Four-Channel Bilateral Control System

• Four-channel bilateral control systems are teleoperation architectures that use four independent communication channels to synchronize both position and force between master and slave robots.
• They employ advanced control laws and observer strategies to compensate for communication delays, dynamic uncertainties, and disturbances, ensuring robust and stable performance.
• Applications include robot-assisted manufacturing, tele-surgery, and secure remote operations, with empirical studies demonstrating low error margins and high task success rates.

A four-channel bilateral control system is a teleoperation architecture that enables simultaneous position and force coordination between spatially distributed master (leader) and slave (follower) robots. It implements four distinct communication/control channels: master-to-slave position, slave-to-master position, master-to-slave force, and slave-to-master force, to achieve high-fidelity remote manipulation with force feedback and posture synchronization. This paradigm is essential for teleoperation in contact-rich, uncertain, and dynamic environments, offering superior transparency and operability relative to simpler unilateral or two-channel schemes.

1. Mathematical and System-Theoretic Foundations

At the core of four-channel bilateral control is the physical modeling of each manipulator as an $n$-DOF rigid-body system subject to friction, gravity, external disturbance, and measurement noise. The joint-space dynamics for the master and slave sides are: $$\begin{aligned} \text{Master:} \ \ & M_m(q_m)\,\ddot q_m + C_m(q_m, \dot q_m)\,\dot q_m + D_m\,\dot q_m + F_m(q_m) + A F_m^2 + n_m = T_m + \tau_h\ \text{Slave:} \ \ & M_s(q_s)\,\ddot q_s + C_s(q_s, \dot q_s)\,\dot q_s + D_s\,\dot q_s + F_s(q_s) + A F_s^2 + n_s = T_s + \tau_e \end{aligned}$$ where $M_i$ is the inertia matrix, $C_i$ the Coriolis/centrifugal effects, $D_i$ viscous friction, $F_i$ includes gravity and Coulomb friction, $A F_i^2$ represents bounded dynamic uncertainties, $n_i$ is measurement noise, $T_i$ control torques, and $\tau_h$, $\tau_e$ are the human and environment interaction torques, respectively (Liao et al., 2018, Yamane et al., 8 Jul 2025).

This structure generalizes across robotic arms (Inami et al., 28 Feb 2025, Takanashi et al., 2023, Yamane et al., 12 Oct 2025), FES-driven human teleoperation (Hasegawa et al., 2018), and even distributed-parameter hyperbolic PDE domains (Sun et al., 2024).

A canonical four-channel law enforces both position and force synchronization:

• Position synchronization: drives $q_m \leftrightarrow q_s$
• Force reflection: enforces $\tau_h + \tau_e \to 0$ at steady state

The closed-loop system is typically rendered passive via appropriate gain/delay tuning and feedback design, guaranteeing stability and convergence of both position and force errors to zero (Liao et al., 2018, Inami et al., 28 Feb 2025, Yamane et al., 8 Jul 2025).

2. Four-Channel Control Law Architectures

The four channels correspond to:

1. Master-to-slave position/velocity reference
2. Slave-to-master position/velocity feedback
3. Master's estimated force/torque to slave
4. Slave's estimated force/torque to master

The generalized torque control laws, e.g. for torque-controlled manipulators: $$\begin{aligned} T_m(t) &= K_m [\hat q_s(t-T_2) - \hat q_m(t)] - B_m \hat{\dot q}_m(t) + K_n [\hat \tau_h(t) - \hat \tau_e(t-T_2)]\ T_s(t) &= K_s [\hat q_m(t-T_1) - \hat q_s(t)] - B_s \hat{\dot q}_s(t) + K_e [\hat \tau_e(t) - \hat \tau_h(t-T_1)]\ \end{aligned}$$ where $\hat q$, $\hat{\dot q}$ are filtered/estimated states and $\hat \tau_h$, $\hat \tau_e$ are observed interaction torques; $T_1, T_2$ denote bounded communication delays. The $K$ matrices enforce position/velocity coupling, while $K_n$, $K_e$ create force reflection loops (Liao et al., 2018, Inami et al., 28 Feb 2025). In Cartesian frameworks, the law is lifted to decouple each translational and rotational DOF via Lie-algebraic rotation matrices and appropriate scaling matrices, yielding fully decoupled scalar sub-dynamics in each channel (Yamane et al., 12 Oct 2025).

For distributed-parameter (PDE) systems, bilateral boundary control is formulated by imposing four independent boundary inputs, transformed via Volterra-type backstepping to enforce zero-state finite-time stabilization across all channels (Sun et al., 2024).

In FES/human teleoperation, the four-channel approach is realized by parallel sliding-mode controllers for each joint and distributing signed control voltages across flexor/extensor stimulation pads (Hasegawa et al., 2018).

3. Advanced Observation and Estimation Strategies

Robustness in four-channel bilateral control is predicated on accurate state and force estimation. Classical observer designs include disturbance observers (DOB) and reaction force observers (RFOB), as used in sensorless low-cost arms (Yamane et al., 8 Jul 2025, Takanashi et al., 2023, Inami et al., 28 Feb 2025). More advanced estimation exploits interval Type-2 Takagi–Sugeno (T-S) fuzzy modeling and moving horizon estimation (MHE) to simultaneously filter noise, capture dynamic uncertainty, and deliver high-fidelity force estimates robustly without an explicit analytical model (Liao et al., 2018). The interval T-S fuzzy approach blends multiple linear models using type-reduced fuzzy memberships and captures the footprint of uncertainty both in antecedent and consequent blends: $$y(k) = \sum_\ell \mu_\ell(k)[\hat A_\ell x(k) + \hat w_\ell + \Delta \hat w_\ell \lambda(k)]$$ where $\lambda(k)\in[-1,1]$ encodes unknown deviations; state/uncertainty are estimated over a fixed time window by MHE, with constraints ensuring ISS via Lyapunov analysis.

Velocity and external force estimation is sometimes accomplished with second-order disturbance observers employing digital IIR filtering and model-based prediction to offset the limitations of low-cost encoders and eliminate the need for force sensors (Yamane et al., 8 Jul 2025).

4. Implementation Modalities and Extensions

Four-channel bilateral control systems have been demonstrated on:

• Multi-DOF torque-controlled manipulators (e.g., CRANE-X7, Phantom Omni/3-DOF haptic devices) (Liao et al., 2018, Inami et al., 28 Feb 2025, Yamane et al., 12 Oct 2025, Yamane et al., 8 Jul 2025)
• Human-in-the-loop FES-controlled finger joints (bidirectional teleoperation via sliding-mode stimulation) (Hasegawa et al., 2018)
• Distributed-parameter hyperbolic PDEs (with four independent boundary actuators and distributed kernel transformations for stability) (Sun et al., 2024)
• Secure/cyber-physical implementations using homomorphic encryption for both signals and controller parameters, ensuring no plaintext control data is exposed over the network or to potential insider threats (Takanashi et al., 2023)

Decoupled scaling in the Cartesian domain allows the parameters governing dynamics—stiffness, damping, and wrench reflection—to be independently tuned along translational/rotational axes, granting high operability even for kinematically mismatched or scaled configurations (Yamane et al., 12 Oct 2025).

Practical four-channel systems include multi-robot/multilateral extensions, such as Motion ReTouch, where high-speed demonstrations are post-processed and edited in both position and force domains, with multilateral force trajectories directly modifiable during replay (Inami et al., 28 Feb 2025).

5. Performance Metrics, Passivity, and Stability

Empirical studies emphasize key performance indices:

• Force-tracking error in free motion and contact (often $<$0.1 Nm for state-of-the-art observers vs. 0.4–0.5 Nm for classical methods) (Liao et al., 2018)
• Position-tracking accuracy, e.g., $|q_m - q_s|<$0.005 rad RMS (Liao et al., 2018), $<$2 mm translation error and $<$0.02 rad orientation error in scaled Cartesian control (Yamane et al., 12 Oct 2025)
• Hardness discrimination (accurate transmission of soft/hard contact) (Takanashi et al., 2023)
• Human-in-the-loop tracking (free-finger teleoperation with 2–4 deg RMS error in FES-driven tasks) (Hasegawa et al., 2018)
• Task-level success rates; e.g., with Motion ReTouch, test-tube transfer success rose from 0/10 (naive replay at $3\times$ speed) to 10/10 after force trajectory editing (Inami et al., 28 Feb 2025)

Stability and passivity are established under Lyapunov (ISS) arguments and careful gain selection, ensuring both position and force channels are globally asymptotically stable (Liao et al., 2018, Inami et al., 28 Feb 2025, Yamane et al., 12 Oct 2025). For Cartesian scaling, independent channel decoupling is achieved, and block-diagonal gain choices guarantee no cross-axis coupling or instability.

6. Applications, Limitations, and Future Directions

Four-channel bilateral control underpins advanced telemanipulation in:

• High-fidelity robot-assisted manufacturing, contact-rich operation, and tele-surgical tasks (Yamane et al., 12 Oct 2025, Inami et al., 28 Feb 2025)
• Haptic feedback and dexterous teleoperation with or without direct force sensors, including on low-cost arms (Yamane et al., 8 Jul 2025)
• Secure remote operation under privacy constraints, extending to encrypted/plausibly deniable telemanipulation (Takanashi et al., 2023)
• Human-to-human and human-robot bilateral interaction via FES (Hasegawa et al., 2018)
• Distributed parameter (e.g., pipeline, transmission line) stabilization using boundary four-channel control (Sun et al., 2024)

Challenges include the need for robust observer tuning in the presence of unmodeled dynamics, management of communication delays and packet loss (especially in encrypted implementations), accurate state estimation for heterogeneous or uncertain manipulators, adaptive or intelligent control laws to handle varying operator/environment dynamics, and hardware constraints (e.g., actuator bandwidth, misalignment in FES pads) (Hasegawa et al., 2018, Takanashi et al., 2023).

Future research directions highlight the integration of time-delay compensation in encrypted control, extension of multilateral/multi-DOF architectures, fully homomorphic controller execution, and coupling with learning-from-demonstration pipelines to further automate and personalize teleoperated task performance (Inami et al., 28 Feb 2025, Yamane et al., 8 Jul 2025, Yamane et al., 12 Oct 2025).