Pseudocompliance Controller

• Pseudocompliance controllers are robot control architectures that emulate compliant, spring–damper behavior through adaptive feedback laws and data-driven predictors.
• They integrate dynamic shaping and friction compensation to safely modulate forces in applications like surgical manipulation, dual-arm assembly, and legged locomotion.
• By blending model-free predictors with structured impedance control, these systems overcome the limitations of physical compliance for robust, real-time performance.

A pseudocompliance controller is a class of robot control architecture that renders compliant, spring–damper-like behavior through dynamic and/or computational means without relying exclusively on physical springs or passive mechanisms. Unlike pure passive compliance or explicit impedance-admittance control that depends on accurate environment or robot modeling, pseudocompliance controllers achieve compliant responses through structured feedback laws, data-driven predictors, and task-space/joint-space mappings, often incorporating friction compensation, dynamic inertia shaping, or model-free force estimation. They are widely deployed in situations where direct physical compliance is infeasible or undesirable, including force-sensitive surgical manipulation, legged locomotion, learning-based policy deployment, continuum robot actuation, dual-arm assembly, and free-floating object alignment.

1. Pseudocompliance Control Principles

Pseudocompliance controllers create compliant behavior by mapping sensor feedback (forces, positions, tensions) through nonlinear or adaptive control laws that emulate mass–spring–damper characteristics. Two primary traditions exist: (1) direct dynamic shaping, in which the control law compensates model nonlinearities and optionally modifies apparent inertia in Cartesian or joint space; (2) model-free or data-driven feedforward, in which learned predictors (e.g., recurrent neural networks) estimate internal robot states, isolating external loads for compliant actuation.

For example, in continuum robots, pseudocompliance is realized by using an LSTM-based RNN as a tension predictor, subtracting it from measured cable forces to estimate external contact, and then enacting a velocity-based compliance law in actuator space that mimics a virtual spring (Jakes et al., 2019). In rigid-body manipulators, computed-acceleration or operational-space controllers employ Jacobian mappings and structured feedback, compensating for friction and dynamic couplings while imposing desired stiffness and damping (Wang, 2 Oct 2025, Pro et al., 8 Sep 2025, Mitchell et al., 29 Apr 2025).

2. Mathematical Formulations and Control Laws

Canonical pseudocompliance architectures incorporate the following mathematical building blocks:

• Spring-Damper Behavior in Task Space:

$$F_{\mathrm{virt}} = K(x_d - x) + D(\dot{x}_d - \dot{x})$$

where $K$ and $D$ are user-specified stiffness and damping matrices.

• Computed-Acceleration Law (SPARC example):

$$\tau_{\mathrm{imp}}(q, \dot{q}) = M(q) J^\dagger(q)[\ddot{x}_d - \dot{J}(q, \dot{q})\dot{q}] + J(q)^\top F_{\mathrm{virt}} + C(q, \dot{q}) \dot{q} + g(q) - \tau_{\mathrm{fric}}(\dot{q})$$

where $\tau_{\mathrm{fric}}$ models joint friction and all dynamic terms are updated at high frequency (Wang, 2 Oct 2025).

• Interpolated Impedance Control (dual-arm example):

$$\tau_{\mathrm{cmd}} = (1-\alpha)\,\tau_q + \alpha\,\tau_x - \hat{\tau}_f + g(q^*)$$

with $\tau_q$, $\tau_x$ denoting joint- and task-space PD torques, $\alpha \in [0,1]$ controlling compliance blending (Mitchell et al., 29 Apr 2025).

• Model-Free Data-Driven Compliance (continuum robot example):

$$\dot{q}_t = \begin{cases} 0, & |\;F_{\mathrm{ext},t}\;|\le \lambda \ -\beta(F_{\mathrm{ext},t}-\lambda\,\mathrm{sign}(F_{\mathrm{ext},t})), & \text{otherwise} \end{cases}$$

where $$F_{\mathrm{ext},t} = F_{\mathrm{meas},t} - \hat{F}_{\mathrm{int},t}$$ and $\hat{F}_{\mathrm{int},t}$ is the RNN’s predicted internal tension (Jakes et al., 2019).

3. Controller Implementations and Software Architectures

Modern pseudocompliance controllers are implemented as real-time modules in popular robotics frameworks:

• CRISP provides Cartesian and joint-space impedance controllers as ROS2 plugins. Controllers receive high-level commands (pose, wrench, joint targets) at arbitrary rates and convert them in real-time (1 kHz update) to joint torques via structured spring-damper laws, friction barriers, and dynamic null-space projections. Compliance is realized by tuning stiffness/damping parameters and leveraging state-of-the-art libraries for kinematics and dynamics (Pinocchio) (Pro et al., 8 Sep 2025).
• Task/Joint-Space Dual-Arm Control integrates dynamic blending between joint- and task-space compliance on dual Kinova Gen3 arms, exposing compliance blend $\alpha$ and stiffness/damping to runtime reconfiguration. A model-free friction observer improves tracking performance, and open-source implementation supports teleoperation, learning-based trajectory streaming, and high-frequency control (Mitchell et al., 29 Apr 2025).
• SPARC Spine Control for quadruped robots utilizes computed-acceleration controllers, real-time friction compensation via smooth Stribeck models, and validated behaviors (linear force-displacement, mass-spring-damper response) to render programmable compliance in multi-DOF spine modules (Wang, 2 Oct 2025).
• Continuum Robot Compliance via RNN is implemented as a feedforward tension predictor followed by a proportional velocity law for each tendon; no explicit backbone or rod model is required, simplifying both software and hardware interface (Jakes et al., 2019).

4. Performance Evaluation Metrics and Experimental Results

Pseudocompliance architectures are assessed by metrics such as:

System/Method	Compliance Mode	Validation Metrics
SPARC Spine	Task space (x, z, θ)	Force-displacement error ≤1.5%, R²≥0.992, phase deviation <1.5%
CRISP (Franka/Kuka/Gen3)	Cartesian & joint space	Steady-state pos err ≈0.8–5.5 mm, rot err ≈0.003–0.1 rad, 20% tracking improvement via dynamic null-space
Dual-Arm Kinova Gen3	Task/joint blend	RMSE 0.41–1.20 cm in pin insertion, up to 30 N human contact
Continuum RNN (tendon)	Actuator space	LSTM tension error ≈2.5 N, insertion forces 5–7 N, no slippage
Free-Floating Objects	Direct force/inertia-shape	Contact forces 0.8–0.9 N, alignment in 2–3 s, no break events

These controllers are shown to yield compliant and safe robot responses across contact, manipulation, and interaction scenarios. Inference: The practical implication is that pseudocompliance architectures provide robust compliance even in robots not physically designed for passive compliance.

5. Applications and Domain-Specific Deployment

Pseudocompliance control has been successful in multiple domains:

• Robotic Manipulation: Dual-arm assembly, submillimetre pin insertion, learning-based trajectory execution, and force-sensitive teleoperation (Kinova Gen3, Franka FR3, KUKA IIWA14) (Mitchell et al., 29 Apr 2025, Pro et al., 8 Sep 2025).
• Legged Locomotion: Programmable, validated spine compliance using joint-space computed-acceleration control on quadrupeds (SPARC) (Wang, 2 Oct 2025).
• Medical Robotics: Nonstationary environment force modulation (surgical manipulation of compliant, moving tissues) via adaptive force controllers (Wijayarathne et al., 2020).
• Continuum Robots: Model-free compliance in single-segment tendon-driven robots using RNN predictors for unpredictable anatomical contact (Jakes et al., 2019).
• Space and Airbed Manipulation: Alignment of free-floating workpieces via direct force control and apparent inertia amplification, outperforming pure impedance control for contact maintenance (Sharma et al., 2020).

6. Tuning Guidelines, Limitations, and Stability Considerations

Consistent guidelines from multiple implementations:

• Stiffness/Damping Selection: Parametrize for critical or desired damping: $D \simeq 2\sqrt{MK}$, adjust K/D axis-wise. Start with low values for safety, increase for precision.
• Dynamic Blending: Ramp compliance blending parameters ($\alpha$) smoothly in hybrid joint/task-space controllers; avoid torque discontinuities.
• Friction Compensation: Employ model-free observers or parametric joint friction models (Stribeck/Coulomb) for accurate torque tracking.
• Force-Control Loops: Tune PI gains ($K_{pFB}, K_{iFB}$) for rapid but non-oscillatory force error convergence; inertia-shaping gains must remain within passivity bounds.
• Null-Space and Joint-Limit Barriers: Use dynamic null-space projectors for redundancy and joint barrier torques for safe operation near limits.

Limitations include necessary retraining of data-driven predictors after mechanical/electrical robot changes, accurate force sensing requirements, and controller reparameterization for new tasks/environments. Stability analyses generally require standard PI/PID passivity and dynamic coupling assessment; overly aggressive inertia shaping or feedback can induce instability, particularly in free-floating or underactuated systems.

7. Contextualization within Compliance Control Research

The pseudocompliance controller paradigm spans from classical computed-torque and impedance formulations to recent real-time, learning-enabled, and friction-compensated implementations compatible with ROS control standards. Unlike classical admittance or impedance controllers, which rely on explicit physical or geometric models, pseudocompliance controllers are defined by their ability to produce virtual compliant behavior via adaptive, computational, or model-free feedback, thus expanding access to compliant manipulation and interaction for a wide variety of robotic platforms and application domains (Wijayarathne et al., 2020, Jakes et al., 2019, Sharma et al., 2020, Wang, 2 Oct 2025, Pro et al., 8 Sep 2025, Mitchell et al., 29 Apr 2025).