Source-linked AI summary
Tendon-Driven Continuum Robot with Modular Stiffness and In-Situ Self Pose Estimation
Guo Ning Sue, Zheng Cao, Junzhe Hu, Xiangyun Bu, David Quinn, Tiancheng Wu, Zackory Erickson, Carmel Majidi
TL;DR
Continuum robots are often task-specific and pose estimation can depend on external sensing infrastructure. This paper combines interchangeable variable-stiffness joints with onboard magnetic, learning-based pose estimation; experiments validate self-sensing and mechanical adaptability in grasping tasks.
Problem
Many continuum robots are task-specific and difficult to reconfigure, while pose estimation often relies on external infrastructure that limits use outside controlled environments.
Source: §I · p. 1Method
The platform combines interchangeable joints with precomputed stiffness and onboard magnetic sensing using a reusable, joint-level learning model.
Source: §I · p. 1, 1) Overview · p. 2Results
Experiments validated mechanical adaptability and effective self-sensing, culminating in a grasping task.
Source: §I · pp. 1–2Takeaways & Limitations
The combination of modularity, variable stiffness, and in-situ pose estimation establishes a platform for future research on continuum robot capabilities.
Source: §VI · p. 8For the 10-linkage system, the maximum stable sampling rate is ∼1.2 Hz, which the authors say is insufficient for tasks requiring fast movements such as factory pick and place.
Source: C. Limitations and Future Work · p. 8
Abstract
from arXiv · showhide
Continuum robots enable smooth shape morphing and safe interaction in confined environments. However, most existing systems are task-specific and depend on external sensing infrastructure, limiting their adaptability and real-world deployment. This paper presents a self-contained modular continuum robotic platform that combines mechanical reconfigurability with onboard pose estimation. The robot is constructed from interchangeable continuum joints with analytically precomputed stiffness, allowing rapid assembly and direct programming of the robot shape. Proprioceptive sensing is achieved using magnetic sensors and a modular learning-based framework, where a single model is trained per joint and reused across configurations. The system is experimentally validated in real world, demonstrating self-sensing capabilities and adaptation without external tracking.
I. INTRODUCTION
Existing continuum robots are often difficult to reconfigure and rely on external tracking, limiting practical deployment. This paper combines modular, variable-stiffness joints with onboard magnetic pose estimation and validates the platform in grasping tasks.
I. INTRODUCTION
- Many existing continuum robots are task-specific and difficult to reconfigure, while pose estimation often depends on external sensing infrastructure.The paper notes that motion-capture, camera, and tracking-rig setups increase cost and complexity and limit use outside controlled environments.Source: §I · p. 1
- The platform combines reconfigurable continuum joints with onboard magnetic sensing and joint-level learning for self pose estimation.A model trained on one joint can be reused across robot joints.Source: §I · p. 1
- Interchangeable joints with precomputed stiffness let users specify robot shapes and deformation profiles while retaining smooth shape morphing and compliance.The platform is designed for rapid assembly, replacement, and reconfiguration to meet different task requirements.Source: §I · p. 1
- Experiments culminate in a grasping task demonstrating mechanical adaptability and effective self-sensing.The contributions also include validation in traversal and grasping tasks.Source: §I · pp. 1–2
II. RELATED WORKS
Related work spans modular continuum designs, variable-stiffness mechanisms, and pose estimation. The paper positions its approach against task-specific or structurally complex designs and sensing methods that require external setups or detailed kinematic priors.
A. Modular Design
- Prior modular continuum designs include general-purpose or locomotion segments –, 3D-printable compliant units,, ball-socket modules, and origami-inspired structures.The paper also describes modular designs as a route to scalable reconfiguration.Source: A. Modular Design · p. 2, §II · p. 2
B. Stiffness Tuning
- Prior stiffness-tuning approaches use customized compliant units, or vary bending stiffness along the body –, but often rely on rigid or complex structures, while soft variants, [19] tend to be less modular.Source: B. Stiffness Tuning · p. 2
C. Pose Estimation
- Pose-estimation work includes vision,, embedded strain sensing, [23], and magnetic sensing,, with vision requiring external setup and magnetic methods requiring detailed kinematic priors.The paper identifies in-situ pose estimation as important when external sensing is unavailable.Source: C. Pose Estimation · p. 2
1) Overview:
The platform uses interchangeable components around identical rigid core segments, compliant joints, and onboard pose-estimation electronics. Joint stiffness is characterized mechanically, while modular boards support magnetic sensing and communication across the assembly.
1) Overview:
- Identical carbon-fiber-reinforced PET core segments connect through TPU joints and accept interchangeable PLA rings and task-specific accessories.The architecture supports an arbitrary number of segments, limited primarily by tendon actuation; the study uses 8- and 10-segment robots.Source: 1) Overview · p. 2
2) Joint Design and Bending Stiffness Characterization:
- Finite-element analysis estimates bending stiffness for hourglass-shaped TPU joints with neck diameters from 3–7 mm by relating reaction moment to bend angle.The analysis uses a nonlinear static model with a 30-degree bend and fixed boundary condition; future work will examine nonlinear joint behavior.Source: 2) Joint Design and Bending Stiffness… · pp. 2–3
3) Electronics and Sensor Design:
- Each segment’s PCB senses a neighboring coil’s magnetic field and includes an IMU, magnetometer, microcontroller, voltage regulation, switching, and logic shifting.The microcontroller bridges SPI communication to the IMU and I2C communication with an Arduino MEGA, which interfaces with the Raspberry Pi for pose inference.Source: 3) Electronics and Sensor Design · p. 3, Figure 2 · p. 3
B. Pose Estimation
The system estimates relative segment position from magnetic-field measurements using a joint-level learning model. Its hemispherical workspace assumptions are supported by motion-capture data, and the data-collection process uses accelerometer measurements to recover ground-truth pose.
B. Pose Estimation
- Unlike permanent magnets, the approach embeds electromagnetic coils as magnetic field sources; coils can be selectively activated for sensing and deactivated to reduce inter-segment interference.Source: B. Pose Estimation · p. 3
1) Working Principle:
- The method maps magnetometer measurements to relative position using a neural network trained over the joint’s reachable workspace, constrained to a dome-like manifold by fixed-arc-length and pivot-center assumptions.The joint design is intended to enforce these assumptions, and Fig. 3(c) empirically supports their validity.Source: 1) Working Principle · p. 3
2) Data Collection:
- One joint-level network is reused across joints because segments use identical manufacturer-matched coils, and independently treating adjacent segment pairs supports arbitrary robot length.Data collection cyclically permutes segment roles across runs to promote generalization despite small coil-to-coil variations; accelerometer measurements provide waypoint pose ground truth rather than commanded motor positions.Source: 1) Working Principle · p. 3, 2) Data Collection · p. 4
- Motion-capture data from 500 waypoints place tip positions on a hemisphere with 0.523 mm RMSE.The figure also reports negligible drift while the robot was locked in a stationary pose for 26 minutes.Source: Figure 3 · p. 4
3) Setup and Training:
The model uses normalized magnetic measurements to predict a direction vector on the hemispherical workspace. It is trained with cosine loss and selected through Bayesian hyperparameter optimization.
3) Setup and Training:
- An MLP with dropout models the relationship between magnetometer readings and position because the magnetic field and position have no temporal dependence.Source: 3) Setup and Training · p. 5
- Azimuth and colatitude are converted to a 3D direction vector to avoid discontinuities from π-wrapping of azimuth.The network receives a normalized magnetometer vector and predicts a normalized direction vector, each with dimension 3.Source: 3) Setup and Training · p. 5
- Cosine loss trains the network by comparing normalized predicted direction vectors with ground-truth direction vectors.Source: 3) Setup and Training · p. 5
- Bayesian optimization selected a network with dimensions [1078,222,212,346], GELU activation, dropout 3.89 × 10−4, and batch size 256.Training used an 85%/15% training/holdout split and AdamW; the search ran for 10 hours with up to 500 epochs per trial.Source: 3) Setup and Training · p. 5
4) Inference:
The trained model runs on a Raspberry Pi 5 with ROS 2, receiving magnetometer data through an Arduino MEGA. Inference samples joints sequentially, yielding an approximately 1.2 Hz pose-estimation rate.
4) Inference:
- The trained model is deployed in ONNX format on a Raspberry Pi 5 running Docker with ROS 2 Humble, with an Arduino MEGA bridging magnetometers to the Pi.Source: 4) Inference · p. 5
- The erratum identifies Eq. (6) as the correct azimuth expression, noting that the earlier version mirrored the result about the North axis and differed in sign for small tilts.The colatitude expression in Eq. (5) is unaffected.Source: 4) Inference · p. 5
- Pose estimation runs at approximately 1.2 Hz because of communication overhead, magnetometer sampling rates, and coil-field settling times.Only one coil is activated at a time to reduce inter-segment magnetic interference, with approximately 80 ms to sample a joint.Source: 4) Inference · p. 5
5) Motion Capture System:
An Optitrack Motive motion-capture system captures robot position during deformation as ground truth for pose-estimation studies.
5) Motion Capture System:
- Robot position during deformation is recorded with an Optitrack Motive motion-capture system as ground truth for pose-estimation studies.Source: 5) Motion Capture System · p. 5
A. Pose Estimation
Pose estimation was evaluated in unobstructed and obstructed planar motion and manual 3D manipulation, while joint stiffness characterization showed how neck diameter can be selected for a desired bending stiffness.
A. Pose Estimation
- 0.025483 m RMSE in Scenario 1 and 0.0395 m RMSE in Scenario 2 measure pose predictions against ground truth.Scenario 1 was unobstructed; Scenario 2 added a box-of-rocks obstruction.Source: Figure 4 · p. 6
1) Unobstructed Planar Motion:
- The unobstructed test activated one tendon as the robot curled on the ground, probing pose estimation without external influences.The setup and result are shown in Fig. 4(a).Source: 1) Unobstructed Planar Motion · p. 6
2) Impeded Planar Motion:
- Obstacle contact from a box of rocks tested pose estimation under disturbances and unknown deformation in a nominally planar setting.The setup and results are shown in Fig. 4(b).Source: 2) Impeded Planar Motion · p. 6
3) Manual 3D Manipulation:
- Under manual 3D bending and curling, motion capture yielded no usable ground truth, but pose estimates appeared qualitatively accurate.Self-occlusion prevented reliable marker tracking during hand manipulation.Source: 3) Manual 3D Manipulation · p. 6, Figure 4 · p. 6
B. Joint Bending Stiffness
- Finite-element strain contours and bending stiffness measurements for 3–7 mm neck diameters illustrate using a quadratic fit to select a diameter for a target stiffness.The fit is presented as a design aid for determining the neck diameter needed for a specified application stiffness.Source: B. Joint Bending Stiffness · p. 6, Figure 5 · p. 6
C. Application Demonstrations
The application demonstrations reconfigured limbs, joints, and contact modules for obstacle traversal, spherical grasping, and cloth handling, while estimating robot shape during all three tasks.
C. Application Demonstrations
- Variable-length limbs and joints with different bending stiffness produced non-uniform curvature that let the robot bend around an obstacle and reach a switch target.Fig. 6(a) shows the configuration and corresponding pose estimate.Source: C. Application Demonstrations · p. 6, Figure 6 · p. 7
- TPU stoppers coated with Eco-Flex 00-30 provided compliant, higher-friction contact for stably grasping an approximately 12 cm sphere.The authors report that replacing contact modules can improve grasping of smooth curved objects.Source: C. Application Demonstrations · p. 6
- Square limbs with red stopper inserts provided stronger local contact forces suited to grasping deformable cloth.This configuration demonstrates reconfiguration for different object geometries and contact conditions.Source: C. Application Demonstrations · pp. 6–7, Figure 6 · p. 7
- Across all three tasks, pose estimation captured neighboring-segment positions and overall body configuration during contact-rich interactions.The authors describe these demonstrations as validating the platform across diverse manipulation tasks.Source: C. Application Demonstrations · p. 7
1) Segment and Joint Modularity:
The platform supports tool-free, module-level hardware changes and variable-stiffness shaping alongside magnetic self-pose estimation, but the initial joint design and sensing system have important scope and speed limits.
1) Segment and Joint Modularity:
- Tool-free segment assembly and module-level replacement simplified maintenance and rapid hardware iteration, though dovetail joints sometimes popped out under high loads and system weight limited functionality.Structural parts, stiffness elements, and task-specific attachments could be replaced with minimal disturbance to sensing hardware.Source: 1) Segment and Joint Modularity · p. 7
2) Joint Stiffness Variation and Characterization:
- The initial stiffness study varied one relatively simple joint geometry; more complex designs will likely require accounting for nonlinear joint deformation.The authors state that the same design and analysis approach could be applied to more sophisticated joints and tasks.Source: 2) Joint Stiffness Variation and… · p. 7
B. Pose Estimation
- The magnetic estimator remained accurate under contact disturbances and produced qualitatively correct estimates during manual 3D manipulation without usable motion-capture ground truth.The authors report RMSE comparable to accelerometer-based self-pose sensing and note that their method requires no kinematic prior, unlike other magnetic approaches [19],.Source: B. Pose Estimation · pp. 7–8
C. Limitations and Future Work
- For the 10-linkage system, the stable sampling rate was approximately 1.2 Hz, insufficient for fast tasks such as factory pick and place; bulky coils also limit integration.The paper identifies parallelized or faster acquisition and PCB-embedded copper-trace coils as future directions.Source: C. Limitations and Future Work · p. 8
VI. CONCLUSION
- The work demonstrates compatibility among variable-stiffness modular design and magnetic machine-learning pose sensing, presenting the platform as a basis for future continuum-robot research.Mechanical analysis was used to tailor joint configurations toward desired actuated shapes.Source: §VI · p. 8