  For soft robots to work effectively in human-centered environments, they 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. Even in the case of rigid manipulators, force
estimation at the end-effector is seen as a non-trivial problem. And indeed,
other 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
(PCC) approximation or matched rigid-body models that do not represent enough
details of the problem. Thus, the applications needed for complex human-robot
interaction can not be built. Finite element methods (FEM) allow for
predictions of soft robot dynamics in a more generic fashion. Here, using the
soft robot modeling capabilities of the framework SOFA, we build a detailed FEM
model of a multi-segment soft continuum robotic arm composed of compliant
deformable materials and fiber-reinforced pressurized actuation chambers with a
model for sensors that provide orientation output. This model is used to
establish a state observer for the manipulator. Model parameters were
calibrated to match imperfections of the manual fabrication process using
physical experiments. We then solve a quadratic programming inverse dynamics
problem to compute the components of external force that explain the pose
error. Our experiments show an average force estimation error of around 1.2%.
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.
