Bilateral Teleoperation with Reaction/Disturbance Observers

• The paper demonstrates integration of reaction and disturbance observers to compensate for model errors and improve teleoperation transparency and stability.
• It details diverse architectures, including four-channel, impedance-based, and fuzzy-MHE frameworks, with explicit delay compensation and scaling.
• Experimental benchmarks validate sub-millimeter position tracking, precise force estimation, and reliable performance under variable delays and disturbances.

Bilateral teleoperation with reaction/disturbance observers constitutes a class of closed-loop control architectures where spatially separated master and slave systems are coupled bidirectionally through real-time feedback of position and force signals, with explicit compensation for unknown dynamics, disturbances, and uncertainties via observer-based estimation. The architectural goal is to establish high-fidelity kinematic and kinesthetic coupling between the human operator (or master-side device) and the remote slave-side robot, achieving robust performance and stability in the presence of model error, delays, and environmental contacts. This article details key developments, control structures, observer formulations, and experimental benchmarks from recent authoritative works.

1. Control Architectures and Observer Integration

Modern bilateral teleoperation frameworks employ a variety of architectures, with the most prominent being four-channel architectures (feedback of both position and force in both directions), impedance-based bilateral schemes, and variations for specialized domains such as aerial manipulation or rehabilitation. Integration of reaction (force) observers and general disturbance observers (DOBs/NDOBs) is a primary differentiator.

• Impedance + NDOB Architecture: As illustrated in "A Teleoperation System with Impedance Control and Disturbance Observer for Robot-Assisted Rehabilitation" (Li, 2024), both master and slave are equipped with task-space impedance controllers and nonlinear disturbance observers (NDOB). NDOBs estimate lumped dynamic errors, friction, and external disturbance torque, and in pHRI (physical human–robot interaction) mode, NDOB can be disabled on the master to maximize backdrivability. The architecture supports real-time mode switching for trajectory-tracking, teleoperation, and demonstration replay.
• Four-Channel with DOB/RFOB: A four-channel encrypted bilateral controller couples PD position and P force loops with local DOBs and reaction force observers (RFOB), allowing both robust disturbance rejection and sensorless estimation of interaction torques at both ends (Takanashi et al., 2023). State-space digital implementations allow embedding both position/velocity and observer state(s) in the real-time loop.
• Model-Based Decentralized Observers: Some schemes, such as the dynamic-subsystem-based approach of (Lampinen et al., 2020), leverage individual model-based controllers at each endpoint (master/slave) with embedded disturbance observers for local force estimation, and couple them through bilateral feedback with explicit delay compensation and scaling for dynamics mismatch or desired telepresence effect.
• Fuzzy-MHE Observers: The use of Type-2 fuzzy logic and Moving Horizon Estimation (MHE) to encapsulate system nonlinearities and estimate disturbances (forces) without precise analytic models has been proposed for high-uncertainty teleoperation under time delay, as in (Liao et al., 2018).

2. Mathematical Formulations of Observers

Observers are deployed to estimate unmeasurable disturbances (external/environment forces, friction, model errors) that are critical for high-transparency bilateral teleoperation.

• Nonlinear Disturbance Observer (NDOB) (Li, 2024):

$$\begin{aligned} L_{\rm obs} &= Y_{\rm obs}\,M_{\rm obs}^{-1} \ p &= Y_{\rm obs}\,\dot q \ \dot z &= -L_{\rm obs}\,z + L_{\rm obs}\left(\hat S\,\dot q +\hat g - \tau - p\right) \ \hat\tau_{\rm NDOB} &= z + p \end{aligned}$$

NDOB compensation is applied by subtracting $\hat\tau_{\rm NDOB}$ from the controller torque command.

• Linear DOB and RFOB (Takanashi et al., 2023): For each single-joint servo with nominal model,

$$\dot q = -g_d\,q(t) + \bar K\,g_d\,i(t) + \bar J\,g_d^2\,\omega(t), \quad \hat\tau^d = q - \bar J\,g_d\,\omega.$$

The true external torque is then estimated:

$\tau^e = \hat\tau^d - f(\theta, \omega),$

where $f(\theta, \omega)$ captures identified nonlinear effects such as gravity and friction.

• Subsystem-based Inverse-Dynamics Observers (Lampinen et al., 2020):

$$\hat f_m = J_m^{-T}(\tau_m - \tau_{mm}), \qquad \dot{\tilde f}_m + C\,\tilde f_m = C\,\hat f_m,$$

where $\tau_{mm}$ is computed from estimated states and identified parameters, and the filtered estimate $\tilde f_m$ is guaranteed by Lyapunov arguments to converge to the true handle reaction force.

• Type-2 Fuzzy + MHE Force Observer (Liao et al., 2018): The plant is modeled via Type-2 T–S fuzzy rules and interval blending; MHE smooths and jointly estimates state and model uncertainty over a window $N$. A Luenberger-type observer applied to the MHE output exponentially converges the force estimate $\hat T_e$ to the true environmental (or human) torque.

3. Bilateral Control Laws Incorporating Observers

Integration of observer outputs fundamentally alters the closed-loop bilateral teleoperation law for robust and transparent operation.

• Sensorless Force Feedback via Virtual Spring (Li, 2024):

$\tau_{\rm ff} = J^T K_{\rm ff}(x_S - x_M)$

Position errors between slave and master are mapped by a virtual spring into torque feedback, obviating the need for physical force sensors.

• Four-Channel Law with Estimated Forces (Takanashi et al., 2023, Liao et al., 2018): Separate PD-type position and P-type force loops are closed with sensorless force estimation through locally running observers. The control law takes a fully discrete state-space form with the observer state updated concurrently and all necessary signals exchanged over the bilateral channel.
• Decentralized Model-Based Law (Lampinen et al., 2020): Each side runs a local velocity-damping controller (VDC) with observer-based compensation, while the connecting channel applies arbitrary (even large) delay, scaling, and manages loop stability by passivity or input-to-state–stability–based proofs.

4. Delay Compensation, Scaling, and Stability

One of the central challenges in bilateral teleoperation is to guarantee stability and passivity under arbitrary time delays and potentially mismatched dynamics.

• Explicit Delay Compensation (Lampinen et al., 2020): The bilateral law incorporates delay operators $e^{-sT}$ directly in remote references, and stability is proven via bounded $H_\infty$ norm conditions on closed-loop transfer functions ($\|G_m\|_\infty\leq 1$). Stability is preserved for arbitrary delay and both position and force scaling.
• Mode Switching and Recovery (Li, 2024, Byun et al., 2024): Logical gates or force-derivative detectors (e.g., Kalman-filtered spike detection upon abrupt contact loss) are used to enable fast and robust switching between teleoperation and autonomous recovery trajectories, avoiding destabilization due to operator reaction lag.
• Classical Passivity and Lyapunov Analysis (Takanashi et al., 2023, Liao et al., 2018): Passivity-based methods are employed to prove that all observer errors, trajectory errors, and position/force mismatches are $L_2\cap L_\infty$ bounded and tend to zero asymptotically for nominally modeled axes and bounded or slowly varying disturbances.

5. Experimental Benchmarking and Performance Outcomes

Rigorous hardware experiments across a range of platforms validate the efficacy and practical utility of observer-empowered bilateral teleoperation architectures.

• Clinical Rehabilitation Robots (Li, 2024): Sub-millimeter trajectory tracking is achieved with NDOB enabled, while pHRI mode allows therapist-driven master manipulation for demonstration and replay. Peak rendered feedback forces with virtual springs reach $\pm7$ N in stiff contact scenarios; disturbance rejection maintains torque errors below 0.5 Nm.
• Heavy-Lift Haptic and Hydraulic Testbeds (Lampinen et al., 2020): Bilateral position tracking achieves $\mathcal{O}(10^{-3})$ m accuracy under position scaling up to 4 and force scaling up to 800 with no significant performance loss under 80 ms one-way delays.
• Encrypted Four-Channel Teleoperation (Takanashi et al., 2023): Bilateral tracking and force feedback are preserved even under full controller and channel encryption, with computation overhead under 2 ms and torque estimation accuracy within $\pm0.2$ Nm.
• Aerial Manipulation with Human Reaction Compensation (Byun et al., 2024): Owing to disturbance observer force estimation plus event-triggered switching, positional overshoot after object extraction is reduced from 0.8934 m to 0.6422 m and recovery is accelerated by approximately 2 s.
• Fuzzy-MHE Approaches (Liao et al., 2018): Experimental comparisons across four observer types highlight that only Type-2/MHE methods maintain observer “no-force” errors at 0.1 Nm (vs. $\geq$0.4 for baselines), with rapid (50 ms) tracking of hard-contact force steps and RMS position errors under 1 mrad.

6. Comparative Attributes of Observer Approaches

The integration of observer types yields distinct tradeoffs in transparency, robustness, computational complexity, and model-dependence. The table below summarizes core characteristics:

Observer Type	Model Dependence	Handling of Uncertainty/Noise
NDOB (model-based)	Requires rough model	Good for matched uncertainties
DOB/RFOB (linear)	Requires identified parameters	Sensitive to parameter drift
Inverse-dynamics + filter	Requires dynamic model	High-performance in calibrated systems
Fuzzy + MHE	Data-driven, low analytic req.	Superior noise/disturbance rejection

Sensorless observers simplify integration and reduce hardware costs, but their performance is ultimately bounded by model fidelity or data set representativeness. Fuzzy/MHE approaches are robust to deep uncertainty but computationally more intensive.

7. Applications and Future Developments

Observer-driven bilateral teleoperation systems are vital in domains demanding robust, high-transparency teleoperation: robot-assisted rehabilitation (Li, 2024), hazardous manipulation with dissimilar manipulators (Lampinen et al., 2020), encrypted/safe tele-robotics (Takanashi et al., 2023), haptic-based aerial manipulation (Byun et al., 2024), and adaptive multi-scenario systems (Liao et al., 2018). Ongoing research focuses on observer adaptation to fast-varying dynamics, data-driven model reduction for real-time feasibility, and deeper integration with learning-based controllers for further minimizing transparency loss and delay-induced artifacts.