This paper presents a novel framework to realize proprioception and
closed-loop control for soft manipulators. Deformations with large elongation
and large bending can be precisely predicted using geometry-based sensor
signals obtained from the inductive springs and the inertial measurement units
(IMUs) with the help of machine learning techniques. Multiple geometric signals
are fused into robust pose estimations, and a data-efficient training process
is achieved after applying the strategy of sim-to-real transfer. As a result,
we can achieve proprioception that is robust to the variation of external
loading and has an average error of 0.7% across the workspace on a
pneumatic-driven soft manipulator. The realized proprioception on soft
manipulator is then contributed to building a sensor-space based algorithm for
closed-loop control. A gradient descent solver is developed to drive the
end-effector to achieve the required poses by iteratively computing a sequence
of reference sensor signals. A conventional controller is employed in the inner
loop of our algorithm to update actuators (i.e., the pressures in chambers) for
approaching a reference signal in the sensor-space. The systematic function of
closed-loop control has been demonstrated in tasks like path following and
pick-and-place under different external loads