ForceMimic Systems: Bilateral Control

• ForceMimic Systems are two-channel frameworks that separate action (command) and reaction (response) signals for precise control and clear teleoperation mapping.
• They employ bilateral controller architectures with independent position and force channels, achieving high generalization in imitation learning experiments.
• The systems enable stable boundary control and observer-based output feedback for managing complex nonlinear dynamics in distributed parameter systems.

ForceMimic Systems (bilateral force-mimicking architectures) refer to a class of control and learning methodologies that rigorously separate and encode both action (command) and reaction (response) information—particularly force and position variables—using paired physical or virtual channels between agents or systems. Core to these approaches is the explicit decomposition of interactions into independent, bidirectional streams: commands (such as intended torque, velocity, or trajectory) delivered from the “master” to the “slave” subsystem, and responses (such as measured contact forces or environmental perturbations) returned from the “slave” to the “master.” This separation is exploited for precise teleoperation, robust imitation learning, stabilization of coupled or distributed parameter systems (e.g., PDE–ODE cascades), and complex multi-agent decision processes under partial information. The distinguishing feature of ForceMimic Systems is their use of bilateral—or two-channel—architectures that afford transparent, stable, and physically interpretable mappings of human or agent “intent” even under uncertainty, high-dimensional nonlinear dynamics, or unpredictable external disturbances.

1. Architectural Foundations and Bilateral Channel Separation

At the core of ForceMimic Systems is the bilateral controller architecture, in which two subsystems (often robots or control agents) are coupled via two distinct communication channels:

• Command channel: Transmits human or operator “intent” as explicit reference signals (e.g., torque, velocity, or position) from the master to slave.
• Response channel: Returns the measured reaction/response (e.g., environmental forces, slave torques) from slave to master.

This bilateral separation is formalized in the “4-channel” (4ch) teleoperation framework, where position synchrony $(\theta_m^{res} - \theta_s^{res} = 0)$ and force transparency $(\tau_m^{res} + \tau_s^{res} = 0)$ are realized through closed-loop control laws for both position and force (Sasagawa et al., 2019). Each side executes an identical position-plus-force controller:

$$\tau_m^{ref} = -C_p (\theta_m^{res} - \theta_s^{res}) - C_f (\tau_m^{res} + \tau_s^{res})$$

$$\tau_s^{ref} = +C_p (\theta_m^{res} - \theta_s^{res}) - C_f (\tau_m^{res} + \tau_s^{res})$$

with $C_p$, $C_f$ denoting the position and force loop gains, respectively.

Dynamic decoupling is maintained via disturbance and reaction-force observers, allowing clean extraction of both “intent” (command) and “reaction” (response) signals for downstream processing and learning (Adachi et al., 2018, Sasagawa et al., 2019).

2. Imitation Learning and Human Skill Generalization

ForceMimic architectures have demonstrated critical importance in imitation learning for robotic manipulation and human-robot cooperation tasks. By leveraging the bilateral channel separation, neural models learn mappings from the system’s state (e.g., positions, velocities, reaction torques of the slave) to the “human intent” signals as measured by the master (Sasagawa et al., 2019).

Distinct learning models are compared:

Model	Command Source	Force Control	Generalization (Success %)
SM-w/o-Force	slave→master	No	60.0
SS-4CH	slave→slave	Yes	51.7
SM-4CH	slave→master	Yes	98.3

Only SM-4CH, which learns the master's command signals as a function of slave state and includes force-feedback, achieves generalization across object types and external perturbations (e.g., spoon-length changes, plate-height offsets, intentional pushing). This demonstrates that strict separation and independent acquisition of force/position channels yield robust, high-generalization policies that cannot be achieved with conventional imitation learning using only position or combined signals (Sasagawa et al., 2019).

3. Bilateral Boundary Control in Distributed Parameter Systems

ForceMimic concepts are applied to bilateral boundary control for PDEs (e.g., reaction-diffusion, wave, and hyperbolic equations). Here, paired actuators at opposing domain boundaries provide independent control input channels. The “backstepping” and folding transformations employed in these works construct explicit, invertible maps that decouple the control effect of each boundary actuator (Vazquez et al., 2016, Chen et al., 2019, Guan et al., 2023, Bekiaris-Liberis et al., 2018). For example:

• The reaction–diffusion kernel $K(x,\xi)$ supporting $|ξ| ≤ |x|$ splits the domain into two independent subproblems—enabling mirror symmetric bilateral controllers with no algebraic interdependence (Vazquez et al., 2016).
• In cascaded PDE–ODE systems, tiered Volterra transformations and folding transformations partition the actuation and feedback laws into separate, explicit gains for each endpoint, leading to exponential stabilization in $L^2 \times \mathbb{R}^n$ (Chen et al., 2019).

Explicit closed-form bilateral controllers generally demonstrate reduced total control effort compared to unilateral (single-actuator) schemes when the system coefficients are large (Vazquez et al., 2016).

4. Bilateral Teleoperation with Sensorless and Dissimilar Architectures

In general teleoperation and haptic systems, ForceMimic Systems enable robust control of dissimilar master–slave pairs, including cases where no force sensors are available. The Virtual Decomposition Control (VDC) framework decomposes the teleoperation problem into two independently designed local controllers—each responsible for its own full nonlinear dynamics and local force feedback (Lampinen et al., 2020). Key advantages include:

• Force-sensor-less operation via inverse-dynamics-based local force estimation.
• Decoupling of motion tracking and force reflection objectives; only filtered velocities, positions, and forces are exchanged.
• Arbitrary scaling in motion and force can be implemented purely in the communication filters.
• Guaranteed $L_2 \cap L_\infty$ stability under arbitrary time delays and component substitutions.

In aggregate, this approach maintains full system stability and high tracking performance in demanding and heterogeneous remote manipulation scenarios.

5. Bilateral Decision-Making: Two-Player LQG and Separation Principles

ForceMimic principles extend to systems where decision making or estimation is distributed over two agents with distinct information sets, as in the two-player LQG problem (Lessard et al., 2013). The bilateral structure in this context is formalized by:

• Sufficient statistics for each controller being its own conditional mean estimate of the global state, constructed via distinct Kalman-type filters.
• Optimal control policies for each agent linear in these local statistics and coupled through explicit forward-backward Riccati-like recursions.

The bilateral separation yields a computational structure where estimation and control can be performed via coordinated but block-tridiagonal (thus efficiently solvable) recursions, maintaining complexity on par with the centralized single-controller case.

6. Observer-Based Output Feedback and Trajectory Generation

In nonlinear and infinite-dimensional systems, ForceMimic architectures facilitate the joint design of bilateral output-feedback controllers and observers (Bekiaris-Liberis et al., 2018). Through explicit local invertible transformations (Hopf–Cole, spatial gauge), and bilateral backstepping kernels, the system design achieves:

• Explicit separation between feedforward trajectory planning (using bilateral boundary actuators) and feedback stabilization.
• Bilateral observer designs using measurements at both ends to generate output-feedback control laws.
• Local exponential stability of the closed-loop system, with the observer error converging to zero and robust output tracking within a provable region of attraction.

The bilateral observer-controller separation closely analogizes the classical estimator–controller separation principle for finite-dimensional linear systems but extends it to classes of nonlinear parabolic PDEs and similar structures.

7. Significance, Generalizations, and Future Directions

ForceMimic Systems provide a mathematical and architectural framework for two-sided (bilateral) separation of action and reaction that is applicable across a broad spectrum of domains: teleoperation, distributed and boundary control, high-fidelity imitation learning, and distributed decision making. The universal feature is the explicit, stable, and invertible separation between command and response—in both physical interaction and information structure—affording transparency, robustness, and generalizability.

Future research directions may include extensions to multi-agent networks, fault-tolerant bilateral architectures, bilateral observer generalizations for nonlinear and higher-dimensional PDEs, and further development of learning-based bilateral controllers that can infer human intent under increased uncertainty and environmental variability.

Cited works:

• (Adachi et al., 2018)
• (Sasagawa et al., 2019)
• (Vazquez et al., 2016)
• (Chen et al., 2019)
• (Lampinen et al., 2020)
• (Guan et al., 2023)
• (Bekiaris-Liberis et al., 2018)
• (Lessard et al., 2013)