Tendon-Based Proprioception: Mechanisms & Applications

• Tendon-based proprioception is the process of extracting body-state information from tendon signals through tendon displacement, tension, and vibration.
• It employs varied methodologies—such as calibrated inversion, potential-energy minimization, and ANN regression—to infer posture, force, and contact from tendon data.
• Applications span robotics and wearable devices, enabling accurate configuration reconstruction, tactile inference, and enhanced human-machine interactions.

Tendon-based proprioception denotes the extraction or modulation of body-state information through tendons, cables, or tendon-analogous transmission paths. In robotics, it commonly refers to estimating posture, deformation, interaction force, or contact state from tendon excursion, tension, resistance, or other transmission-state variables; in human–machine interfaces, it also includes deliberate tendon vibration to induce kinesthetic illusion or alter perceived resistance (Parvaresh et al., 10 Feb 2025, Varghese et al., 2019, Polcz et al., 28 Jan 2026, Song et al., 9 Feb 2026). Across these uses, the tendon is not merely a transmission element: it becomes either the sensing substrate itself or the physiological target through which proprioceptive signals are perturbed.

1. Conceptual scope and biomechanical basis

A recurring biomechanical premise is that posture is not determined by geometry alone, but by the coupled state of tendon excursion, tendon force, stiffness, and pre-tension. In the strain-energy formulation of slow tendon-driven limb motion, tendon excursion satisfies $$\Delta \mathbf{s}=-\mathbf{R}^T\Delta\boldsymbol{\theta}$$, muscle–tendon force is $$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$, and equilibrium requires $$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$ (Babikian et al., 2015). A central result is that stable nontrivial postures require pre-tension: if $\Delta \mathbf{l}_0=0$, the only equilibrium posture is the reference posture. This makes baseline tendon tension mechanically indispensable rather than a mere offset.

This mechanical picture aligns with the engineering literature in which tendon-side variables are treated as privileged internal coordinates. In tendon-driven robotic hands and continuum robots, measured tendon displacement or tension is used as a proxy for joint configuration, distributed deformation, contact timing, or interaction force because those variables are embedded in the actuation path itself (Lee et al., 16 Sep 2025, Zhang et al., 8 Mar 2026). This suggests that tendon-based proprioception is best understood as inference on a constrained manifold of routing, elasticity, and equilibrium rather than direct angle readout.

A distinct but related line of work treats tendons as a stimulation target rather than a measurement site. Tendon or muscle vibration is described as activating primary muscle spindle afferents, inducing kinesthetic illusions of position, motion, and force, and interacting with tonic vibration reflex and effort-related mechanisms (Hirao et al., 2022, Song et al., 9 Feb 2026). In that setting, tendon-based proprioception is not read out but deliberately biased.

A useful contrast is provided by wearable deep-pressure substitution for PIEZO2 loss of function. That device maps elbow angle to forearm pressure through a linear actuator and cylindrical tactor, explicitly framing the method as sensory substitution rather than restoration of endogenous proprioception, and not as a tendon-targeted method (Kodali et al., 2022). The distinction clarifies a common misconception: not every proprioceptive interface is tendon-based merely because it is mechanical or wearable.

2. Tendon-side variables and transduction strategies

The literature uses several transduction strategies, all centered on the same idea: a tendon path carries information because its state changes with motion and interaction.

In the proprioceptive origami manipulator, three stainless-steel conductive threads simultaneously serve as actuation tendons and proprioceptive sensors. Their effective resistance follows the resistive relation $R=\rho l/A$, so shortening the active tendon segment decreases resistance; a Wheatstone bridge, Arduino acquisition, MATLAB filtering, and a calibrated resistance-to-length mapping convert this signal into tendon lengths for kinematic reconstruction (Parvaresh et al., 10 Feb 2025). Here the tendon is literally a variable resistor embedded in the actuation path.

In the anthropomorphic underactuated hand with a miniature cable-driven series elastic actuator, the directly measured variables are tendon excursion $x$ and sliding-block displacement $\Delta x_{\mathrm{sb}}$. Tendon tension is then obtained from the SEA geometry and spring pack as

$$F_{\mathrm{tension}} = 2k_{\mathrm{sea}}\,\Delta x_{\mathrm{sb}},$$

while the sliding-block displacement satisfies

$$\Delta x_{\mathrm{sb}}=\frac{x-\ell(\theta_1,\theta_2)}{2}.$$

This gives tendon force sensing and tendon displacement sensing in a single compact module integrated into otherwise sensorless fingers (Lee et al., 16 Sep 2025).

The simulated high-DoF anthropomorphic hand assumes access to two actuator-side measurements: root-tendon tensions $f_{\mathrm{m}}$ and motor-shaft tendon displacements $$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$0. Those variables are combined with a branched tendon-network model, linear tendon elasticity, and junction force balance to estimate hidden joint angles and internal tendon elongations (Polcz et al., 28 Jan 2026). The tendon is thus a networked sensing medium rather than a single scalar channel.

In proximal-integrated force sensing for cable-driven continuum robots, cable tensions are fused with a proximal 6-axis force/torque sensor. The defining equation is

$$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$1

so external contact force is obtained by subtracting actuation-induced cable force from the measured base wrench (Zhang et al., 8 Mar 2026). This is still tendon-based proprioception, but in a collaborative form: cable sensing alone is insufficient, while cable sensing plus proximal wrench sensing becomes informative enough for 3D contact-force and contact-location inference.

The bio-inspired shoulder sensing suit uses neither force sensing nor conductive tendons. Instead, it measures path-length change of four routed stainless-steel tendons whose geometry mimics shoulder muscle synergies. Each tendon terminates at a Celesco SP1-12 string potentiometer, and the four displacement channels are mapped to shoulder azimuth and elevation by an ANN (Varghese et al., 2019). The sensed quantity is curvilinear tendon-path stretch over the body surface.

The tendon-driven soft robotic finger takes yet another route: an ATI 6-axis force/torque sensor is placed in series with the tendon path and only the axial load is recorded. The authors describe this as a tendon strain signal, and use it to infer texture and stiffness from internal loading fluctuations rather than from skin-like tactile arrays (Cheng et al., 2021).

Some systems extend tendon-based proprioception to transmission-state sensing more broadly. DexHand 021 treats motor current, motor position, motor velocity, joint position, joint velocity, and temperature as internal variables informative about tendon force and joint torque, and learns a Gaussian Process Regression map from these signals to torque for compliant grasp control (Yuan et al., 5 Nov 2025). A plausible implication is that in routed cable systems, proprioception may be distributed across the entire transmission rather than isolated to a single tendon sensor.

3. Inference from tendon signals to configuration and interaction

Once a tendon-side variable is measured, the central problem becomes inversion: how to map it to hidden configuration or external interaction.

The origami manipulator exemplifies calibration-driven inversion. Free-thread resistance was first shown to correlate linearly with length, and load sensitivity under cyclic loading up to 10 N was negligible at $$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$2. Installed-tendon behavior was then calibrated with a cubic fit,

$$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$3

with coefficients $$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$4, $$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$5, $$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$6, $$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$7, and fit quality $$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$8, $$\mathbf{f}=-\mathbf{K}(\Delta \mathbf{s}+\Delta \mathbf{l}_0)$$9 (Parvaresh et al., 10 Feb 2025). The calibrated tendon lengths are inserted into a single-section piecewise constant curvature model to recover section length, bending plane, curvature, and end-effector position.

The underactuated SEA hand uses minimum potential energy rather than direct curve fitting. Total potential energy is the sum of SEA elastic energy, joint torsional spring energy, and gravity, and finger posture is predicted by minimizing $$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$0 subject to joint range and SEA travel constraints (Lee et al., 16 Sep 2025). During grasping, the measured tension–excursion profile is compared to the free-flexion reference with a 50-sample, 50 ms sliding-window RMSE. Contact is detected when the RMSE exceeds threshold, proximal versus distal contact is classified by slope 75 ms later, and post-contact slope is used as a relative stiffness descriptor. This produces a rule-based proprioceptive pipeline for contact timing, posture reconstruction, stiffness discrimination, and disturbance detection.

The simulated anthropomorphic hand formulates joint estimation as a nonlinear feasibility problem. A branch-excursion equation,

$$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$1

is coupled to a junction-force equilibrium equation,

$$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$2

and solved for joint angles and internal tendon elongations with CasADi, IPOPT, and MUMPS (Polcz et al., 28 Jan 2026). Here tendon tension is not auxiliary; it is the constraint that disambiguates internal branch states.

The continuum-robot work also turns a high-dimensional inverse problem into a structured optimization. After contact force is obtained from proximal force decoupling, contact location is reduced to a scalar arc-length variable $$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$3 along the backbone, and the remaining estimation problem is

$$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$4

where $$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$5 is the discrepancy between prescribed and model-predicted cable length (Zhang et al., 8 Mar 2026). This is supported by a beam constraint model, capstan friction, cable elasticity, and geometric chaining.

The shoulder sensing suit uses a learned inverse map rather than an explicit mechanical inversion. Sensor space is

$$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$6

joint space is

$$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$7

and the trained ANN reconstructs shoulder azimuth and elevation from the four tendon-path changes (Varghese et al., 2019). The soft finger similarly relies on feature engineering and statistical classification: Fourier magnitudes from 0 to 30 Hz at 0.33 Hz resolution encode texture, while slope, intercept, and correlation coefficient from a static hold phase encode stiffness (Cheng et al., 2021).

These inference strategies differ sharply in formalism—cubic calibration, potential-energy minimization, constrained nonlinear solving, beam-constrained optimization, ANN regression, and statistical classification—but they share a common structure. The tendon signal itself is usually not yet the state estimate; it becomes useful only after installation-specific calibration or model-based interpretation.

4. Robotic embodiments and functional capabilities

The most direct use of tendon-based proprioception is configuration reconstruction. In the origami continuum manipulator, conductive tendons enabled self-contained reconstruction of manipulator configuration and end-effector position without relying on external vision for state feedback (Parvaresh et al., 10 Feb 2025). The reported resistance swing during bending was only about $$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$8–$$\mathbf{R}\mathbf{K}\mathbf{R}^T\Delta\boldsymbol{\theta}=\mathbf{R}\mathbf{K}\Delta\mathbf{l}_0$$9, but the system still produced tendon-length estimates usable for forward kinematics.

In anthropomorphic underactuated hands, the sensed tendon channel is often overloaded with multiple functions. The SEA-based hand estimates contact timing, joint angles, relative object stiffness, and finger-configuration changes indicating external disturbances, and uses those estimates for grasp posture reconstruction, handling of deformable objects, and blind grasping with proprioceptive-only object recognition (Lee et al., 16 Sep 2025). Finger-level experiments and hand-level demonstrations yielded average joint-angle errors of $\Delta \mathbf{l}_0=0$0 for the drill and wine glass and $\Delta \mathbf{l}_0=0$1 for the pear.

DexHand 021 extends the same principle toward force-aware manipulation. Although it does not directly measure tendon tension with in-line tendon load cells, it estimates joint torque from internal transmission variables and uses that estimate in an admittance controller. The reported force validation yielded mean force estimation errors of 0.192 N for the index finger and 0.15 N for the thumb, while multi-object grasping reduced joint energy consumption by an average of 31.19% compared to PID (Yuan et al., 5 Nov 2025). This suggests that tendon-based proprioception in dexterous hands can be organized around internal force estimation rather than explicit geometry reconstruction alone.

The simulated high-DoF ACB hand demonstrates encoderless gesture tracking from tendon displacement and tension alone. Most joints were tracked within $\Delta \mathbf{l}_0=0$2, fingertip position errors fell below 5 mm for 5 of the 6 gestures, and feedforward improved settling time, but roll angles and distal joints remained notably harder to estimate (Polcz et al., 28 Jan 2026). The result is less a claim of universal identifiability than a proof that tendon-side sensing can close a control loop even in a highly articulated hand.

Continuum robots reveal the strongest extension from posture sensing to interaction sensing. Proximal-integrated force sensing estimated shape with average tip position errors of 0.29–0.56 mm depending on the constraint regime, 3D contact force with sub-gram to low-gram average error depending on the experiment, and contact location with average errors such as 0.43 mm in passive body contact and 0.73 mm in a 3D-force experiment (Zhang et al., 8 Mar 2026). Here tendon-based proprioception is not limited to “where am I?” but includes “what am I touching?” and “where am I touching it?”

The tendon-driven soft finger pushes the concept toward internal tactile inference. Under systematic cross validation, the tendon-load signal enabled 100% texture discrimination and 99.7% stiffness discrimination (Cheng et al., 2021). This is not tactile sensing at the skin, but tactile inference through the tendon pathway.

At the same time, tendon-actuated morphology does not guarantee that tendon state alone is sufficient. In the acoustic soft end-effector POE, a Position-KNN baseline using only servo encoder positions achieved 5.67 mm average and 20.21 mm maximum unidirectional Chamfer distance, whereas the audio-based POE-M achieved 4.91 mm average and 11.98 mm maximum (Yoo et al., 2024). The paper explicitly states that “the tendons can not fully constrain the pose.” This is an important boundary condition for the field: tendon-based proprioception is powerful, but in compliant bodies it may need to be fused with body-state sensing.

5. Wearable systems and perceptual interfaces

Wearable tendon-based proprioception often uses routed tendon geometry rather than force sensing. The shoulder sensing suit routes four PTFE-coated stainless-steel tendons along lines approximately parallel to pectoralis major, the deltoid heads, teres major, and latissimus dorsi, and reconstructs shoulder azimuth and elevation from their path-length changes (Varghese et al., 2019). Tested against motion capture over 29,551 frames and 246.26 s of motion, the best ANN using all four sensors and one hidden layer with 25 neurons achieved approximately $\Delta \mathbf{l}_0=0$3 RMSE in azimuth and $\Delta \mathbf{l}_0=0$4 in elevation. This suggests that muscle-synergy-inspired tendon routing can form an artificial proprioceptive layer for complex joints where rigid encoders are impractical.

Human-interface work uses tendon stimulation rather than routed sensing. Song, Kim, and Yoon’s finger tendon vibration system applied 80 Hz vibration to the palmar or dorsal side of the proximal phalanx and found that short-duration FTV requires a minimum duration of 0.75 s, produces direction-specific perceived movement primarily at the proximal phalanx, and at 0.75 s induces average proximal-phalanx movements of $\Delta \mathbf{l}_0=0$5 for flexion and $\Delta \mathbf{l}_0=0$6 for extension (Song et al., 9 Feb 2026). In VR rendering, FTV improved body ownership relative to no vibration and simple vibration, and participants described it as resistance with clear direction.

A related VR study on wrist and elbow tendon vibration interpreted the perceptual effect less as a clean directional illusion and more as a change in sensory weighting. Inner-tendon vibration increased the applicable visual motion-gain range by about 13% without users detecting the visual/physical discrepancy, left pseudo-weight JND essentially unchanged at $\Delta \mathbf{l}_0=0$7 without vibration versus $\Delta \mathbf{l}_0=0$8 with vibration, and produced a heaviness effect equivalent to a no-vibration gain of 0.64 (Hirao et al., 2022). The paper argues that tendon vibration can act simultaneously as noise on haptic motion cues and as an additional haptic cue increasing perceived weight.

These wearable and perceptual systems clarify that tendon-based proprioception need not mean measurement of tendon tension alone. It may also mean deliberate manipulation of tendon-related afferent pathways to alter movement perception, effort perception, or embodiment. A plausible implication is that “tendon-based proprioception” is best treated as a family of tendon-centered sensing and stimulation strategies rather than a single sensor technology.

6. Limits, misconceptions, and open directions

Several limitations recur across the literature. The first is signal fragility. In the origami manipulator, the full operating resistance change was only about $\Delta \mathbf{l}_0=0$9–$R=\rho l/A$0, and the authors explicitly note that improved hardware with signal amplification before post-processing/filtering would improve sensing resolution (Parvaresh et al., 10 Feb 2025). In the shoulder suit, real tendon signals showed lag and hysteresis relative to virtual tendon paths because of friction, compliance, and routing through anatomically constrained regions such as the axillary fossa (Varghese et al., 2019). In FTV studies, effects varied across users, calibration could take 5–15 minutes, and the kinesthetic effect was not instantaneous (Song et al., 9 Feb 2026).

The second limitation is structural ambiguity. Soft or underactuated bodies often admit multiple shapes for similar tendon states. POE makes this point explicitly: tendon positions do not uniquely determine body shape under compliance, hysteresis, internal tendon friction, and external contact, and encoder-only shape inference performed markedly worse in the worst case than acoustic body sensing (Yoo et al., 2024). The simulated high-DoF hand showed especially poor observability in roll angles and distal joints, and gesture G5, a clenched fist with strong contact and extreme flexion, produced the clearest estimation breakdown (Polcz et al., 28 Jan 2026).

The third limitation is model dependence. The SEA hand neglects friction in its energy model and warns that absolute object stiffness cannot be obtained because exact contact location is not known (Lee et al., 16 Sep 2025). The continuum-robot estimator assumes single-point contact for localization and collapses multi-point contact to an equivalent resultant point, even though resultant force can still be estimated accurately (Zhang et al., 8 Mar 2026). DexHand 021 relies on learned compensation precisely because cable transmissions exhibit elasticity, friction, hysteresis, velocity dependence, and temperature effects (Yuan et al., 5 Nov 2025). These examples show that tendon-based proprioception is often only as reliable as the accompanying model or calibration.

A common misconception is that any proprioceptive estimate internal to a tendon-driven robot is automatically “tendon-based.” The literature is more precise. The quadruped entanglement paper uses joint encoders, motor current monitoring, and a momentum-based observer; it is strongly relevant to leg-based proprioception but explicitly not a tendon-sensing paper (Yim et al., 2023). The PIEZO2-LOF wearable uses deep pressure on the forearm as a surrogate for elbow angle; it is explicitly sensory substitution and not a tendon-targeted approach (Kodali et al., 2022). Conversely, some systems are tendon-driven yet choose non-tendon proprioceptive channels because tendon state alone is inadequate, as in POE’s acoustic body-state sensing (Yoo et al., 2024).

The main open direction suggested across the field is fusion. This suggests hybrid estimators that combine tendon displacement or tension with body-state sensing, proximal wrench sensing, or learned transmission compensation. The literature already points toward several such moves: improved analog front ends for resistive tendons (Parvaresh et al., 10 Feb 2025), learning-based processing of tension profiles in underactuated hands (Lee et al., 16 Sep 2025), possible hybrid actuator-state plus body-state estimation in soft robots (Yoo et al., 2024), multi-finger FTV and richer spatiotemporal patterns in wearable kinesthetic feedback (Song et al., 9 Feb 2026), and broader proximal collaborative sensing for continuum robots (Zhang et al., 8 Mar 2026). The field therefore appears to be converging on a technically specific conclusion: tendon signals are highly informative, but they are rarely self-sufficient without calibration, mechanics-aware inference, or complementary sensing.