The finite element method (FEM) is a powerful modeling tool for predicting soft robots' behavior, but its computation time can limit practical applications. In this article, a learning-based approach based on condensation of the FEM model is detailed. The proposed method handles several kinds of actuators and contacts with the environment. We demonstrate that this compact model can be learned as a unified model across several designs and remains very efficient in terms of modeling since we can deduce the direct and inverse kinematics of the robot. Building upon the intuition introduced in (Ménager et al., 2023), the learned model is presented as a general framework for modeling, controlling, and designing soft manipulators. First, the method's adaptability and versatility are illustrated through optimization-based control problems involving positioning and manipulation tasks with mechanical contact-based coupling. Second, the low-memory consumption and the high prediction speed of the learned condensed model are leveraged for real-time embedding control without relying on costly online FEM simulation. Finally, the ability of the learned condensed FEM model to capture soft robot design variations and its differentiability are leveraged in calibration and design optimization applications.

Soft slender robots have attracted more and more research attentions in these years due to their continuity and compliance natures. However, mechanics modeling for soft robots interacting with environment is still an academic challenge because of the non-linearity of deformation and the non-smooth property of the contacts. In this work, starting from a piece-wise local strain field assumption, we propose a nonlinear dynamic model for soft robot via Cosserat rod theory using Newtonian mechanics which handles the frictional contact with environment and transfer them into the nonlinear complementary constraint (NCP) formulation. Moreover, we smooth both the contact and friction constraints in order to convert the inequality equations of NCP to the smooth equality equations. The proposed model allows us to compute the dynamic deformation and frictional contact force under common optimization framework in real time when the soft slender robot interacts with other rigid or soft bodies. In the end, the corresponding experiments are carried out which valid our proposed dynamic model.

In this article, we propose a new continuum robotics approach for haptic rendering and comanipulation. This approach is illustrated using a robotic interface with six motorized fixed axes connected by deformable beams, in parallel, to an end effector with 5 degrees of freedom. Apart from the rotation of the motors, this design has no articulation, and the motion of the end effector is achieved by deformation of the beams. The flexible beams are equipped with bending sensors, and the motors have encoders. We use a nonlinear finite element mechanical model of the robot based on a mesh of beam elements that is computed in real time at 20 Hz. The bending sensors are incorporated into the model, which allows us to obtain an accurate estimate of the force exerted by the user on the end effector. The model enables a new methodology for calculating the workspace of the continuum haptic device. The model also is propagated to a higher frequency loop (500 Hz), which performs sensing and control of the robot at high rates, using an admittance-type control to command new positions of the actuators. We show that this control methodology allows haptic rendering of virtual walls that are stiffer than the natural stiffness of the robot. Finally, we demonstrate the use of the device for simple comanipulation tasks.

Soft robot is an emergent research field which has variant promising applications. However, the design of soft robots nowadays still follows the trial-and-error process, which is not at all efficient. This paper proposes to design soft robots by pre-checking controllability during the numerical design phase. Finite-element method is used to model the dynamics of silicone soft robots, based on which the differential geometric method is applied to analyze the controllability of the points of interest. Such a verification is also investigated via model order reduction technique and Galerkin projection. The proposed methodology is finally validated by numerically designing a controllable parallel soft robot.

This paper is concerned with state estimation for continuous-time nonlinear systems. By means of a polytopic exact representation of the system using interpolation functions whose premise variables can be unmeasured, the differential mean value theorem and a quadratic Lyapunov function are used to provide conditions in the form of linear matrix inequalities, guaranteeing the state estimation error to be asymptotically driven to zero. A robust extension of the proposed observer design performing H∞ disturbance rejection is also presented. Examples illustrating the effectiveness of the developed novelties against former results are included.

In this paper, we propose a strategy for the control of soft robots with visual tracking and simulation-based predictor. A kinematic model of soft robots is obtained thanks to the Finite Element Method (FEM) computed in real-time. The FEM allows to obtain a prediction of the Jacobian matrix of the robot. This allows a first control of the robot, in the actuator space. Then, a second control strategy based on the feedback of infrared cameras is developed to obtain a correction of the effector position. The robust stability of this closed-loop system is obtained based on Lyapunov stability theory. Otherwise, to deal with the problem of image features (the marker points placed on the end effector of soft robot) loss, a switched control strategy is proposed to combine both the open-loop controller and the closed-loop controller. Finally, experiments on a parallel soft robot driven by four cables are conducted and show the effectiveness of these methods for the real-time control of soft robots.

This paper aims at providing a novel approach to modeling and controlling soft robots. Based on real-time Finite Element Method (FEM), we obtain a globally defined discrete-time kinematic model in the workspace of soft robots. From the kinematic equations, we deduce the soft-robot Jacobian matrix and discuss the conditions to avoid singular configurations. Then, we propose a novel observer based control methodology where the observer is built by Finite Element Model in this paper to deal with the control problem of soft robots. A closed-loop controller for position control of soft robot is designed based on the discrete-time model with feedback signal being extracted by means of visual servoing. Finally, experimental results on a parallel soft robot show the efficiency and performance of our proposed controller.

In this paper, a novel approach for controller design and H∞disturbance rejection of continuous-time Takagi-Sugeno descriptor models, is presented. This approach is based on a matrix transformation [1] which eliminates the parameter dependency of the linear matrix inequalities arising in some recent results. The proposed approach is an alternative to former results on the same subject (includes and outperforms previous results or act as a complement of other approaches) as shown both theoretically and via illustrative examples.

In this paper, a line-integral fuzzy Lyapunov function is proposed for stability and stabilization of continuous-time Takagi-Sugeno descriptor models. The scheme enhances the relaxation due to the Lyapunov function by combining it with an application of the Finsler's lemma which allows an independent controller design up to second order systems. The proposed approach includes and outperforms former results on the same subject as shown both theoretically and via illustrative examples.

This paper presents a novel approach for controller design of Takagi-Sugeno models based on decoupling a quadratic Lyapunov function from a progressively more complex non-parallel distributed compensation control law. Inspired in recent results from the linear parameter varying literature, which provide a way to find parameter-dependent linear matrix inequalities, the proposed generalization includes former PDC quadratic cases as well as some recent approaches. Examples are provided to illustrate the aforementioned contributions.

This paper addresses the problem of the position/force tracking in teleoperation system and proposes a haptic proxy control scheme. Compared to previous works, communication delays are assumed to be both time-varying and asymmetric, and the response of the synchronization and the transparency are improved. The control design is performed using Linear Matrix Inequality (LMI) optimization based on Lyapunov-Krasovskii functionals (LKF) and H∞control theory. With the designed controllers, the simulations of different working conditions, such as abrupt motion and wall contact, are performed and show the effectiveness of the proposed solution.

This paper deals with the stabilization of a class of discrete nonlinear models, namely those in the Takagi-Sugeno form; its main goal is to reduce conservatism of existing stabilization conditions using a special class of candidate Lyapunov functions and an enhanced control law. It is shown that the use of the aforementioned Lyapunov function leads to less-pessimistic solutions. The usefulness of the new control law is shown through several examples.

Many Takagi–Sugeno (T--S) fuzzy control-synthesis problems in the literature are expressed as the problem of finding decision variables in a double convex sum (fuzzy summation) of positive definite matrices. Matrices’ coefficients in the summation take values in the standard simplex. This paper presents a triangulation approach to the problem of generating simplicial partitions of the standard simplex in order to set up a family of sufficient conditions and, in parallel, another family of necessary ones for fuzzy summations. The conditions proposed in this paper are asymptotically exact as the size of the involved simplices decreases; its conservativeness vanishes for a sufficiently fine partition (sufficiently dense mesh of vertex points). The set of conditions is in the form of linear matrix inequalities (LMIs), for which efficient software is available.

This paper presents a new approach for stability analysis and Hinfincontroller design of Takagi-Sugeno (TS) models. The analysis considers information derived from existing or induced order relations among the membership functions. Partitioning of the state-space and the use of piecewise conditions arise naturally as a consequence of induced order relations. Conditions under the novel approach can be expressed as linear matrix inequalities (LMIs). Examples are provided that show the advantages over the classical quadratic approach.

In this paper the relaxed stability conditions and the design of stabilization controller for discrete Takagi-Sugeno fuzzy time-delay model are considered through a new approach using specific Lyapunovpsilas functions. Firstly, we give some relaxed sufficient conditions for stability of discrete T-S time-delay model via LMIs. Secondly, we consider the problems of stabilization for such models in two different cases, whether the time-delay is known or unknown. All the presented results outperform previous ones found in the literature and several examples are presented to illustrate the effectiveness of the method.

Conditions about the stabilization of Takagi-Sugeno fuzzy models can systematically be derived and solved usually using linear matrix inequality problems. Current research tries to lower any pessimism. However, often it leads to an important increase in the number of decision variables, and problems become unsolvable. In this correspondence, we choose to reduce the number of decision variables while not raising the conservatism in comparison with previous results. This correspondence deals with the discrete case, which is harder to solve. We supply results about the stabilization, the regulator problem, and also H( infinity) control.

This work deals with relaxed conditions for the stabilization of discrete-time Takagi-Sugeno models. The paper is based on previous results which are the best known to our knowledge. These results consider the A-sample variation of a candidate Lyapunov function to derive LMI stabilization conditions. This paper gives some enhancement of these results and shows their effectiveness through some examples.