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

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 $\pm 0.3$ 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 $R^{2}=0.98$ with the mean-absolute error of 0.005 N. Also, the sensor exhibited mean-absolute errors of $0.007 \pm0.005$ N, $0.008 \pm 0.006$ N, and $0.011 \pm 0.008 \ \mathbf{N}$ 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.