Curvature and force estimation for a soft finger using an EKF with unknown input optimization

Sensory data such as bending curvature and contact force are essential for controlling soft robots. However, it is inconvenient to measure these variables because sensorizing soft robots is difficult due to their inherent softness. An attractive alternative is to use an observer/filter to estimate the variables that would have been measured by those sensors. Nevertheless, an observer/filter requires a model which can be analytically demanding for soft robots due to their high nonlinearity. In this paper, we propose an Unknown Input Extended Kalman Filter (UI-EKF) consisting of an EKF interconnected with a UI-optimizer to respectively estimate the state (curvature) and unknown input (contact force) for a pneumatic-based soft finger based on an identified nonlinear model. We also prove analytically that the estimation errors are bounded. Experimental results show that the UI-EKF can perform the estimation with high accuracy, even when the identified system model is not accurate and the sensor measurement is noisy. In other words, the proposed framework is able to estimate proprioceptive (internal) and exteroceptive (external) variables (curvature and contact force respectively) of the robot using a single sensor (flex), which is still an open problem in soft robotics.