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To aid in real-world situations, soft robots need to be able to estimate their state and external interactions based on proprioceptive sensors. Estimating disturbances allows a soft robot to perform desirable force control. However, even in the case of rigid manipulators, force estimation at the end-effector is seen as a non-trivial problem. And indeed, current approaches to address this challenge have shortcomings that prevent their general application. They are often based on simplified soft dynamic models, such as the ones relying on a piece-wise constant curvature approximation or matched rigid-body models that do not represent enough details of the problem. This severely limits applications in complex human-robot interaction. Finite element method (FEM) based modeling allows for predictions of soft robot dynamics in a more generic fashion. Here, using the soft robot modeling capabilities of the frame-work SOFA, we built a detailed FEM model of a multi-segment soft continuum robotic arm composed of compliant deformable materials and fiber-reinforced pressurized actuation chambers. In addition, a model for sensors that provide orientation output is presented. This model is used to establish a state observer for the manipulator. The sensor model is adequate for representing the output of flexible bend sensors as well as orientations provided by IMUs or coming from tracking systems, all of which are popular choices in soft robotics. Model parameters were calibrated to match imperfections of the manual fabrication process using physical experiments. We then solve a quadratic programming inverse statics problem to compute the components of external force that explain the pose mismatch. Our experiments show an average force estimation error of around 1.2&#x0025;. As the methods proposed are generic, these results are encouraging for the task of building soft robots exhibiting complex, reactive, sensor-based behavior that can be deployed in human-centered environments.

Model-Based Disturbance Estimation for a Fiber-Reinforced Soft Manipulator using Orientation Sensing