Localized Motion Dynamics Modeling of A Soft Robot: A Data-Driven Adaptive Learning Approach

Soft continuum robots are more and more used in various applications due to the multiple advantages offered by the properties of hyper-elastic soft materials, such as resilience, flexibility, etc. Despite all these essential properties that make the soft robots good candidates for some real-life needs (form enclosure grasping, obstacle-free navigation, etc.), controlling their shape remains challenging because of their hyper-redundancies. This letter investigates an inverse dynamics model-based shape control of soft continuum robots in the presence and absence of external efforts. To that end, modeling based on Pythagorean Hodograph (PH) curves with prescribed lengths is combined with Euler-Bernoulli modeling to reconstruct the robot shapes and then calculate the actuator inputs in the case of external efforts. Thus, a relationship between the actuator inputs and the PH control points is obtained. With the above strategy, the actuator inputs can be computed accordingly, and therefore, real-time shape control of the soft robots for various tasks becomes possible. The results of the proposed approach are validated both numerically and experimentally using two classes of soft continuum robots - a Fluidic Elastomeric Actuator (FEA), describing a 2D soft finger robot, with a single and multiple phalanges, and a 3D continuum manipulator, namely the Compact Bionic Handling Assistant (CBHA).

In this paper, we present a novel method for controlling an unmanned ground vehicle (UGV) by using a new machine learning technique, Deterministic Learning (DL). With DL the robot is able to learn and recognize four specifically designed body gestures, which represent four corresponding moving directions (i.e., left, right, forward, and backward) of the controlled UGV. A Kinect camera is employed to collect human body skeleton data of a user. Eight specifically-designed features are extracted and utilized to train radial basis function neural networks (RBFNNs). The dynamics of the human arm waving motion is guaranteed to be accurately identified, represented, and stored as an RBFNN model with converged constant NN weights, which facilitates rapid recognition in the online identification phase. However, learning time of and storage space of RBFNNs grow exponentially with the number of features. In order drastically reduce required computations and storage space, we propose to split the features in subgroups, and use each subgroup to learn a smaller independent. In the online identification phase, the trained RBFNNs are used to analyze and identify any new incoming gestures. The identification results of all RBFNNs are then fused together following a probabilistic approach, and the gestures of the user are interpreted as commands for the UGV.

Soft robots are primarily composed of soft materials that can allow for mechanically robust maneuvers that are not typically possible with conventional rigid robotic systems. However, owing to the current limitations in simulation, design and control of soft robots often involve a painstaking trial. With the ultimate goal of a computational framework for soft robotic engineering, here we introduce a numerical simulation tool for limbed soft robots that draws inspiration from discrete differential geometry based simulation of slender structures. The simulation incorporates an implicit treatment of the elasticity of the limbs, inelastic collision between a soft body and rigid surface, and unilateral contact and Coulombic friction with an uneven surface. The computational efficiency of the numerical method enables it to run faster than real-time on a desktop processor. Our experiments and simulations show quantitative agreement and indicate the potential role of predictive simulations for soft robot design.

This research investigates designing a continuum soft robot and proposing a kinematic matching control to enable the robot to perform a specified medical task, which in this paper is the transesophageal echocardiography (TEE). A multi-chamber soft robot was designed and fabricated based on the molding of separate layers. The method of transformation matrices was used to develop the kinematic models, and a control method using Jacobian matrices was proposed to manipulate the robot. A prototype was made based on a multi-chamber multi-layer design. The system contains three segments that can be actuated independently to mimic the active bending part of the respective probe. Kinematic models were developed. Negative pressure (vacuum) was used as actuation input. An open-loop controller inspired by a redundancy resolution technique was proposed to make the soft robot tip follow the desired path, i.e.the path of the rigid ultrasound probe. It is concluded that the soft solution can perform the required task as the reachable points of the TEEtip cover the proposed robot workspace and the proposed control can be used for maneuvering in arbitrary trajectories.

Simulating soft robots offers a cost-effective approach to exploring their design and control strategies. While current models, such as finite element analysis, are effective in capturing soft robotic dynamics, the field still requires a broadly applicable and efficient numerical simulation method. In this letter, we introduce a discrete differential geometry-based framework for the model-based inverse design of a novel snap-actuated jumping robot. Our findings reveal that the snapping beam actuator exhibits both symmetric and asymmetric dynamic modes, enabling tunable robot trajectories (e.g., horizontal or vertical jumps). Leveraging this bistable beam as a robotic actuator, we propose a physics-data hybrid inverse design strategy to endow the snap-jump robot with a diverse range of jumping capabilities. By utilizing a physical engine to examine the effects of design parameters on jump dynamics, we then use extensive simulation data to establish a data-driven inverse design solution. This approach allows rapid exploration of parameter spaces to achieve targeted jump trajectories, providing a robust foundation for the robot's fabrication. Our methodology offers a powerful framework for advancing the design and control of soft robots through integrated simulation and data-driven techniques.

This article introduces a model-based robust control framework for electrohydraulic soft robots. The methods presented herein exploit linear system control theory as it applies to a nonlinear soft robotic system. We employ dynamic mode decomposition with control (DMDc) to create appropriate linear models from real-world measurements. We build on the theory by developing linear models in various operational regions of the system to result in a collection of linear plants used in uncertainty analysis. To complement the uncertainty analyses, we utilize ("H Infinity") synthesis techniques to determine an optimal controller to meet performance requirements for the nominal plant. Following this methodology, we demonstrate robust control over a multi-input multi-output (MIMO) hydraulically amplified self-healing electrostatic (HASEL)-actuated system. The simplifications in the proposed framework help address the inherent uncertainties and complexities of compliant robots, providing a flexible approach for real-time control of soft robotic systems in real-world applications.

Advancement in technology has seen to a rise in applications of soft robots and the demands for their control are also growing. At present, the pressure control system is bloated and slow to respond, which makes the continuous control of soft robot based on pressure-driven more difficult than that of the rigid. In nature, arthropods use the combination of fluid resistance in blood vessels and lymphatic vessels to achieve limbs bending, which provide inspirations for the control of soft robots. In this study, based on the spider limb control, six proportional solenoid valves are designed, each of which can be quickly connected with other valves to form the required hydraulic bridge. Based on theoretical analysis and computational fluid dynamics (CFD) simulation, the pressure control characteristics of type A, B, and C hydraulic Bridges are presented. Through experiments, the relationship between pressure and control current is found to verify the relevant features of the hydraulic system. Because of the good pressure control characteristics of the C-bridge, it is used to drive the soft robotic arm. The experimental results show that this water hydraulic system can control soft robots continuously.

Soft robots demonstrate superior flexibility and maneuverability than traditional rigid robots in many emerging applications. However, it is challenging to have a general modeling and control methodology to deal with soft body dynamics and its interactions with environment. We present a spline-based modeling and control framework for soft robotic systems. The dynamic model is built on non-uniform rational Bsplines (NURBS) that captures material and physical properties of soft body, while preserving exact geometric dynamics with environmental interactions. Using the NURBS-based dynamic model, the robotic optimal control based on general predictive control is designed through coordination among the finite number of control points. Therefore, the infinite-dimensional motion of soft body can be realized by significantly reduced finite particle motion control. We demonstrate the performance of the modeling and motion control framework using the snakeinspired robot simulations and experiments.

This paper proposes a novel decentralized approach to kinematic control of soft segmented continuum robots based on a consensus strategy. The robots under consideration deform in a plane according to a multi-segment Piecewise Constant Curvature (PCC) kinematic model in which each segment is represented as an equivalent rigid-link Revolute-Prismatic-Revolute (RPR) mechanism. In our approach, we assume that each segment of the robot is equipped with sensors to measure joint variables in its local coordinate frame and can communicate with its two adjacent segments. Our consensus-based decentralized control strategy provides an alternative to conventional control methods, which solve the inverse kinematic problem by using computationally intensive numerical methods to calculate the robot's Jacobian matrix at each time instant. We investigate the stability and convergence properties of proposed controllers for position regulation and trajectory tracking tasks and provide theoretical guarantees on the controllers' performance. We evaluate the controllers in simulation for scenarios in which the robot's tip must reach a certain position or follow a specified trajectory. We compare the performance of the position regulator for different controller gains, and we find that a simulated 15-link robot can track a complex reference trajectory with an average root-mean-square error of only 0.16% of the robot's initial length.

The application of radial basis function neural networks (RBFN) to predict the ultimate torsional strength of reinforced concrete (RC) beams is explored in this study. A database on torsional failure of RC beams with rectangular section subjected to pure torsion was retrieved from past experiments in the literature; several RBFN models are sequentially built, trained and tested. Then the ultimate torsional strength of each beam is determined from the developed RBFN models. In addition, the predictions of the RBFN models are also compared with those obtained using the ACI 318 Code equations. The study shows that the RBFN models give reasonable predictions of the ultimate torsional strength of RC beams. Moreover, the results also show that the RBFN models provide better accuracy than the existing ACI 318 equations for torsion, both in terms of root-mean-square error and coefficients of determination.

Effectively avoiding methane accidents is vital to the security of manufacturing minerals. Coal mine methane accidents are often caused by a methane concentration overrun, and accurately predicting methane emission quantity in a coal mine is key to solving this problem. To maintain the concentration of methane in a secure range, grey theory and neural network model are increasingly used to critically forecasting methane emission quantity in coal mines. A limitation of the grey neural network model is that researchers have merely combined the conventional neural network and grey theory. To enhance the accuracy of prediction, a modified grey GM (1,1) and radial basis function (RBF) neural network model is proposed, which combines the amended grey GM (1,1) model and RBF neural network model. In this article, the proposed model is put into a simulation experiment, which is built based on Matlab software (MathWorks.Inc, Natick, Masezius, U.S). Ultimately, the conclusion of the simulation experiment verified that the modified grey GM (1,1) and RBF neural network model not only boosts the precision of prediction, but also restricts relative error in a minimum range. This shows that the modified grey GM (1,1) and RBF neural network model can make more effective and precise predict the predicts, compared to the grey GM (1,1) model and RBF neural network model.

Achieving accurate closed-loop position control of soft robots remains an ongoing research problem, due to the challenges posed by underactuation, elastic nonlinearities, and material creep. Although soft driving technologies relying on tendons and smart material transducers (e.g., dielectric elastomers, shape memory alloys) offer more ease of controllability compared to pneumatics, the corresponding controller design problem becomes even more challenging because of additional nonlinear effects. Those include a configuration-dependent actuation matrix, that stems from the kinematics of the actuation, and control input saturation, which is especially critical for smart material actuators. In this article, we investigate for the first time the closed-loop position control of a soft-robotic system driven by dielectric elastomer actuators. The objective is to regulate the robot state to a constant setpoint, accounting for the effects of open-loop instability, underactuation, control input saturation, and constant external disturbances. To achieve this goal, we propose a model-based feedback scheme, which combines a stabilizing energy-shaping controller with a robustifying PI-like law. After presenting the general theory, a linear matrix inequalities algorithm is proposed to practically address the controller design in spite of strong model nonlinearities. Experimental validation conducted on a prototype of the soft-robotic system confirms the effectiveness of the proposed control approach.

Fluidic soft robots have the advantages of inherent compliance and adaptability, but they are significantly restricted by complex control systems and bulky power devices, including fluidic valves, fluidic pumps, electrical motors, as well as batteries, which make it challenging to operate in narrow space, energy shortage, or electromagnetic sensitive situations. To overcome the shortcomings, we develop portable human-powered master controllers to provide an alternative solution for the master-slave control of the fluidic soft robots. Each controller can supply multiple fluidic pressures to the multiple chambers of the soft robots simultaneously. We use modular fluidic soft actuators to reconfigure soft robots with various functions as control objects. Experimental results show that flexible manipulation and bionic locomotion can be simply realized using the human-powered master controllers. The developed controllers which eliminate energy storage and electronic components can provide a promising candidate of soft robot control in surgical, industrial, and entertainment applications.

As a link for energy transfer between the land and atmosphere in the terrestrial ecosystem, karst vegetation plays an important role. Karst vegetation is not only affected by environmental factors but also by intense human activities. The nonlinear characteristics of vegetation growth are induced by the interaction mechanism of these factors. Previous studies of this relationship were not comprehensive, and it is necessary to further explore it using a suitable method. In this study, we selected climate, human activities, topography, and soil texture as the response factors; a nonlinear relationship model between the karst normalized difference vegetation index (NDVI) and these factors was established by applying a back propagation neural network (BPNN), a radial basis function neural network (RBFNN), the random forest (RF) algorithm, and support vector regression (SVR); and then, the karst NDVI was predicted. The coefficient of determination (R2), mean square error (MSE), root mean square error (RMSE), and mean absolute percentage error (MAPE) of the obtained results were calculated, and the mean R2 values of the BPNN, RBFNN, RF, and SVR models were determined to be 0.77, 0.86, 0.89, and 0.91, respectively. Compared with the BPNN, RBFNN, and RF models, the SVR model had the lowest errors, with mean MSE, RMSE, and MAPE values of 0.001, 0.02, and 2.77, respectively. The results show that the BPNN, RBFNN, RF, and SVR models are within acceptable ranges for karst NDVI prediction, but the overall performance of the SVR model is the best, and it is more suitable for karst vegetation prediction.

Soft robots have great potential in surgical applications due to their compliance and adaptability to their environment. However, their flexibility and nonlinearity bring challenges for precise modeling, sensing, and control, especially in constrained cavities. In this article, a simple, compact two-segment soft robot for flexible laser ablation is proposed. The proximal hydraulic-driven segment can offer omnidirectional bending so as to navigate toward lesions. The distal segment driven by tendons enables precise, fast steering of laser collimator for laser sweeping on lesion targets. The dynamics of such mechanical steering motion can be enhanced with a metal spring backbone integrated along the collimator, thus facilitating the control with certain linearity and responsiveness. A soft robot modeling and control scheme based on Koopman operators is proposed. We also design a disturbance observer so as to incorporate the controller feedback with real-time fiber optic shape sensing. Experimental validation is conducted on simulated or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex-vivo</i> laser ablation tasks, thus evaluating our control strategies in laser path following across various contours/patterns. As a result, such a simple compact laser manipulation can perform up to 6 Hz sweeping with precision of path following errors below 1 mm. Such modeling and control scheme could also be used on an endoscopic laser ablation robot with unsymmetric mechanism driven by two tendons.