computational models capable of estimating valuable information from sensor data. In this article, we present a new model-based proprioceptive system for slender soft robots based on strain sensing and a strain-based modeling approach called Geometric Variable-Strain (GVS). We develop a flexible 2-Plate 6D strain sensor (Flex-2P6D) capable of measuring the 6 dimensions (6D) strain at specific points of the soft robot with an accuracy higher than 95%. Coupled with the GVS approach, the proposed methodology is able to directly measure the configuration variables and reconstruct complex robot shapes with very high accuracy, even in very challenging conditions. The sensors are embedded inside the soft body, which makes them also suitable for underwater operation and physical interaction with the environment. Something that we also demonstrate experimentally. We believe that our approach has the potential to be applied across a wide variety of applications, including observation and exploration missions, as well as human-robot interaction, where the states of the system are required for implementing precise closed-loop control and estimation methods.

Integrated Design Fabrication and Control of a Bioinspired Multimaterial Soft Robotic Hand

Machines that mimic humans have inspired scientists for centuries. Bioinspired soft robotic hands are a good example of such an endeavor, featuring intrinsic material compliance and continuous motion to deal with uncertainty and adapt to unstructured environments. Recent research led to impactful achievements in functional designs, modeling, fabrication, and control of soft robots. Nevertheless, the full realization of life-like movements is still challenging to achieve, often based on trial-and-error considerations from design to fabrication, consuming time and resources. In this study, a soft robotic hand is proposed, composed of soft actuator cores and an exoskeleton, featuring a multimaterial design aided by finite element analysis (FEA) to define the hand geometry and promote finger's bendability. The actuators are fabricated using molding, and the exoskeleton is 3D-printed in a single step. An ON-OFF controller keeps the set fingers' inner pressures related to specific bending angles, even in the presence of leaks. The FEA numerical results were validated by experimental tests, as well as the ability of the hand to grasp objects with different shapes, weights, and sizes. This integrated solution will make soft robotic hands more available to people, at a reduced cost, avoiding the time-consuming design-fabrication trial-and-error processes.

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.

QPSO-MPC based tracking algorithm for cable-driven continuum robots

Cable-driven continuum robots (CDCRs) can flexibly travel through narrow space for complex workspace tasks. However, it is challenging to design the trajectory tracking algorithm for CDCRs due to their nonlinear dynamic behaviors and cable hysteresis characteristics. In this contribution, a model predictive control (MPC) tracking algorithm based on quantum particle swarm optimization (QPSO) is designed for CDCRs to realize effective trajectory tracking under constraints. In order to make kinematic analysis of a CDCR, the forward and inverse mapping among actuation space, joint space and work space is analyzed by using the piecewise constant curvature method and the homogeneous coordinate transformation. To improve the performance of conventional MPC for complex tracking tasks, QPSO is adopted in the rolling optimization of MPC for its global optimization performance, robustness and fast convergence. Both simulation and operational experiment results demonstrate that the designed QPSO-MPC presents high control stability and trajectory tracking precision. Compared with MPC and particle swarm optimization (PSO) based MPC, the tracking error of QPSO-MPC is reduced by at least 43 and 24%, respectively.

Modeling of Soft Pneumatic Actuators with Different Orientation Angles Using Echo State Networks for Irregular Time Series Data

Modeling of soft robotics systems proves to be an extremely difficult task, due to the large deformation of the soft materials used to make such robots. Reliable and accurate models are necessary for the control task of these soft robots. In this paper, a data-driven approach using machine learning is presented to model the kinematics of Soft Pneumatic Actuators (SPAs). An Echo State Network (ESN) architecture is used to predict the SPA’s tip position in 3 axes. Initially, data from actual 3D printed SPAs is obtained to build a training dataset for the network. Irregular-intervals pressure inputs are used to drive the SPA in different actuation sequences. The network is then iteratively trained and optimized. The demonstrated method is shown to successfully model the complex non-linear behavior of the SPA, using only the control input without any feedback sensory data as additional input to the network. In addition, the ability of the network to estimate the kinematics of SPAs with different orientation angles θ is achieved. The ESN is compared to a Long Short-Term Memory (LSTM) network that is trained on the interpolated experimental data. Both networks are then tested on Finite Element Analysis (FEA) data for other θ angle SPAs not included in the training data. This methodology could offer a general approach to modeling SPAs with varying design parameters.

Review of the exponential and Cayley map on SE(3) as relevant for Lie group integration of the generalized Poisson equation and flexible multibody systems

The exponential and Cayley maps on SE(3) are the prevailing coordinate maps used in Lie group integration schemes for rigid body and flexible body systems. Such geometric integrators are the Munthe–Kaas and generalized- α schemes, which involve the differential and its directional derivative of the respective coordinate map. Relevant closed form expressions, which were reported over the last two decades, are scattered in the literature, and some are reported without proof. This paper provides a reference summarizing all relevant closed-form relations along with the relevant proofs, including the right-trivialized differential of the exponential and Cayley map and their directional derivatives (resembling the Hessian). The latter gives rise to an implicit generalized- α scheme for rigid/flexible multibody systems in terms of the Cayley map with improved computational efficiency.