An Enhanced Proprioceptive Method for Soft Robots Integrating Bend Sensors and IMUs

TL;DR

This work tackles long-term proprioception for soft robots by fusing off-the-shelf bend sensors with IMUs. The authors introduce a drift-corrected, two-stage sensor fusion framework: a PCC-based kinematic model provides shape estimates, and two linear Kalman filters (one for orientation and one for coordinates) fuse bend and IMU data, with covariance parameters tuned by gradient descent. A drift-anchor using bend readings mitigates IMU yaw drift, enabling continuous operation for 45 minutes and achieving a RMSE of $16.96$ mm ($2.91\%$ of total length), a $56\%$ improvement over IMU-only baselines. The approach is cheap, vision-free, and scalable to longer or more articulated robots, with demonstrated robustness across no-load, external force, and obstacle-contact conditions, and clear pathways to 3D extension using multi-axis bend sensing.

Abstract

This study presents an enhanced proprioceptive method for accurate shape estimation of soft robots using only off-the-shelf sensors, ensuring cost-effectiveness and easy applicability. By integrating inertial measurement units (IMUs) with complementary bend sensors, IMU drift is mitigated, enabling reliable long-term proprioception. A Kalman filter fuses segment tip orientations from both sensors in a mutually compensatory manner, improving shape estimation over single-sensor methods. A piecewise constant curvature model estimates the tip location from the fused orientation data and reconstructs the robot's deformation. Experiments under no loading, external forces, and passive obstacle interactions during 45 minutes of continuous operation showed a root mean square error of 16.96 mm (2.91% of total length), a 56% reduction compared to IMU-only benchmarks. These results demonstrate that our approach not only enables long-duration proprioception in soft robots but also maintains high accuracy and robustness across these diverse conditions.

Figures (7)

• Figure 1: Overview of our proposed proprioceptive sensing method for soft robots using off-the-shelf IMUs and bend sensors. Shape estimation is based on a piecewise constant curvature model using segment-tip orientations. IMU drift is corrected using bend-sensor references before fusion, enabling 45-minute continuous operation.
• Figure 2: Experimental setup for validating the sensing method. (A) Planar robot test rig. (B) $N$th link with two actuators, four bend sensors (yellow), and two IMUs (blue) located between parallel sensors. (C) Full robot showing fiducial markers and sensing points for output comparison.
• Figure 3: A PCC kinematic model is used to map sensor readings to an estimate of the robot's shape. The robot is assumed to consists of a chain of rigid and constant curvature segments.
• Figure 4: Flowchart showing enhanced proprioception. The process starts with signals from the bend sensor and IMU, passes through an algorithm, and results in two output data: orientation in the ${S_i}$ frame, $\theta^i$, and position in the ${S_i}$ frame, $P_{s_{i}}^i$, which are used to estimate the position of the end-effector. The orientation at each sensing point and the estimated end-effector position of each segment are then compared with the ground truth, denoted as $GT_{\theta{\{S_i}\}}^i$ and $GT_{P{\{W}\}}^i$, respectively, obtained from fiducial markers, and the RMSE is calculated based on the distance between the two positions.
• Figure 5: IMU drift was observed over 900 seconds (15 minutes) while periodically changing the orientation of a sensing segment between -20 and 20 degrees. (A) The figure presents the orientation trend from the bend sensor and IMU using a moving average. The IMU error accumulates over time, indicating significant drift. (B) IMU correction results are compared to raw IMU values, demonstrating that the corrected IMU closely follows the ground truth.