Sensorless Force Control: Approaches & Applications

• Sensorless force control is a methodology that infers forces using actuation signals and indirect measurements, eliminating the need for dedicated sensors.
• It employs dynamic model inversion, disturbance observers, and neural estimators to achieve accurate closed-loop force regulation.
• This approach is applied in wearable robotics, precision assembly, and soft systems to overcome sensor limitations while ensuring robust performance.

Sensorless force control refers to methodologies in which the forces or torques applied or experienced by a robotic actuator, manipulator, wearable device, or soft system are estimated and regulated without relying on direct force or torque sensors. Instead, the underlying actuation signals, dynamic models, and indirect measurements (such as motor currents, shaft positions, or deformation cues) are leveraged to achieve closed-loop force modulation. This class of approaches encompasses rigorous model-based observers, data-driven estimators, disturbance observers, and hybrid surrogates, providing viable alternatives for applications where conventional force sensors are impractical due to cost, fragility, integration constraints, or requirements for distal transparency.

1. Fundamental Principles of Sensorless Force Control

Sensorless force control systems reconstruct the interaction force between actuator and environment via inference from measurable electrical or kinematic variables. Key strategies include:

• Dynamic Model-Based Estimation: Actuator and transmission dynamics, potentially incorporating transmission friction and compliance, are explicitly modeled. The interaction force is inferred as the residual torque or force required to produce the observed motion, given the commanded input (e.g., (Bardi et al., 26 Jun 2024, Best, 2023, Bahari et al., 19 Sep 2025)).
• Observer-Based Estimation: Disturbance observers (DOb) and reaction-torque observers (RTOb) filter the difference between a nominal plant model and observed behavior to estimate unmeasured external torques or forces, frequently formulated and analyzed in the discrete-time domain (Sariyildiz, 2023).
• Neural and Data-Driven Surrogates: Machine learning, typically multilayer perceptrons (MLPs) or Gaussian processes, is used to map internal or proprioceptive signals (joint states, currents) to an estimated end-effector wrench (Shan et al., 2023, Bahari et al., 19 Sep 2025).
• Kinesthetic and Deformation Cues: For soft or underactuated systems, force regulation is achieved through explicit control of deformation or curvature—serving as a proxy for contact force, given a well-characterized geometry–force relationship (Herrera et al., 1 Oct 2024).

Each approach’s viability and fidelity are tied to actuator class, transmission nonidealities, bandwidth requirements, and the quality/availability of system identification and training data.

2. Model-Based Sensorless Force Estimation Techniques

In rigid manipulators and wearable devices, explicit dynamic models underlie most sensorless force control frameworks:

• Direct Model Inversion: In quasi-direct-drive actuation (QDD), such as cable-driven exosuits (Bardi et al., 26 Jun 2024) and robot hands (Best, 2023), the transmitted force is estimated from the applied motor torque, accounting for static friction losses and transmission geometry. For instance, in (Bardi et al., 26 Jun 2024), output cable tension is computed as

$$T_{\rm out} = T_{\rm in}\,\left[1 - \mathrm{sgn}(V_{\rm cable})\,\frac{2\mu\sin(\phi/2)}{1+\mathrm{sgn}(V_{\rm cable})\,\mu\sin(\phi/2)} \right]$$

where $T_{\rm in}$ is inferred from measured motor torque and pulley radius, and a compact Coulomb friction model is identified via benchtop experiments.

• Observer Structures: The disturbance observer RTOb-DOb dual-loop in (Sariyildiz, 2023) uses:
  • An inner DOb filtering current and model residuals to shunt friction and internal disturbances.
  • An outer RTOb to estimate contact torque solely from motor current and velocity, tuned via discrete-time transfer functions.

Key stability conditions are formulated explicitly in terms of observer gains, inertia ratios, and the avoidance of non-minimum phase zeros in the characteristic equation.

• State-Space and Minimal Observers: Four-channel bilateral teleoperation (Yamane et al., 8 Jul 2025) uses a minimal-order observer for external torque, leveraging a precise regressor-based dynamics identification. The observer operates under the assumption that the rate of change of $M^{-1}(\theta)\tau_{\rm ext}$ is negligible, enabling joint real-time estimation of velocity and external torque with explicit stability and bandwidth properties.
• Physics-Informed Surrogates: For complex, highly parameterized electromechanical actuators, (Bahari et al., 19 Sep 2025) anchors a Gaussian process to a first-principles model, learning only the residuals from experimental data. The surrogate fuses model-based and data-driven inference for robust force estimation under regimes with highly nonlinear transmission efficiencies.

3. Data-Driven and Kinesthetic Approaches

When explicit modeling is infeasible or too restrictive:

• Neural Network Regression: (Shan et al., 2023) substitutes end-of-arm F/T sensors with an MLP trained on joint positions, velocities, accelerations, and motor currents. Data collection spans free-space, sliding contact, hand-guiding, and tight assembly, explicitly segregated for training and fine-tuning to the target regime. The estimator achieves force RMSEs as low as $\sim1.1-2.2$ N (contact) and allows admittance and hybrid force-position schemes without sensor feedback.
• Deformation-Based Proxies: In soft robotics (Herrera et al., 1 Oct 2024), force control is accomplished by regulating the desired deflection ($\Delta\theta_{d,i}$) relative to the configuration at contact. The relation

$$F_{\rm normal}(\Delta\theta_d) \approx 0.013\;\mathrm{N/deg} \times \Delta\theta_d$$

is established empirically and closed-loop force is modulated by controlling bending, requiring only vision-based or strain-sensor feedback. This achieves force accuracy $\leq\,\pm0.03$ N at 5 Hz bandwidth.

• Actuator Current Feedback: For QDD hands, (Best, 2023) establishes a one-to-one mapping between torque command, measured current, and external contact force, with current-based estimates low-pass filtered to suppress motor and transmission noise.

4. Experimental Validation, Performance Metrics, and Trade-Offs

The efficacy of sensorless force control is typically quantified by force-tracking RMSE, response bandwidth, and impact on downstream functional performance. Key findings include:

System/Reference	Sensorless Force RMSE	Bandwidth	Other Metrics / Findings
Cable exosuit (Bardi et al., 26 Jun 2024)	0.71 Nm (18% of assist)	N/A	Comparable to load-cell-based; EMG reduction 30-38% (assist)
Soft gripper (Herrera et al., 1 Oct 2024)	≤0.03 N (single finger)	~5 Hz	Two-finger pull-out: peak force linear to bending
Rigid manipulator (Shan et al., 2023)	1.1-2.2 N (in-contact)	100 Hz data	Pin insertion (100 μm clearance) successful only after fine-tuning
Robot hand (Best, 2023)	≤0.5 N (fingertip)	200 Hz	≤20 ms force-disturbance settling; fragile object handling
Teleop 4-ch (Yamane et al., 8 Jul 2025)	0.52 Nm (joint torque MAE)	8 Hz	Angle error 0.61°; force feedback boosts IL success
RTOb-DOb (Sariyildiz, 2023)	<0.1 N (ideal tuning), >20% err (off-nominal)	(noted via sampling)	Validated stability bounds, waterbed trade-off

Trade-offs inherent to sensorless strategies include:

• Accuracy vs. Simplicity: Omission of force sensors simplifies system integration but increases sensitivity to modeling error, Coulomb/stiction friction (especially at reversals), and transmission nonidealities (Bardi et al., 26 Jun 2024).
• Bandwidth vs. Noise Robustness: Increased observer gains or GP flexibility raise closed-loop bandwidth at the cost of amplified noise or peaking in the sensitivity function (Sariyildiz, 2023).
• Task Dependence of Learning Approaches: Neural estimators require fine-tuning to regime (contact, sliding, manipulation), and model generalization is limited by data coverage (Shan et al., 2023).
• Comfort and Ergonomics in Wearables: Modest increases in discomfort (e.g., shoulder cuff in (Bardi et al., 26 Jun 2024)) were noted due to hardware design tuned for transparency rather than ergonomic optimality.

5. Application Domains

Sensorless force control is applied in diverse domains:

• Wearable Robotics: Cable-driven upper-limb exosuits with all-proximal sensing (Bardi et al., 26 Jun 2024) enable cost reduction, simpler don/doff, and sub-Nm torque fidelity, albeit requiring mechanical designs that minimize friction and stiction.
• Robotic Manipulation: Model- and learning-based estimation enables high-precision assembly (e.g., peg-in-hole $\leq$100 μm clearance) and safe hand-guiding without external F/T sensors (Shan et al., 2023), and dexterous handling in QDD robot hands (Best, 2023).
• Soft and Underactuated Systems: Vision-based or embedded curvature estimation in soft grippers provides sensorless force modulation for compliant grasping (Herrera et al., 1 Oct 2024).
• Teleoperation: Multi-channel bilateral teleoperation with sensorless force feedback (4-channel schemes) enables high-fidelity human-in-the-loop demonstration and data collection for imitation learning, outperforming vision-only or unilateral schemes in manipulation tasks (Yamane et al., 8 Jul 2025, Lampinen et al., 2020).
• Heavy-Duty Manipulation: Physics-informed Kriging surrogates integrated into hierarchical VDC frameworks enable robust force tracking in electromechanical linear actuators under high payloads, with sub-1% error in the rated force range (Bahari et al., 19 Sep 2025).

6. Stability, Robustness, and Design Guidelines

Ensuring robust closed-loop performance in sensorless force control involves explicit analysis and tuning of observer gains, inner/outer loop structures, and plant-parameter identification:

• In observer-based architectures (Sariyildiz, 2023), stability is subject to waterbed effects (discrete-time Bode integral constraints), and gain tuning must avoid non-minimum-phase zeros; recommended observer-time constants and gain intervals are formulated in closed-form.
• For data-driven surrogates (Bahari et al., 19 Sep 2025), sufficient training coverage, regularization, and cross-validation are necessary to prevent regression away from validated operating points.
• Model-matching and careful compensation of nonlinearities (e.g., gravity, friction, Coriolis terms) are critical to avoid bias and to maximize the accuracy of inferred forces (Yamane et al., 8 Jul 2025, Best, 2023).
• Hybrid kinematic–kinesthetic approaches require reliable, high-fidelity detection of system state (e.g., bending angle), and controller gain retuning when system compliance properties change (Herrera et al., 1 Oct 2024).

7. Limitations and Prospects

Sensorless force control, while obviating the need for dedicated force or tactile sensors, remains fundamentally limited by the accuracy of system models, fidelity of state estimation, and quality of actuator current or deformation sensing. Observed issues include residual errors due to frictional stiction and mechanical hysteresis (Bardi et al., 26 Jun 2024), reduced closed-loop bandwidth under heavy loads (Bahari et al., 19 Sep 2025), and dependence on egocentric sensing for soft hands (Herrera et al., 1 Oct 2024). Ongoing research directions include improved leakage modeling in transmission pathways, adaptive or learning-based observer gain optimization, model-based sensorless control for large-DOF or spatially-distributed systems, and integration with embedded or stretchable sensor technologies for improved reliability. Emergent approaches in imitation learning and teleoperation leverage high-fidelity sensorless force control for scalable data collection and human-robot interaction (Yamane et al., 8 Jul 2025), suggesting increasing relevance in both industrial and assistive domains.