Versatile graceful degradation framework for bio-inspired proprioception with redundant soft sensors

Abstract

Reliable proprioception and feedback from soft sensors are crucial for enabling soft robots to function intelligently in real-world environments. Nevertheless, soft sensors are fragile and are susceptible to various damage sources in such environments. Some researchers have utilized redundant configuration, where healthy sensors compensate instantaneously for lost ones to maintain proprioception accuracy. However, achieving consistently reliable proprioception under diverse sensor degradation remains a challenge. This paper proposes a novel framework for graceful degradation in redundant soft sensor systems, incorporating a stochastic Long Short-Term Memory (LSTM) and a Time-Delay Feedforward Neural Network (TDFNN). The LSTM estimates readings from healthy sensors to compare them with actual data. Then, statistically abnormal readings are zeroed out. The TDFNN receives the processed sensor readings to perform proprioception. Simulation experiments with a musculoskeletal leg that contains 40 nonlinear soft sensors demonstrate the effectiveness of the proposed framework. Results show that the knee angle proprioception accuracy is retained across four distinct degradation scenarios. Notably, the mean proprioception error increases by less than 1.91°(1.36%) when $30\%$ of the sensors are degraded. These results suggest that the proposed framework enhances the reliability of soft sensor proprioception, thereby improving the robustness of soft robots in real-world applications.

Keywords: graceful degradation; neural network; proprioception; redundant sensors; self-adaptation; soft sensors and actuators.

FIGURE 1

A simple example of non-unique mapping. One resistive soft sensor (white) is embedded in a pressure-driven soft extending actuator (blue) with tubings (black). When the sensor is partially torn, its resistance typically increases (Hegde et al., 2023). Consequently, the distorted sensor readings (upside) become identical to those of a healthy sensor with a longer actuator length (bottom), leading to non-unique mapping.

FIGURE 2

The simulation testbed and architecture of the proposed framework. Supplementary Figure S1 in the supplemental material provides the detailed process flow. The $u_t$ , ${\theta }_t$ , and $y_t$ represent the control input, the target state for proprioception, and the sensor readings at time step $t$ . The LSTM is responsible for fault detection, while the TDFNN performs proprioception. First, the LSTM zeroes out statistically abnormal sensor readings. These processed readings are then input to the TDFNN, which outputs the estimated states. As a result, the framework achieves graceful degradation and realizes reliable proprioception despite diverse degradation in the constituent soft sensors.

FIGURE 3

Musculoskeletal leg models used in the experiments.

FIGURE 4

Example of simulated sensor response (blue) and corresponding sensor length (red). This sensor was attached to the Short Biceps (SB).

FIGURE 5

The average RMSEs of proprioception for each of the degradation scenarios. Five trials were conducted for both the Separate and Consecutive datasets. The error bar indicates the standard deviation. The blue bars show the proprioception results without the fault detection.

FIGURE 6

An example of proprioception with the Consecutive dataset. (A) The actual angle of the knee joint angle (blue dotted line), the result without degradation (green dash dot line), and the result with different degradation for every 20 s (red line). (B) The corresponding result of the fault detection for one of the sensors of each muscle. The blue line denotes the actual sensor readings. The red line and band denotes ${\widehat{\mu }}_t$ and $3{\widehat{\sigma }}_t$ , respectively. The grey vertical bands indicate successful fault detection, while the pink ones display false positives.

FIGURE 7

Proprioception RMSEs with different percentages of degraded sensors. The RMSE values are the average of five trials, and the error bars indicates the standard deviations. The blue bars show the proprioception results without fault detection.

FIGURE 8

The average proprioception RMSEs with different musculoskeletal leg models. The error bars indicate the standard deviations of the five trials. (A) Separate dataset. (B) Consecutive dataset.

FIGURE 9

The contribution of the meta-voting algorithm to prevent external loads from affecting proprioception accuracy. (A) The actual angle of the knee joint angle (blue dotted line), the result without the meta-voting (green line), and the result with the meta-voting (red line). The foot position (i.e., the knee joint angle) was fixed at $t=50$ . (B) Examples of the corresponding LSTM outputs. The blue line denotes the actual sensor readings. The red line and band denotes ${\widehat{\mu }}_t$ and $3{\widehat{\sigma }}_t$ , respectively. The pink vertical bands display false positives.