Controlling continuum robots' shape to operate in confined, enclosed environments is challenging, since it cannot rely on external observation. Existing embedded shape sensing methods, although they can provide shape reconstruction, are insufficient to enable real-time shape control due to limitations in reconstruction accuracy, computational speed, and compatibility with shape-state representation. In this work, we present an embedded shape-sensing framework that uses readily available IMU and actuator feedback to reconstruct the continuum-robot shape with a neural network, providing accurate shape feedback at 400Hz for physical closed-loop control. We systematically investigate four key reconstruction design choices: shape-state representation, network architecture, training objective, and sensing inputs, through more than 5,000 trained models on one- and three-segment continuum robots. The selected framework achieves global shape errors of 0.9%L and 1.7%L (of the robot length) for the one- and three-segment systems, respectively. In closed-loop control, one-segment tip tracking achieves a 6.1%L error and three-segment shape control achieves a 2.3%L global shape error, whereas IMU--PCC reconstruction using the same uncompensated measurements fails. Enclosed-space experiments further demonstrate operation without external observation. These results provide a practical framework for translating readily available embedded sensing into high-rate feedback for continuum robot closed-loop control.
Figures & tables
Fig. 1: Overview of the proposed embedded shape-sensing and control framework for continuum robots working in enclosed space. Readily available embedded sensing reconstructs the shape state x^k for closed-loop control without external observation. External motion capture provides ground-truth supervision only during training. Video: https://youtu.be/sBmrXCk2B-4 .
Ref.
Seg.
Sensor
Reconstructed Tip Error (% L )
Rate (Hz)
Closed-Loop Control
[ 23 ]
1
IMU
0.91
60
×
2
IMU
1.21
60
×
[ 10 ]
2
Strain
1.8
–
✓ (tip)
[ 9 ]
3
Strain
2.6
–
×
[ 24 ]
2
FBG + IMU
3.6
–
×
[ 5 ]
2
IMU
4.1
20
×
TABLE I: Comparison of embedded shape-sensing methods and their validation in closed-loop continuum-robot control.
Fig. 2: Three-segment continuum robot and embedded sensing system. (a) Physical prototype consisting of base, middle, and tip segments mounted on a three-layer motor bank. (b) Interlocking vertebrae and orthogonally arranged NiTi hinge. (c) Integrated IMU and motion-capture marker mount. (d) Communication architecture for seven IMUs and nine motors. (e) Tendon-routing configuration within each segment. (f) Three-layer motor bank with guiding pulleys and three motors per layer.
Fig. 3: Ablation study of embedded full-body shape reconstruction using eglobal for the one-segment (a)–(d) and three-segment (e)–(h) robots. The four columns evaluate (a),(e) network architecture, (b),(f) shape-state representation, (c),(g) training objective, and (d),(h) sensing inputs. Values above the box plots denote the mean global shape error in millimeters. S1–S4 denote the increasing sensing configurations: S1: encoder; S2: encoder + IMU; S3: encoder + IMU + torque; and S4: encoder + IMU + torque + input ( uk−1 ).
Fig. 4: Embedded full-body shape reconstruction on the one- and three-segment continuum robots. (a), (c) Reconstruction error distributions for the MLP, LSTM, and CC estimators on the one- and three-segment systems, respectively. (b), (d) Representative reconstructed configurations compared with the motion-capture reference.
Fig. 5: One-segment tip tracking of a “tmech” reference trajectory using external and embedded shape feedback. (a) Tip trajectories using MoCap, MLP, and LSTM feedback. (b) Corresponding tip tracking errors over time.
Fig. 6: Three-segment full-body shape control using external and embedded shape feedback. (a) Representative target shapes and steady-state robot configurations obtained using MoCap, MLP, and LSTM feedback. (b) Front and top views of the controlled robot for Shape 5. The target shape is shown as a semi-transparent overlay on the measured robot configuration. (c) Tip, global, and local shape-control RMSE over 10 randomly selected target shapes.
Fig. 7: Enclosed-space demonstrations using the proposed embedded shape sensing and control framework without external observation. (a)–(c) Obstacle slalom, 0–60 s, (d)–(f) confined-aperture traversal, 60–120 s, and (g)–(i) tip targeting, 120–180 s.