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.

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 presents a development of a new method dedicated to the modeling and control of Continuum Robots, based on the Finite Element Method (FEM) using quasi-static assumption. The modeling relies on a discretization of the continuum robots using 6 DoFs Frames along the structure of the robot that is compatible with the modeling of a sequence of rigid vertebras. When the robot's structure relies on rods with constant sections, internal forces are computed with beam elements, placed between two adjacent frames, that applies forces and torques. In the opposite, when the robot is composed of a complex shape deformable backbone separated by the rigid vertebras, a domain decomposition strategy is used to obtain an equivalent stiffness between two vertebras using volumetric FEM. In both cases, for solving the whole robot model and inverting it in real-time, the numerical method takes advantage of the serial nature of continuum robots, using a Block-Tri-Diagonal solver. The factor of improvement in the computation time reaches several order of magnitude compared to a classical FEM model, while keeping a good precision. The method has also been implemented and tested on a real pneumatic CBHA trunk designed by Festo Robotics and some complementarity examples have been generated numerically.