Friction

Low-friction surfaces challenge bipedal locomotion by limiting the contact forces available during stepping. Inspired by penguin waddling, we investigate how lateral torso motion and center of mass (COM) placement affect locomotion as surface friction changes. Using a five-actuator biped, we compare an upright-gait strategy with a penguin-inspired torso-over-stance-leg strategy across multiple COM placements in simulation and hardware. In the 3-D simulator MuJoCo, we sweep through sinusoidal leg and hip actuation parameters across four friction coefficients mu = 0.1, 0.3, 0.5, 0.7. In simulation, torso-over-stance-leg motion produces more successful controllers and higher forward speeds at low friction, with the highest speed occurring for the high-COM configuration. Hardware experiments show the same low-friction speed trend: at mu=0.12, torso-over-stance-leg motion increases forward speed and reduces cost of transport at both tested COM ratios, and the higher COM also improves both measures. The high-COM penguin configuration is the fastest and most energy efficient while maintaining low sideways foot motion. At mu=0.45, the COM trend reverses: the lower-COM configurations are faster and more energy efficient, while gait strategy has little effect on forward speed but still changes sideways foot motion. These results show that the effects of lateral torso motion and COM placement depend on the available friction, and that forward speed, energy use, and slip-related foot motion can be modulated with a penguin-inspired torso motion on hardware.

Machine-learning surrogate models offer a promising alternative to high-fidelity Computational Fluid Dynamics (CFD) simulations for aerodynamic analysis and design. However, constructing accurate surrogates for realistic aircraft configurations remain challenging due to complex geometries, multiple flow regimes, and limited training data. This work presents the methodology that achieved first place in the ONERA CRM Wall Distribution Regression Challenge, which focuses on predicting pressure and skin-friction coefficient distributions over the NASA Common Research Model wing-body-pylon-nacelle configuration under different operating conditions. The proposed approach formulates the problem as a conditional neural field mapping spatial coordinates, surface normals, and operating conditions to aerodynamic wall quantities. Fourier feature encoding, a relative squared error objective aligned with the challenge metric, ensemble learning, and $k$-fold cross-validation are progressively introduced to improve prediction accuracy and exploit the limited training data. Beyond presenting the final methodology, the paper documents the successive model design choices that led to the winning solution through a comprehensive ablation study and discusses several alternative approaches that were investigated but ultimately discarded. On the hidden competition test set, the proposed methodology achieves an overall score of 8.81, outperforming the strongest organizer-provided baseline, which achieved a score of 8.64, while requiring approximately three orders of magnitude fewer trainable parameters. These results illustrate that carefully designed coordinate-based neural fields constitute an efficient and robust framework for aerodynamic surrogate modeling on complex geometries under limited-data conditions.

A finite-difference bowed-string model with implicitly resolved Stribeck friction is presented, with a regime diagnostic, the Schelleng bow-force limits on four strings, and a comparison of learned bow controllers. Implicit resolution is necessary, and quantitatively so: a lagged contact force cannot capture the string on a discrete grid, so no stick phase forms at any bow force. With friction, impedance and quality factor taken from published measurement rather than fitted, all four strings return a stick fraction of 89.1% against an ideal 90%. Schelleng's maximum bow force is recovered on every string. The minimum is not: it follows $Z v_b β^{-1}$ rather than the predicted $Z^2 v_b β^{-2}$, reducing both squared dependences to first powers. Six controllers at matched capacity, over four strings and twenty seeds each, place a gated recurrent network ahead of a feedforward one, by most under a mid-stroke disturbance. The feedforward network completes more strokes only from a start the model's own playability map places outside the Helmholtz region. A minimal gated variant fails because gates computed from the input alone cannot clear a latched state. Training loss selects neither the capacity nor the context length, and no learned controller improves on the lookup rule that generated its labels. That bound has a domain. Regressing the controller's score on the rule's gives a slope of 0.32, more than ten standard errors below unity, so the controller overtakes the rule where the rule fails and is bounded by it where it holds. Under a rigid finger stop the plant is provably invariant, so transfer loss between pitches belongs to the controller alone and is traced to one feature. A regime classifier without a stick test labels small-amplitude periodic slipping as Helmholtz motion, and a harmonicity measure rates a string the bow never grips above Helmholtz motion.

Diffusion models have recently emerged as expressive generative priors for planning and control. This paper studies Action Diffusion, an action-sequence diffusion formulation used as an open-loop proposal distribution for a point-mass system with dry friction and stiction. In this benchmark, motion starts only when the applied input exceeds a static-friction threshold, so effective controls occupy a small and temporally structured subset of the action-sequence space. A compact conditional 1D U-Net generates bounded control sequences conditioned on initial and target states. We compare it with uniform random shooting, random shooting from the same structured dataset prior, and the Cross-Entropy Method (CEM). Results show that Action Diffusion reduces terminal error and stuck steps, especially in low-sample regimes. These results indicate that conditional diffusion provides an effective mechanism for generating temporally coherent control sequences that overcome stiction by conditioning and recombining structured control primitives from the training prior for state-to-state open-loop control.

Productive dialogue alignment requires distinguishing \emph{surface coordination} (acknowledgments and smooth task progression) from \emph{epistemic alignment} (convergence of belief states); standard preference-based methods typically optimize response-level preferences without explicitly modeling the latter. We operationalize Theory-of-Mind (ToM) inference as a control signal within Frictive Policy Optimization by extracting, at each referring expression, a four-part belief structure: the speaker's intended referent, the addressee's interpretation, and each participant's model of the other's belief. This makes friction mechanically computable from epistemic-state comparisons, capturing \emph{silent divergence}, where both participants proceed confidently while grounding to different referents. We evaluate the signal at two levels. At the representation level, ablating the second-order channel reduces misunderstanding recall from $65\%$ to $26\%$. At the policy level, reward-shaping (FAR) and trust-region (FTR) variants improve intervention F1 and warranted-context calibration over DPO, with Brier scores independently supporting the calibration gains. Across three training runs, FAR and FTR remain substantially more stable, whereas DPO varies widely and can degrade intervention competence already present in the base policy. Thus, ToM-grounded friction provides a trainable signal for context-sensitive intervention under referential belief divergence.

Overlapped friction ridge patterns are a recurring problem in latent fingerprints recovered from crime scenes and in live-scan scenarios where residual fingerprints on the sensor may corrupt subsequent acquisitions. Existing approaches for separating overlapped fingerprints either rely on rule-based orientation field completion that requires strong domain knowledge or train end-to-end deep neural networks that do not account for domain-specific considerations. This work introduces a diffusion-based pipeline for separating component fingerprints from an image containing overlapping friction ridge patterns. We formulate the separation problem as an inpainting task and progressively learn a diffusion model for this task in multiple stages. Starting from a pre-trained Stable Diffusion model, we progressively incorporate a fingerprint prior, add the ability to complete partial fingerprints, and finally propose \textbf{overlap-aware inpainting} that reconstructs each component print using a diffusion inpainting model based on multi-channel conditioning. Experiments on two public datasets demonstrate that component fingerprints reconstructed using the proposed diffusion-based inpainting method can match with their mated counterparts with very high probability.

Generative AI tools for creative work tend to be designed around the goal of removing friction, on the assumption that smoother iteration and faster output translate into more value for the designer. We argue, however, that this framing leaves out something important about how design ideation works, namely reflection-in-action. The act of accepting, rejecting and reworking candidate ideas is both a path to a final outcome and the process through which designers develop the rationale that allows them to think with their ideas and to communicate them to others. This becomes particularly important in group ideation, where ideas need to be expressed and explained to others to allow the group to extend, reject or combine them further. We suggest that AI in design ideation might be more usefully thought of as a friction agent for reflection rather than as a smoothing agent for output. This reframing opens up a different role for AI in design ideation, one that supports designers in building and carrying rationale rather than substituting for it.

Classical grasp quality metrics assume one deterministic friction coefficient and therefore cannot assess whether a grasp maintains force closure across plausible friction values. We present FIRMGrasp, a family of grasp quality metrics that incorporates friction uncertainty through Conditional Value-at-Risk (CVaR). At confidence level $β$, we evaluate the force-closure margin at the mean of the adverse friction tail. This evaluation defines the risk-adjusted margin $\varepsilon^{(β)}$, the inscribed-ball radius of the corresponding grasp wrench space. We prove that $\varepsilon^{(β)}$ varies monotonically with $β$, remains differentiable in the grasp parameters, and certifies that any grasp with $\varepsilon^{(β)} > 0$ achieves force closure with probability at least $β$. Across 1,599 LEAP Hand and Allegro Hand grasps, $\varepsilon^{(β)}$ identifies friction-sensitive grasps that receive high nominal Ferrari-Canny scores, and 53% of the nominally force-closed grasps lose closure in the adverse friction tail. The nominal margin ranks a successful grasp above a failed grasp with probabilities of only 0.53 in the shake test and 0.67 in the pick test, whereas $\varepsilon^{(β)}$ achieves 0.63 and 0.78. At an adverse friction coefficient of 0.2, 70% of grasps with positive $\varepsilon^{(β)}$ withstand a simulated lift and lateral pull, compared with 25% of grasps with positive nominal margin and nonpositive $\varepsilon^{(β)}$. We also synthesize grasps with positive $\varepsilon^{(β)}$ for the RealHand L6 and LEAP Hand, both of which retain the object during adverse-friction lifts. In MuJoCo trials with the RealHand L6, 95% of grasps that establish contact and have positive $\varepsilon^{(β)}$ retain the object at the same adverse friction coefficient.

Existing approaches to frictional contact dynamics typically either modify the Coulomb law to improve numerical robustness or solve the exact law in a fully coupled monolithic form. However, in its reduced form, exact Coulomb friction can be written as a cone complementarity problem with an augmented velocity, which reveals a natural split between a cone-constrained linear response and a scalar non-associated coupling induced by tangential velocity. We exploit this structure in the solver design. Our method uses an outer iteration to update the non-associated coupling explicitly, and an inner solve for a strongly convex cone-constrained quadratic program. This separation also makes the inner solver modular, so different numerical schemes can be used without changing the outer iteration. We evaluate the method on rigid-body benchmarks with stick-slip transitions and frictional stacking, and show that it reproduces exact Coulomb complementarity without smoothing or relaxing the friction law.

Safe navigation within the spinal subarachnoid space is constrained by its narrow, compliant, and delicate anatomy. Conventional catheters and continuum robots rely on proximal pushing, generating friction and shear along the tissue device interface that limit distal controllability and increase the risk of neural injury. Here, we present a 2 mm diameter eversion-growing robotic platform that enables friction minimised extension and steering within the human spinal subarachnoid space, validated through computational modelling, phantom experiments, and intact human cadaver studies. The robot integrates a miniature endoscope for real time intrathecal visualisation and advances by pressure driven tip eversion, localising motion to the distal tip while minimising translational sliding of the deployed body. Phantom experiments demonstrated reductions of 65.2% in mean interaction force and 48.0% in peak interaction force compared with matched push-based insertion. Physics based modelling showed that eversion based growth redistributed tissue loading, reducing local stress concentrations and interfacial shear relative to conventional insertion. In an intact human cadaver, the system achieved 150 mm of controlled intrathecal extension with concurrent fluoroscopic and endoscopic visualisation, providing access across multiple vertebral levels from a standard lumbar entry point. Postprocedural laminectomy and durotomy revealed no observable macroscopic disruption of the dura mater or surrounding neural structures. These results provide the first mechanically characterised and multimodally validated demonstration of eversion-based robotic navigation in intact human spinal anatomy, establishing a quantitative and procedural foundation for future intrathecal interventions. Further validation in larger anatomical cohorts and under physiological conditions will be required before clinical translation.

Non-prehensile manipulation enables flexible material handling with part carriers, but friction-based support makes high-speed motions failure-prone, while slower operation increases cycle time. Proactive failure prediction is therefore essential for efficient and reliable performance, yet existing approaches remain limited by key constraints, including sensitivity to dynamic actions and high dependence on known policy structures. Furthermore, existing methods and datasets lack a precise characterization of the latest intervention time, leaving it unclear whether a detected failure can still be prevented through timely intervention. In this paper, we investigate lift-and-place tasks for non-prehensile material handling manipulation and propose a more effective approach to predicting precursors to failures (PREFAIL) by analyzing the relative motion of target objects with respect to the carrier. We further introduce a dataset that precisely identifies the latest intervention time for risky manipulations, enabling rigorous evaluation of whether a failure prediction is actionable. We validate our approach on both simulation and real-world datasets. Our experimental results demonstrate that PREFAIL substantially improves both the accuracy and timeliness of responses to failure precursors.

Closed-loop wall control learnt by multi-agent reinforcement learning can lower skin-friction drag in turbulent channels, but these gradient-based policies are trained on small periodic boxes and exhibit reduced performance when carried over to a larger domain. We recently showed that such policies are also prone to saturated bang-bang actuations that collapse into standing streamwise waves whose scale is set by the computational box rather than by the near-wall cycle, and proposed architectural fixes that avoid these degeneracies. Here, we employ Evolution Strategy (ES) to optimise a recurrent closed-loop controller directly on a large turbulent channel at $\mathit{Re}_τ\simeq180$, evaluating policy performance over full flow episodes using an energy-aware criterion and processing candidate policies in parallel. To our knowledge, this is the first application of an evolution strategy to the control of a turbulent flow. The ES controller reduces the skin friction by about $26\%$, exceeding the gradient-based multi-agent controller of Cavallazzi et al. (2026), GRU-MARL, trained on a minimal box ($17\%$), and marginally exceeding classic opposition control (OC, $22\%$). A wall-normal decomposition of the friction, Reynolds-stress profiles and anisotropy invariants show that the ES and opposition-controlled flows follow separate trajectories through the buffer layer, reaching comparable drag reduction by different reorganisations of the near-wall turbulence. In particular, the ES actuation correlates predominantly with the streamwise velocity fluctuations rather than with the wall-normal velocity that classical OC targets.

AI agents that generate final answers based on user input often do not meet the needs of creative fields. Fields such as structural design and architecture need interactive systems that help users externalise and develop ideas, explore alternatives, and refine partial solutions. The final product of such designs needs to comply with many constraints concerning, e.g., spatial configuration, mechanical behaviour, material quantities, and costs. These constraints create friction in the design process, which can stimulate novel and creative solutions. In this paper, we discuss the misalignment between current generative AI goals to remove friction and provide final solutions and the needs of creators, such as structural designers, who develop ideas through iterative work. We present the design dimensions of systems allowing for constrained human-AI co-creation that rely on vision-language models making structural exploration conversational, multimodal, and responsive to evolving human intent in ways that follow and augment the discipline's creative process. Through a pilot design interface based on these principles and a study with experts in the field, this paper shows how structural designers perceive interactive AI systems and how such systems can support design space exploration by reducing repetitive modelling friction while preserving reflective design friction.

Forecasting leaderboards rank models by predictive quality, but their winners are often read as deployment-ready top-1 advice. That reading can fail when forecasts are passed through a fixed decision interface, such as an alert threshold, a top-k budget, or a switching-cost policy. We study when a forecast-side winner can be certified as deployment-actionable for a specified interface and deployed utility. We introduce a fail-closed certification protocol whose gates are sufficient evidential conditions for a strong claim: a friction-caused, non-tie, statistically supported, and recurrent deployment-side reversal. Traffic-Hourly provides a certified anchor: winners agree at zero friction, but positive switching friction makes the forecast winner deployed-suboptimal. A locked native audit tests overclaiming: across 22 verified candidates and 362 full-grid cells, 155 apparent forecast/deployment winner inversions are blocked before certification. The contribution is not a new forecaster, metric, or universal utility, but a conservative protocol for deciding when forecasting leaderboard winners should be read as deployment-actionable top-1 advice.

Lower-limb exoskeletons require actuation systems that can provide accurate joint torque control while preserving low mass and encumbrance. Conventional architectures often rely on independently actuated joints and joint-level torque sensors, increasing system complexity and weight. This paper presents a novel differential actuation architecture for hip-knee flexion/extension, enabling cooperative torque sharing between two motors via a linear differential mapping between motor and joint. To compensate for transmission losses, a model-based friction estimation strategy is developed and experimentally implemented, allowing accurate joint torque estimation without the need for torque sensors. The proposed solution is validated on a physical prototype, demonstrating the feasibility of sensorless torque estimation in a differentially actuated hip-knee module of a lower-limb exoskeleton.

Accurate prediction of electrical power consumption is essential for energy-aware motion planning, battery management, and thermal monitoring in battery-powered humanoid robots. This letter presents a physics-based, linear-in-parameters model for the electrical power consumption of the seven-degree-of-freedom left arm of the UnitreeG1 humanoid robot. The proposed formulation combines actuator loss terms with a baseline-torque correction that captures changes in gravity-compensation load and enables accurate prediction of negative net power trajectories. Pairwise interaction terms are introduced to model power coupling during simultaneous multi-joint motion. Model parameters are identified from experimental data collected on a physical UnitreeG1 using onboard power measurements as the regression target. Across 897 trajectories covering single-joint and coordinated arm motions at multiple speed levels, the identified model achieves $R^2 = 0.933$ with an RMSE of 1.07 (W). Validation on 46 trajectories executed at previously unseen speeds yields $R^2 = 0.965$, demonstrating strong generalisation beyond the identification dataset. Analysis of the identified parameters reveals distinct power-consumption characteristics across the arm, with viscous friction dominating most joints (shoulder pitch and all three wrist joints), copper losses dominating shoulder yaw and the elbow, and shoulder roll uniquely dominated by Coulomb friction.

Most learned dexterous grasp generators relegate contact forces to a downstream verification step, so a kinematically-plausible pose can still violate the conditions for a stable physical grasp. We address this with EquiDexFlow, an SE(3)-equivariant flow-matching model that jointly predicts wrist pose, joint angles, fingertip contacts, surface normals, and contact forces from an object point cloud. Our architecture projects contacts onto the object surface and forces into the Coulomb friction cone by construction, so placement and friction compliance hold without loss penalties. We prove end-to-end SE(3) equivariance and verify it empirically over 200 rotations, with wrist residuals below $0.04^\circ$ and exactly zero joint deviation. Trained on 8,100 force-closure grasps across 81 objects for the 16-DoF Allegro Hand, our model achieves zero friction violations, the best composite score, and the lowest wrench residual among all ablation variants. We retarget decoded fingertip contacts to a 16-DoF LEAP Hand via per-finger inverse kinematics, and our hardware-feasible refinement places every joint at least 5% inside its actuator envelope while preserving wrench balance. On the physical robot, retargeted EquiDexFlow-decoded grasps complete open-loop pick-and-hold trials on all six test objects, with every asymmetric object succeeding at both the canonical pose and a $120^\circ$ co-rotation. Videos, code, and checkpoints are available at https://equidexflow.github.io.

In autonomous racing, especially in competitions such as Formula Student Driverless, precise planning of the target velocity of a race car is crucial for competitive lap times and stable driving behavior. Especially at high speeds, Velocity Planning (VP) is a significant challenge as it has to be performed in real time, taking into account track layouts, environmental influences, mechanical tolerances, and the resulting control inaccuracies. In this paper, we present a novel approach to VP that dynamically adapts to such changing conditions. Instead of estimating the physical Tire-Road Friction Coefficient (TRFC), a continuous scaling factor is inferred indirectly from vehicle stability. This factor not only reflects the effective tire-road interaction but also captures effects of control inaccuracies. From this, we generate a continuous friction map, which serves as a robust, adaptive basis for computing the optimal target speed, accounting for both vehicle and environmental limits. Our proposed approach was evaluated on a real Formula Student race car, showing a lap time improvement of 35 % over ten laps and an average increase of 8 % compared to a non-adaptive approach.

In fulfillment centers, diverse objects move continuously from inbound to outbound operations and can become jammed due to excessive conveyor friction, incorrect orientation, or mechanical failures. Traditional jam detection approaches rely on object detection models to identify objects, followed by tracking algorithms (such as IoU overlap and Kalman filtering) to monitor motion over time. This pipeline requires thousands of manual annotations, consuming approximately two weeks of effort, and is limited to annotated object classes. We present a training-free, object-agnostic jam detection method that eliminates the need for labeled data. Our approach uniformly samples reference points within the monitoring region when no objects are present. As objects occlude these points, we detect motion. When a sufficient fraction remains occluded beyond a temporal threshold, we classify the event as a jam. Unlike conventional point tracking--which treats occlusion as a failure case--our approach repurposes occlusion as a detection signal, monitoring whether reference points remain persistently occluded rather than tracking where they move. Our experimental evaluation on 1,069 videos demonstrates that AllTracker achieves 100.00% precision and 93.33% F1 score, significantly outperforming classical sparse tracking methods while maintaining training-free deployment. This approach offers three key advantages: (1) no training data or manual annotations, (2) object-agnostic generalization to arbitrary object types, and (3) significantly reduced development time.

Direct physical guidance is a natural means of teaching and interacting with robots, and robotic skins make a key contribution by enabling sensitive contact sensing and localization. This paper presents a tactile-proprioceptive sensor fusion framework for natural physical human-robot interaction. Tactile cues from pneumatic skin pads serve as contact indicators that bypass the ambiguity between frictional residues and applied external forces, enabling highly sensitive contact detection without explicit friction identification. We fuse these cues with motor-current-based proprioception to reconstruct multi-axis contact forces on the robot surface. To maintain accuracy during motion, we employ a temporal convolutional network (TCN) to mitigate friction hysteresis during stick-slip transitions, reducing uncertainty at contact onset and yielding smooth, responsive guidance. We validate the approach on a skin-integrated robot arm: (i) multi-axis forces are reconstructed in stationary contacts, and (ii) simultaneous force estimation and kinesthetic teaching are demonstrated. Results indicate improved sensitivity and responsiveness across diverse contact conditions compared with tactile-only and proprioceptive-only baselines, supporting tactile-proprioceptive fusion as a reliable pathway to safe, intuitive physical human-robot interaction.

Accurately estimating object mass and friction is fundamental to reliable robotic manipulation. While interactive perception is powerful, most approaches rely on specialized hardware like force/torque sensors, limiting scalability. This paper introduces PhyPush, a physics-guided Transformer that estimates an object's mass and friction coefficient using only end-effector velocity from a single push, data readily available on standard robotic arms. By incorporating Newton's second law and the Coulomb friction model through a physics-guided loss, the model improves physical consistency and generalizes to unseen objects and surfaces. Across diverse setups, PhyPush consistently achieves highly accurate estimations in challenging out-of-domain conditions. In simulation, it reduces error by over 10% compared to a baseline with privileged force data, while in real-world experiments, it successfully zero-shot transfers from simulation to outperform a purely data-driven baseline.

Developing dynamic models for tendon-driven continuum robots is challenging due to their nonlinear, high-dimensional, and friction-dominated dynamics. This paper presents a comparative study of data-driven system identification methods, including N4SID, ARX, and SINDYc, for modeling a tendon-actuated continuum robot with rolling joints developed at CERN. Despite the high number of joints of the robot, experimental analysis reveals that a two-degree-of-freedom dynamic model can accurately capture the system dynamics, owing to strong kinematic dependencies between the joints. The models are validated against experimental data, and used in the design of a model predictive controller, demonstrating their feasibility for real-time control.

Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling inherent to classical Archard and Greenwood-Williamson models, severely restricting their functional range. Here, we propose a framework for the inverse design of tribological metainterfaces engineered for programmable contact behaviors. By utilizing general axisymmetric asperities, we unlock nonlinear macroscopic responses unattainable by standard Hertzian contacts. To solve the inverse problem, we embed a fully differentiable contact mechanics engine within a neural network and a quadratic optimizer. We leverage regularized physical gradients to automatically discover non-standard topographies that reproduce complex target friction laws, with only a few asperities in unit cells. The predicted designs are strictly validated against high-fidelity Boundary Element Method (BEM) simulations. This framework bridges data-driven optimization and rigorous physics, offering a scale-invariant pathway for discovering functional tribological surfaces.

Adaptive control of Euler-Lagrange systems is challenging when friction is governed by a finite-horizon internal state that is not directly observable from joint measurements. In this setting, the measured closed-loop state is no longer Markovian, and standard certainty-equivalence adaptive laws may lose their convergence guarantees. The paper proposes a meta-control architecture in which the gains of a computed-torque controller are generated by a self-attention block processing a short window of recent motion history. The number of attention heads is selected before policy training through a surrogate analysis of the autocovariance of the memory-state gradient along the temporal window. This surrogate is based on a temporal adaptation of an incremental rank-tracking framework previously developed by the authors. The selected head count is then fixed and used as an architectural hyperparameter in a reinforcement-learning stage, where the policy is trained under a shielded admissibility constraint. The approach is tested on a 2-DOF manipulator with nonlinear friction and variable payload. In the short and matched memory regimes, the single-layer attention-only meta-controller outperforms a deeper Transformer baseline, with tracking-error reductions of 12 and 19 percentage points, respectively. The reported effect sizes are large, with d approximately -1.1 and -2.1, and Mann-Whitney p < 0.05 in both cases. In the long memory regime, however, the advantage disappears. Four out of ten training runs show either divergence or payload-invariant policy collapse, revealing a weakness in the static Phase-1 head-count prescription. This motivates moving rank-tracking inside the reinforcement-learning loop, allowing attention heads to be pruned or grown at runtime instead of fixed before training.

Accurately estimating friction coefficients between arbitrary material pairs is critical for robotics, digital fabrication, and physics-based simulation, but exhaustive pairwise testing scales quadratically with the number of materials. We introduce a proxy-based modeling framework that approximates any pairwise friction $f(A,B)$ from a small, fixed set of proxy materials $C=[c_1,\dots,c_k]$ by learning a per-material embedding $z_A = g(f(A,c1),\dots,f(A,ck))$ and a fusion function $p$ such that $f(A,B)\approx p\big(z_A,z_B\big)$. We present deterministic and probabilistic realizations of $g$ and $p$, procedures for selecting diverse proxy sets, and mechanisms for handling missing or noisy proxy measurements. The learned embeddings are compact, interpretable, and enable calibrated uncertainty estimates for downstream decision making. On simulated and measured friction datasets, our approach achieves high predictive accuracy, robust performance with partial observations, and substantial experimental savings by significantly reducing pairwise testing.

Drifting Models [Deng et al., 2026] train a one-step generator by evolving samples under a kernel-based drift field, avoiding ODE integration at inference. The original analysis leaves two questions open. The drift-field iteration admits a locally repulsive regime in a two-particle surrogate, and vanishing of the drift ($V_{p,q}\equiv 0$) is not known to force the learned distribution $q$ to match the target $p$. We derive a contraction threshold for the surrogate and show that a linearly-scheduled friction coefficient gives a finite-horizon bound on the error trajectory. Under a Gaussian kernel we prove that the drift-field equilibrium is identifiable: vanishing of $V_{p,q}$ on any open set forces $q=p$, closing the converse of Proposition 3.1 of Deng et al. Our friction-augmented model, DMF (Drifting Model with Friction), matches or exceeds Optimal Flow Matching on FFHQ adult-to-child domain translation at 16x lower training compute.

Coordination research collapses four objects: operative control, authorization, a model-derived friction score, and observed outcomes. The Axiom of Consent is a stake-weighted unanimity principle; majority and supermajority thresholds are explicit relaxations, not versions of the axiom. Decision loci are structural facts, whereas authorization and legitimacy require normative and measurement premises. Alignment, calibrated stakes, and information deficit are candidate coordinates, and F = sigma(1 + epsilon)/(1 + alpha) is a phenomenological ansatz. The Replicator-Optimization Mechanism supplies a conditional persistence interface: irreducibility suffices for its finite, static, positive-fitness continuous-time Perron result; primitivity is required only for the corresponding discrete-time power convergence, and the componentwise ranking is narrower. Neither persistence result derives authorization. A resource-allocation instantiation specifies an identification contract but observes no authorization acts or effective voice. Its exploratory MARL companion uses target-vector correlation and observation noise as narrow proxy treatments, not measures of general alignment or information deficit. Under that proxy and reward-gap design, the composite loses to an independent-effects model and a feasible-centred frozen crossing yields the opposite interaction direction. Cooperative target correlation lowers the gap under shared-state contention; separable IQL is structurally invariant and separable VDN is a non-detection. Paired partial sharing modulates the gradient without establishing an exact dose law or endpoint equivalence. Target support changes opposition and residual-policy conclusions. The surviving contribution is an authorization architecture and measurement discipline, not a universal friction law.

Off-policy reinforcement learning suffers from extrapolation errors when a learned policy selects actions that are weakly supported in the replay buffer. In this study, we address this issue by drawing an analogy to static friction. From this perspective, the replay buffer is represented as a smooth, low-dimensional action manifold, where the support directions correspond to the tangential component, while the normal component captures the dominant first-order extrapolation error. This decomposition reveals an intrinsic anisotropy in value sensitivity that naturally induces a stability condition analogous to a friction threshold. To mitigate deviations toward unsupported actions, we propose Frictional Q-Learning, an off-policy algorithm that encodes supported actions as tangent directions using a contrastive variational autoencoder. We further show that an orthonormal basis of the orthogonal complement corresponds to normal components under mild local isometry assumptions. Extensive empirical results on standard continuous-control benchmarks consistently demonstrate robust and stable performance compared with competitive baselines.

Tendon transmissions reduce distal inertia and add compliance, yet routing, slack, and friction govern motion and force transfer. Mainstream rigid-body robotics simulators such as MuJoCo do not jointly resolve moving noncircular contact, unilateral tension, and segment friction. We present MuJoCable, which adds a reduced-order, configuration-dependent cable transmission to MuJoCo. Its routing algorithm jointly optimizes an ordered path across moving analytic and mesh surfaces. A unilateral axial law, directional Capstan propagation, and nodal virtual work map this path to segment tensions and body forces. The warm-started engine plugin applies these forces during simulation and exposes route and load states for design. Pulley benchmarks recover analytical transmission relations with a Capstan-ratio error below 0.5%. On the underactuated 18-joint SpiRobs, MuJoCable reveals friction-driven load growth and proximal redistribution of joint rotation that the native tendon does not represent. Hardware tests on SpiRobs and a tendon-route-coupled finger reproduce observed motion sequences. By making physical threading executable, MuJoCable brings transmission sources of the simulation-to-reality gap into route, cable, and actuator design before fabrication.