Bilateral Control Separation

Updated 26 January 2026

Bilateral control separation is a design principle that partitions a system into independent, modular controllers operating on local dynamics and interconnected via minimal signals.
In teleoperation and nonlinear robotics, it enables sensorless force estimation and robust decentralized control by exchanging low-dimensional, filtered signals.
In distributed LQG and PDE control, the separation facilitates tractable estimation-control recursions and guarantees local stability under uncertainties and delays.

Bilateral control separation refers to architectural and methodological design principles by which overall control of a distributed, partitioned, or two-sided (“bilateral”) system is divided into independent—or at least modular—subsystem controllers, each acting on a physically or informationally separated component. These independently designed controllers are then reconnected only through a carefully structured interconnection, such as a communication channel, boundary interface, or coupling law. The separation enables each side to be analyzed, synthesized, and stabilized independently to the extent possible, with rigorous guarantees for the overall system even in the presence of system heterogeneity, uncertainty, or communication delays.

1. Fundamental Concepts of Bilateral Control Separation

At its core, bilateral control separation involves partitioning a system into two subsystems—often called “master” and “slave,” “Player 1” and “Player 2,” or “left” and “right” boundaries—such that each can be designed and stabilized using only local dynamics and measurements. Direct coupling terms, global state inversion, or joint computation are avoided in favor of a structured separation. The interconnection is typically realized via a channel that exchanges abstracted signals (forces, velocities, conditional means, or boundary states), formalizing the minimum necessary interaction to ensure overall control objectives.

The architectural premise, as seen in force-sensor-less teleoperation (Lampinen et al., 2020), partially nested two-player LQG systems (Lessard et al., 2013), and viscous Hamilton–Jacobi PDE control (Bekiaris-Liberis et al., 2018), is that stability and performance can be preserved or even enhanced by enforcing such separation, provided the coupling channel is appropriately designed.

2. Bilateral Control Separation in Teleoperation and Nonlinear Robotics

The application to bilateral teleoperation—where a human interacts with a master device to control a distant, potentially dissimilar slave manipulator—epitomizes bilateral control separation (Lampinen et al., 2020). In this context, the approach consists of:

Modeling each of the master manipulator (robot), the human operator’s limb, and the slave manipulator as fully independent nonlinear systems (with full parameterization of inertia, Coriolis, gravity, and coupling effects where relevant).
Designing decentralized model-based controllers for each manipulator using Virtual Decomposition Control (VDC), so that control synthesis and adaptive parameter estimation are fully local.
Incorporating the human operator via an explicit dynamic model in the master controller.
Exchanging only low-dimensional, filtered signals (typically Cartesian velocities and contact or reaction force estimates) across the communication channel.
Ensuring that each side needs no direct knowledge of the other’s detailed structure, model, or state space.
Establishing that local L₂∩L_∞ stability suffices for the closed-loop system, provided the bilateral channel enforces structured velocity–force coupling with gains designed using small-gain (H∞) principles.

This methodology removes the need for force sensors by reconstructing all necessary quantities from local measurements, model-based observers, or reaction force estimates, closing any algebraic estimation loops under explicit small-gain conditions (Lampinen et al., 2020).

3. Structural Separation in Distributed and Two-Player LQG Control

For stochastic, linear-quadratic-Gaussian (LQG) systems with two controllers—each with access to only partial measurements and controls—the bilateral control separation principle extends the classical separation of estimation and control from single-controller systems to partially nested multi-controller cases (Lessard et al., 2013). The key structural results include:

Each controller’s sufficient statistic is its conditional mean of the global state, computed from its local information set.
Estimation and control recursions for both players are coupled but structurally separated: each player propagates its own forward Kalman filter and backward Riccati recursion, but the filter and gain computations are intrinsically intertwined due to information asymmetry.
The full system can be solved by constructing and solving a block-tridiagonal linear system over the entire time horizon, preserving O(T) complexity, and thus computational tractability equivalent to the centralized case.

The bilateral separation principle in this context ensures that both estimation (filtering) and control (gain computation) can be individually synthesized, and their interconnection reduces to efficiently solvable coupled recursions (Lessard et al., 2013).

4. Output-Feedback and Observer-Based Bilateral Separation for PDEs

In the control of boundary-actuated distributed parameter systems, especially viscous Hamilton–Jacobi PDEs (Bekiaris-Liberis et al., 2018), bilateral control separation manifests as follows:

Trajectory-planning, state-feedback, and observer modules are each designed independently by transforming the nonlinear PDE into a linearized form via invertible feedback transformations (Hopf–Cole and stretching).
Explicit feedforward boundary controls produce desired reference trajectories by solving the associated linear PDE via flatness-based series expansions.
Bilateral state-feedback controllers enforce tracking of the reference using full-state linear backstepping laws applied independently at both boundaries.
Nonlinear observers, using measurements from both boundaries, estimate the internal state, feeding appropriate boundary signals back to the controllers.
The output-feedback closed loop, obtained by replacing true states by their estimates, is shown to decompose into a cascade of an exponentially converging observer error subsystem and the exponentially stable state-feedback subsystem.
Regional stability and regions of attraction are characterized explicitly, as invertibility of the transformations and well-posedness of backstepping holds only for sufficiently small initial errors (Bekiaris-Liberis et al., 2018).

Table: Summary of Bilateral Control Separation Features Across Domains

Domain/Example	Separation Aspect	Channel/Interface
Teleoperation (Lampinen et al., 2020)	Independent master/slave VDC controllers, force/velocity exchange	Cartesian velocity, scaled force
Two-player LQG (Lessard et al., 2013)	Separate estimation/control at each player, coupled recursions	Conditional mean, block-tridiagonal recursion
PDE boundary control (Bekiaris-Liberis et al., 2018)	Modular design: feedforward, feedback, observer, linearized couplings	Boundary state, output injection

5. Force Separation and Learning Applications

Bilateral control separation is also leveraged for data-driven robot learning. In imitation learning for object manipulation (Adachi et al., 2018), bilateral control systems are exploited to:

Cleanly separate and record the "acting" forces generated by the human operator (master side) and the "reaction" forces resulting from environmental contact (slave side) using a dual-robot, four-channel setup.
Enforce that the master and slave positions coincide, and that action–reaction force pairs sum to zero, yielding unmixed supervisory signals for both position and force.
Provide high-fidelity, unambiguous labels to train neural-network-based controllers (RNNs/LSTMs), enabling both accurate reproduction and generalization to new physical configurations.

Test results demonstrate that such architectures, especially when using "command predictor" models that interface modularly with pre-designed local controllers, result in robust, stable, and generalizable policies for contact-rich manipulation tasks (Adachi et al., 2018).

6. Experimental Demonstrations and Stability Guarantees

Empirical validation across modalities confirms the efficacy of bilateral control separation:

Force-sensor-less bilateral teleoperation achieves <3 mm RMS position errors and <5% force reflection error under large scaling factors and in the presence of 80 ms communication delays (Lampinen et al., 2020).
In two-player LQG, the block-recursion solution ensures that distributed controllers achieve centralized-level optimality with tractable complexity (Lessard et al., 2013).
Output-feedback controllers for Hamilton–Jacobi PDEs demonstrate exponential convergence within explicit regions of attraction, as ensured by local invertibility of the required transformations (Bekiaris-Liberis et al., 2018).
In robotic imitation learning, separated force/position training signals enabled policies that generalize to unseen geometries and contact conditions (Adachi et al., 2018).

7. Significance, Limitations, and Context

Bilateral control separation provides a systematic framework for distributed and modular control/estimation across diverse domains—robotics, networked stochastic control, and PDE systems. Its advantages include:

Decoupling high-bandwidth inner dynamics from low-bandwidth communication/exchange, supporting high-performance local control while maintaining global coordination.
Modularization of design, analysis, and verification, facilitating scalability and adaptation across heterogeneous or evolving system components.
Enabling force/feedback sensorless operation and robust learning signal extraction.
Guaranteeing stability under uncertainty, scaling, and delay, provided small-gain or region-of-attraction conditions are satisfied.

Limitations typically stem from local (not global) stability, requirements for invertibility of transformation maps, and the intricacy of gain/law design in the presence of coupled dynamics. Nonetheless, bilateral separation substantially reduces complexity for otherwise intractable coupled problems and supports rigorous, efficient synthesis of high-performance distributed controllers.

References: (Lampinen et al., 2020, Lessard et al., 2013, Bekiaris-Liberis et al., 2018, Adachi et al., 2018).