Enhanced Model-Free Dynamic State Estimation for a Soft Robot Finger Using an Embedded Optical Waveguide Sensor

TL;DR

Soft robots require proprioception amid nonlinear dynamics and underactuation. The authors embed a semidivided-core stretchable optical waveguide sensor into a PneuNet finger and train NARX networks to estimate end-effector state from sensor signals and pressures without manually decoupling strain modes. The full-signal model MC achieves a $51\%$ reduction in end-effector position error (from $5.70$ mm to $2.80$ mm) with notable gains in x/y tracking, demonstrating strong data-driven state estimation for soft robots. This work provides a practical pathway toward MPC-enabled control of soft grippers using advanced optical sensors and paves the way for more structured multimodal soft sensors in learning-based soft-robot perception and control.

Abstract

In this letter, an advanced stretchable optical waveguide sensor is implemented into a multidirectional PneuNet soft actuator to enhance dynamic state estimation through a NARX neural network. The stretchable waveguide featuring a semidivided core design from previous work is sensitive to multiple strain modes. It is integrated into a soft finger actuator with two pressure chambers that replicates human finger motions. The soft finger, designed for applications in soft robotic grippers or hands, is viewed in isolation under pneumatic actuation controlled by motorized linear stages. The research first characterizes the soft finger's workspace and sensor response. Subsequently, three dynamic state estimators are developed using NARX architecture, differing in the degree of incorporating the optical waveguide sensor response. Evaluation on a testing path reveals that the full sensor response significantly improves end effector position estimation, reducing mean error by 51\% from 5.70 mm to 2.80 mm, compared to only 21\% improvement to 4.53 mm using the estimator representing a single core waveguide design. The letter concludes by discussing the application of these estimators for (open-loop) model-predictive control and recommends future focus on advanced, structured soft (optical) sensors for model-free state estimation and control of soft robots.

Figures (7)

• Figure 1: Custom PneuNet finger with integrated waveguide featuring a semidivided core. (a) Waveguide design and cross section photo. (b) Four views of the full PneuNet finger design.
• Figure 2: 2DOF PneuNet soft finger actuation and system. (a) Example actuation states including full pressure in both inlets (flexion) as well as left and right bending for the PneuNet finger. (b) Pneumatic system for soft finger actuation and image capturing setup. (c) Example image of the recorded data set and its image processing.
• Figure 3: Soft finger work space and waveguide sensor characterization. (a) Work space on a $9 \times 9$ grid of different input pressure values. (b) Waveguide sensor signal over soft finger work space for single values, average, logarithmic ratio.
• Figure 4: Recorded data and neural network architecture. (a) Excerpt of actuation, recorded soft finger end effector position, and sensor data. (b) NARX neural network architecture for open and self-loop operation.
• Figure 5: Mean error for soft finger path estimation on the test data set in open and self loop and relative decrease of model $M_B$, $M_C$ toward $M_A$.