Accurate Embedded Force Sensor for Soft Robots with Rate-dependent Deep Neural Calibration

Abstract

Embedding force sensors on soft robots have been a major challenge impeding accurate feedback control of soft robots. A major challenge in embedding force sensors onto soft robots is in their rigidity, size, and shape. In this study, a soft smart polymer-based soft sensor for soft robotic application is proposed, prototyped, calibrated, and tested for force prediction accuracy. The sensing element of the proposed sensor was made of gelatin-graphite composite that we previously showed its piezoresistivity. Three sensing elements were molded into a soft body (soft robot) and variation of the voltage across them was measured in real-time in response to external loads. A rate-dependent deep neural calibration network was trained with the three voltages and their temporal rates when the soft body was subjected to tri-axial external forces in the range of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\pm 0.3$</tex> N. Afterwards the calibrated sensor was used in a series of validation tests to assess its accuracy. The proposed calibration showed the goodness of fit of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R^{2}=0.98$</tex> with the mean-absolute error of 0.005 N. Also, the sensor exhibited mean-absolute errors of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.007 \pm0.005$</tex> N, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.008 \pm 0.006$</tex> N, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.011 \pm 0.008 \ \mathbf{N}$</tex> for estimating the external forces along x, y, and z directions. Moreover, the proposed calibration did not exhibit observable hysteresis thanks to its rate-dependent calibration schema.