Adaptive Robotic Friction Modeling

• Adaptive robotic friction modeling is a field that integrates bio-inspired hardware, data-driven estimators, and hybrid physics-informed techniques to adapt friction properties in real-time.
• It leverages methods such as symbolic regression, residual learning, and probabilistic estimation to manage load-dependent, hysteretic, and directionally asymmetric friction phenomena.
• Applications range from robotic manipulation and prosthetics to autonomous vehicles, ensuring robust sim-to-real transfer and real-time friction compensation.

Adaptive robotic friction modeling encompasses the set of concepts, methods, and mechanisms used to identify, represent, and exploit frictional phenomena in robotic systems in an adaptive fashion—that is, updating or reconfiguring the underlying friction model or the hardware’s frictional behavior in response to changes in operating conditions, system state, contact scenario, or observed data. This field integrates model-based, data-driven, and hybrid physics-informed learning techniques with the development of reconfigurable hardware and embedded estimation architectures to enable precision, efficiency, and robustness in robotic actuation and manipulation.

1. Bio-Inspired and Variable Friction Mechanisms

Adaptive friction hardware mechanisms modulate the contact friction state in response to load or actuation, providing controlled transitions between low- and high-friction regimes. The bio-inspired adaptive pulley system (Dermitzakis et al., 2014) exemplifies this class. Here, the design uses a dual-material system with low-friction steel pins overlaying a high-friction silicone substrate. At low and moderate external loads, tendon contact is limited to the pins, minimizing friction and energy losses. At higher loads, the pins compress into the silicone substrate, recruiting the high-friction contact and effectively boosting output force in post-eccentric configurations. The frictional output transitions are described by:

• Capstan equations:

$$F_{t}^{e} = F_{l} e^{-\mu \alpha} \ F_{t}^{c} = F_{l} e^{\mu \alpha}$$

(where $F_{t}$ is tendon force, $F_{l}$ load, $\mu$ the coefficient of friction, and $\alpha$ the contact angle).

• A sigmoid transfer function enables smooth friction switching:

$S(F_l) = \frac{1}{1 + e^{-(F_r - F_{thr})}}$

The total friction force is a weighted sum of each material’s contribution, modulated by this transfer.

Other variable-friction end-effectors include origami-inspired surfaces capable of rapid, parametric switching between high-friction and low-friction contact (Lu et al., 15 Apr 2024), load-dependent friction-variable surfaces with embedded sensing (e.g., CAVS (Nojiri et al., 2022)), and friction-changing robotic finger epidermides. These hardware implementations motivate friction models that include state-dependent switching or continuous blending based on explicit mechanical deformation or force thresholds.

2. Adaptive Identification and Data-Driven Friction Models

Modern robotic tasks require friction models that not only reproduce steady-state values, but also capture dynamics, memory effects (hysteresis), direction asymmetries, and environment- or task-induced variations. Static model forms (Coulomb, viscous, Stribeck) are increasingly augmented or replaced with learned models:

• Physics-Informed Neural Networks (PINNs) combine data fitting with physical constraints on motion, often imposing the governing equations of motion (EoMs) or friction-specific ODEs (e.g., LuGre’s bristle dynamics) directly in the training loss (Sorrentino et al., 16 Oct 2024, Ozmen et al., 16 Apr 2025). These are used to identify friction behavior in systems ranging from underactuated mechanisms to humanoid robots with high-ratio harmonic drives.
• Symbolic regression (SR) discovers explicit, interpretable formulas from data for friction torque as a function of joint velocity, load, or their signs, providing equations expandable to include additional dependencies (Scholl et al., 19 May 2025).
• Probabilistic latent variable models (Vantilborgh et al., 20 Dec 2024) introduce neural parametrizations for both frictional effects and latent (unobserved) state dynamics, integrated with the lumped-parameter robot model, and are identified via expectation-maximization and sequential Monte Carlo methods. These approaches handle unmodeled or unknown dynamics, particularly important for nonstationary or hysteretic friction regimes.
• Residual learning architectures incrementally adapt a base friction model (often a neural network trained on ideal or symmetric data) to new or asymmetric operating conditions with minimal additional data (e.g., a ~43 s dataset) (Scholl et al., 2023). The correction network is structured to operate on inputs (such as the sign of velocity) that efficiently encapsulate discontinuity or unmodeled complexity.
• Excitation-optimized adaptive control-based estimators use linear parameterization of otherwise nonlinear friction effects (stiction, Stribeck, etc.), combined with excitation trajectory optimization and backstepping, to ensure unbiased parameter convergence and robust friction estimation without torque sensing (Huang et al., 8 Sep 2024).

3. Multimodal and Probabilistic Friction Estimation

When surface friction varies spatially on manipulated objects or in environmental contacts, estimation may benefit from integrating multiple sensing modalities and probabilistic modeling:

• Joint visuo–haptic object models (Le et al., 2020) use limited haptic exploration to directly measure local friction coefficients and RGB-D vision for point cloud feature extraction; a joint Gaussian Mixture Model (GMM) captures the visuo–haptic correlation, and Gaussian Mixture Regression (GMR) is used to infer friction coefficient maps for regions not physically explored. This enables grasp planners to sample gripper contacts at high-friction locations, boosting grasp reliability.
• In motion planning for autonomous vehicles, real-time fusion of predictive (vision-based, forward-looking, but low-accuracy) and local dynamic (high-accuracy, but only available under slip) friction estimates is best achieved with heteroscedastic Gaussian Process regression (Svensson et al., 2021). Uncertainty is spatially varying and encoded in the GP posterior; the final friction estimate $\hat{\mu}(s)$ at spatial coordinate $s$ is conservatively selected as the lower 95% confidence bound:

$\hat{\mu}(s) = \eta_*(s) - 1.96 \sigma_*(s)$

This framework prioritizes both safety (non-overestimation) and long-horizon planning.

4. Adaptive Friction Control and Compensation

Adaptive friction models are embedded within robot control architectures to enable real-time compensation and tracking:

• Certainty-equivalence adaptive control can be used for friction parameter estimation and compensation, especially with linearized or linear parameterizations of nonlinear friction (e.g., using tanh and exponential basis functions), with bias reduction via backstepping (Huang et al., 8 Sep 2024). Robustness is improved by optimizing excitation trajectories over the joint space.
• Composite learning control (CEL), blending instantaneous and memory-based error signals, exponentially accelerates the estimation of discontinuous friction (Coulomb, stick–slip) under relaxed excitation conditions and with reduced high-gain feedback needs (Pan et al., 2022). This is crucial for compliance, energy-efficiency, and smooth torque production in industrial arms.
• Immersion and invariance (I&I) observers enable globally convergent friction compensation even when direct velocity measurement is infeasible (Romero et al., 31 Jul 2025). By coupling a dynamic observer (augmenting the system’s dimension) with specifically constructed proportional and integral correction terms for friction parameters, one can estimate both velocity and nonlinear friction terms, e.g.,

$$\dot{x}_2 = -\theta_1 x_2 - \theta_2 \tanh(v x_2) + u$$

and employ adaptive laws that guarantee Lyapunov stability and convergence for the estimation errors.

5. Physics-Based vs. Data-Driven and Hybrid Model Transferability

Adaptive modeling strategies must balance physical interpretability, identifiability, robustness, and adaptability:

• Extended friction models for simulation (including Stribeck, load-dependent, directionally asymmetric, and even quadratic load-dependent models) are parameterized and identified on servo actuators and facilitate sim-to-real transfer for control and reinforcement learning by improving simulation fidelity (Duclusaud et al., 11 Oct 2024).
• Physics-informed learning frameworks embed model structure (such as the LuGre friction ODEs) directly into neural estimators, ensuring physical plausibility, greater data efficiency (learning from a few seconds of data), and superior sim-to-real generalization compared to heuristic or black-box models (Ozmen et al., 16 Apr 2025).
• Symbolic regression unites interpretability with adaptability, allowing friction models to be easily retrained or extended as new variables become available.

6. Applications in Manipulation, Locomotion, and Soft Robotics

Adaptive friction modeling has demonstrated impact across a wide range of robotic systems:

• In tendon-driven anthropomorphic prosthetics: Adaptive friction switches, pulleys, and sheathes enable muscle-like force asymmetries and actuator downsizing (Dermitzakis et al., 2014).
• In robotic grippers: Load-switchable, origami-inspired, or camera-sensed variable-friction surfaces allow seamless transition between firm gripping (high friction) and precise object manipulation (low friction) (Nojiri et al., 2022, Lu et al., 15 Apr 2024).
• In autonomous vehicles: Real-time Bayesian and GP-based fusion of heterogeneous friction estimates directly improve safety and agility under varying and uncertain road conditions (Svensson et al., 2021, Vaskov et al., 2023).
• In robotics simulators and sim-to-real transfer: Static friction has been identified as a key factor in the sim-to-real gap; explicit parameter identification and inclusion of static friction in domain randomization is essential for successful policy transfer, especially in challenging terrains (Hu et al., 3 Mar 2025).
• In extra-robotic fingers and prosthetics: Friction-scaled vibrotactile feedback enables human users to sense incipient slip conditions and adapt grip force in real time, with discrimination accuracy above 94% in psychophysical experiments (Afzal et al., 19 Mar 2025).

7. Challenges and Outlook

Major open challenges and ongoing directions in adaptive robotic friction modeling include:

• Generalization and minimal data: Many physics-informed and residual learning methods now deliver high-accuracy friction estimation or adaptation using less than a minute of data from a new scenario (Scholl et al., 2023, Ozmen et al., 16 Apr 2025).
• Robust online adaptation: Increasing model complexity to capture phenomena such as load dependence, directionality, and hysteresis (often via latent variable neural network architectures (Vantilborgh et al., 20 Dec 2024)) raises identification and computational demands. Techniques such as sparse regression (SINDy (Fehr et al., 2022)), symbolic regression (Scholl et al., 19 May 2025), and composite learning (Pan et al., 2022) address this by leveraging structure and data memory.
• Sensor and actuation limits: Approaches enabling velocity- or torque-sensorless adaptation (e.g., I&I observer-based control (Romero et al., 31 Jul 2025)) extend applicability to cost-constrained and low-infrastructure platforms.
• Transferability and sim-to-real: Adaptivity, interpretability, and transferability of friction models are essential for maintaining performance in complex, changing, or unmodeled environments. Embedding physical constraints into learning models is increasingly shown to be critical in bridging the sim-to-real gap for advanced robot morphologies and underactuated tasks (Ozmen et al., 16 Apr 2025, Duclusaud et al., 11 Oct 2024, Hu et al., 3 Mar 2025).
• Integration with multimodal sensors and actuation: Future systems are likely to use tightly-coupled sensor networks (e.g., embedded cameras, force sensors, distributed tactile arrays) and adaptive surfaces to switch frictional behavior at high speed and granularity, integrated with model-based or learned estimators.

Adaptive robotic friction modeling thus constitutes a multifaceted field encompassing advanced estimation algorithms, physically-informed machine learning, variable-friction hardware, and integrated sensorimotor architectures, with broad implications across manipulation, locomotion, and human–robot interaction.