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The technological differences between traditional robotics and soft robotics have an impact on all of the modeling tools generally in use, including direct kinematics and inverse models, Jacobians, and dynamics. Due to the lack of precise modeling and control methods for soft robots, the promising concepts of using such design for complex applications (medicine, assistance, domestic robotics, etc.) cannot be practically implemented. This paper presents a first unified software framework dedicated to modeling, simulation, and control of soft robots. The framework relies on continuum mechanics for modeling the robotic parts and boundary conditions like actuators and contacts using a unified representation based on Lagrange multipliers. It enables the digital robot to be simulated in its environment using adirectmodel. The model can also be inverted online using an optimization-based method which allows to control the physical robots in the task space. To demonstrate the effectiveness of the approach, we present various soft robots scenarios including ones where the robot is interacting with its environment. The software has been built on top of SOFA, an open-source framework for deformable online simulation and is available athttps://project.inria.fr/softrobot/. [ABSTRACT FROM PUBLISHER]