Tools: Alignment Charge: A New Control Primitive for Friction and Adhesion in Navigational Cybernetics 2.5

Alignment Charge: A New Control Primitive for Friction and Adhesion in Navigational Cybernetics 2.5 ## Why Every Control System Gets This Wrong ## The Core Idea: Friction as a Controllable Variable ## Formalization ## Interaction Feature Vector ## Normalization ## Determination of the Alignment Charge ## Charge Stabilization: Suppressing Runaway ## Stability Property: Anti-Chatter and Bounded Regime Tracking ## Effective Friction and Adhesion as Functions of Q_A ## Lemma: Monotone Friction Response ## Contact Micro-Model: Ultrasonic Friction Modulation ## The Control Loop ## Fixation: Anti-Chatter via Hysteresis and Dwell ## Why Q_A Is Not a Friction Estimator ## Where Classical Control Fails ## Classical Compensation vs. Alignment Charge ## Spin and Drift: The Rotational Mismatch Correction ## The Extension: Context, Moment State, and Sleep ## What This Changes ## For Robotics ## For Manipulation ## For Wearables and Human–Machine Interfaces ## Energy and Trade-Offs ## Architectural Position ‌‌​This paper discloses one node of a larger architectural framework — Navigational Cybernetics 2.5 — which addresses long-horizon adaptive systems, structural admissibility, and identity continuity under bounded resources. The alignment charge formalism presented here is an absolutely minuscule part of that architecture, shown in isolation to illustrate how NC2.5 principles translate into concrete engineering primitives. Every robot that has ever slipped on a wet floor has something in common with every prosthetic hand that has ever crushed a grape: both treated friction as a given — a passive environmental parameter to be compensated, not controlled. This is not a sensor problem. It is an architectural omission. In classical control, friction and adhesion are modeled as external constants of the medium — numbers you measure, estimate, and work around. The Coulomb model gives you a static coefficient. LuGre gives you a dynamic one. PID compensates for the result. Adaptive regulators adjust gains. Force/torque controllers push harder when the surface gets slippery. But none of these systems control friction itself. They control the response to friction. The coefficient of friction remains a parameter of the environment — something that happens to the system, not something the system regulates. To be clear: the physical mechanisms for modifying contact conditions — ultrasonic vibration, electrostatic fields, thermal modulation — are well known and individually well studied. What does not exist is a normalized architectural layer that treats the system–medium alignment as a formally defined, stabilizable control variable, closes the loop through interaction physics rather than through controller gains, and integrates regime logic (hysteresis, dwell, anti-chatter) as a standard part of the control topology. The novelty is not in the physics. It is in the architecture. I want to propose that architecture. What if the degree of alignment between a system and its contact medium were not a passive observation but a formally defined, stabilizable, and controllable internal variable? Not a sensor reading. Not a model parameter. Not an error signal. A new kind of state variable — one that lives in the interaction itself. I call this variable the Alignment Charge, denoted Q_A(t). The Alignment Charge is formed from measurable features of the system–medium interaction: contact impedance, phase mismatch, dielectric response, microvibration spectra, stick-slip indicators, medium response latency. But — and this is the critical architectural distinction — Q_A(t) is not determined exclusively by control error, energy, entropy, coherence, or derivatives of the system state. It is a formally independent interaction variable, irreducible to standard control metrics. Once Q_A(t) exists as a defined quantity, something remarkable becomes possible: effective friction µ_eff(t) and effective adhesion A_eff(t) become functions of Q_A — and therefore controllable through the regulation of Q_A, without requiring an increase in mechanical effort. The system does not push harder. It aligns better. Let the system measure a vector of interaction features at the contact zone: z(t) = [z₁(t), z₂(t), …, zₙ(t)] These components may include contact impedance, resistance, conductivity, phase mismatch, response delay, spectral features of microvibrations, local thermo-electric oscillations, dielectric changes, stick-slip indices, or any parameters reflecting the medium's response to the system's action. Features are normalized to a common scale: z̃ᵢ(t) = (zᵢ(t) − μᵢ) / (σᵢ + ε), ε > 0 where μᵢ and σᵢ are running estimates of mean and scale. The alignment charge is computed as a bounded mapping from the normalized feature vector: Two non-limiting examples: In both cases, Q_A is bounded, smooth, and interpretable: higher values indicate better alignment between the system and the medium; lower values indicate mismatch. A note on terminology: I use "charge" rather than "index" or "indicator" deliberately. An index is a passive diagnostic — you read it. A charge is something that accumulates, stabilizes, depletes, and drives dynamics. Q_A is stabilized through derivative suppression, held through dwell, and used as the control object that closes the actuation loop. It is consumed by drift and restored by alignment. The term reflects the functional role, not a physical analogy to electric charge. Raw Q_A may fluctuate under transient perturbations. To prevent chatter and oscillatory switching, we compute first and second derivatives: Q̇_A(t) = (Q_A(t) − Q_A(t−Δ)) / Δ Q̈_A(t) = (Q̇_A(t) − Q̇_A(t−Δ)) / Δ and form a stabilized charge: Q_A^stab(t) = Q_A(t) − k₁·Q̇_A(t) − k₂·Q̈_A(t), k₁, k₂ ≥ 0 This is derivative suppression — the same principle I use extensively in the broader NC2.5 architecture to suppress incoherent jerk in adaptive dynamics. Here, it serves a specific purpose: the stabilized charge becomes the control object, free from transient noise. Other suppression forms — clipping, Huber, median filtering, bounded monotone damping — are equally admissible. The architectural point is the same: stabilize before you control. The stabilized charge is constructed to ensure bounded operation and suppression of high-frequency oscillations in the interaction regime. The stabilized charge is then defined as: Q_A^stab(t) = Q_A(t) − k₁·Q̇_A^b(t) − k₂·Q̈_A^b(t), k₁, k₂ ≥ 0 Property 1 — Boundedness. Under bounded φ and bounded (clipped) derivative terms, Q_A^stab(t) remains bounded for all t: Q_A^stab(t) ∈ [Q_min − k₁d₁ − k₂d₂, Q_max + k₁d₁ + k₂d₂]. No amplification beyond design limits can occur. Property 2 — Stationary Regime Tracking. If the interaction regime becomes stationary so that Q_A(t) → Q̄ and Q̇_A(t), Q̈_A(t) → 0, then Q_A^stab(t) → Q̄. The stabilized charge tracks the stationary alignment state without steady-state offset in the non-saturated regime. (Note: under derivative clipping saturation, a bounded bias proportional to k₁d₁ + k₂d₂ may persist during transients; it vanishes as derivatives decay below clip thresholds.) Property 3 — High-Frequency Suppression. The derivative terms penalize rapid variations in Q_A. This is equivalent to penalizing high-frequency components of Q_A via derivative feedback; under standard discrete-time assumptions, it attenuates oscillations with periods near Δ while preserving slow drift components. Short impulsive perturbations generate large derivative terms, which are subtracted in Q_A^stab, reducing oscillatory switching between contact modes. This constitutes selective dissipation: fast oscillations are damped; slow alignment drift remains observable. Property 4 — Non-Chatter Mode Hold. Let hysteresis thresholds and dwell time T_dwell define entry and exit conditions: |Q̇_A| < θ₁, |Q̈_A| < θ₂ for duration T_dwell. Then the hold regime cannot oscillate faster than the dwell constraint permits. Under bounded perturbations that do not exceed exit thresholds for the required duration, mode switching is prevented. This is not Lyapunov equilibrium stability — the system tracks a time-varying interaction state. It is regime stability: bounded, non-oscillatory control of contact mode under bounded disturbances. Now the key step. We define effective friction and effective adhesion as bounded functions of the stabilized charge: µ_eff(t) = µ₀ · g(Q_A^stab(t)) A_eff(t) = A₀ · h(Q_A^stab(t)) where g(·) and h(·) are bounded monotone functions. One non-limiting example: g(Q) = (µ_min / µ₀) + (1 − µ_min / µ₀) · 1/(1 + exp(β(Q − Q*))) where Q* is an alignment threshold and β controls the steepness of the transition. This means: as the alignment charge increases (better system–medium alignment), effective friction can decrease — and the system slides more efficiently, with less energy loss, without increasing normal force. Conversely, if alignment decreases (mismatch, drift, surface change), friction rises, the system slows, and stability is preserved. For adhesion, the coupling works in the complementary direction: better alignment can increase effective adhesion for gripping, holding, or stabilizing contact. The coupling between alignment charge and effective friction must preserve interpretability and prevent control inversion. Let µ_eff(t) = µ₀ · g(Q_A^stab(t)), where g: ℝ → [µ_min/µ₀, 1] is continuous and strictly monotone. Without loss of generality, assume g'(Q) ≤ 0, meaning higher alignment corresponds to lower effective friction (sliding regime). The complementary adhesion case follows analogously with g'(Q) ≥ 0. If g(Q) is continuous and strictly monotone, and Q_A^stab(t) is bounded and free of chatter (as established above), then: (i) µ_eff(t) is bounded within physical design limits: µ_eff(t) ∈ [µ_min, µ₀]. (ii) Any monotone change in Q_A^stab(t) produces a monotone change in µ_eff(t). No inversion or non-physical regime switching can occur. (iii) Small perturbations in Q_A^stab(t) produce proportionally bounded changes in µ_eff(t), with sensitivity governed by g'(Q). Thus, control authority over alignment translates directly and predictably into control authority over effective friction. Corollary (Regime Consistency). If the contact regime is defined by thresholds in Q_A^stab, and g(Q) is monotone, then regime transitions in Q_A^stab correspond one-to-one with regime transitions in µ_eff. No hidden friction regime exists outside the alignment variable. Stability of Q_A^stab implies stability of the friction regime. The same reasoning applies symmetrically to effective adhesion A_eff. To ground the alignment charge in concrete physics, consider a minimal contact model. A rigid body of mass m moves on a surface with baseline Coulomb friction coefficient µ₀ under normal load F_N. A piezoelectric actuator embedded in the contact pad generates ultrasonic vibration at frequency f and amplitude a_n normal to the surface. The well-known effect (reported in tribology literature since the 1960s, systematically studied by Storck et al. 2002, Dong & Dapino 2014, among others) is that normal ultrasonic vibration reduces the time-averaged effective friction by periodically reducing the instantaneous contact force. Under sinusoidal excitation a_n(t) = A sin(2πft), the contact force oscillates as: F_contact(t) = F_N − m·(2πf)²·A·sin(2πft) When the vibration amplitude is sufficient that the contact force momentarily reaches zero (separation condition: m·(2πf)²·A ≥ F_N), the time-averaged tangential resistance drops. The effective friction becomes: µ_eff ≈ µ₀ · (1 − T_sep / T_period) where T_sep is the fraction of each cycle during which contact is lost, and T_period = 1/f. Now map this onto the alignment charge architecture: The closed loop: measure impedance/vibration features → compute Q_A → adjust A and f → contact physics change → new impedance reading. The loop closes through the physics of ultrasonic contact modulation, not through gain adjustment. This is one physical instantiation. Electrostatic modulation (squeeze-film effect), thermal softening of contact interfaces, and active microtexture deformation follow the same architectural pattern — different physics, same Q_A control topology. The system now operates a closed loop: The interaction parameter to be changed is not normal force. It is selected from: local vibration or ultrasonic stimulation, electrostatic field modulation, local temperature regime, active microtexture or micropneumatic state, controlled acoustic probing, or compliance modulation. The actuation modifies contact conditions, which modifies the interaction features measured in step 1 — closing the loop through the physics of interaction, not through an error signal. When stability conditions are satisfied: |Q̇_A(t)| < θ₁ and |Q̈_A(t)| < θ₂ for a duration T_dwell the system holds the current alignment state Q̄_A = Hold(Q_A^stab(t)). Entry and exit thresholds may differ (hysteresis), ensuring that transient fluctuations do not cause oscillatory regime switching. This is the "contact held / contact changed" mode — binary, stable, and free from chatter. This is the objection that must be addressed head-on: "You are just estimating the friction coefficient with extra steps". No. The distinction is architectural, not quantitative. A friction estimator is an observer. It takes sensor data, infers µ, and feeds that estimate into a controller that adjusts force, trajectory, or gain. The friction coefficient remains an environmental parameter — the estimator watches it, the controller reacts to it. The loop closes through the controller's response to the estimate, not through the physics of the contact itself. Q_A is a control object. It is not an estimate of µ — it is an independent variable from which µ_eff is derived. The system does not observe friction and then compensate. It regulates Q_A through non-mechanical actuation (electrostatic, ultrasonic, thermal, microtexture), and µ_eff changes as a consequence — because the physical conditions of the contact have been altered. The difference becomes concrete in the control loop topology: In the estimator architecture, friction is something you learn about. In the Q_A architecture, friction is something you change. These are not two descriptions of the same thing. They are two different control topologies with different actuation channels, different closed-loop paths, and different achievable outcomes. A friction estimator cannot reduce µ_eff below the physical coefficient of the surface-material pair by adjusting gains alone. Q_A-based actuation can modify the physical interaction conditions — through ultrasonic vibration, electrostatic modulation, thermal adjustment, or surface-state change — that determine what the effective coefficient actually is. This is not a violation of physics; it is a change of the contact regime itself. (Ultrasonic friction reduction has been observed and systematically studied in tribology — see, e.g., Storck et al. 2002, Dong & Dapino 2014; the contribution here is the formal control architecture that makes it a closed-loop, stabilizable process rather than an open-loop physical effect.) Consider a mobile robot traversing a surface whose friction coefficient changes faster than the adaptive controller's convergence rate — for example, a floor with alternating wet and dry patches at intervals shorter than the estimator's sliding window. A PID controller with friction compensation will oscillate between under- and over-correction, because its gain adaptation lags behind the surface changes. An adaptive controller with LuGre estimation will produce transient force spikes at each transition, because the model parameters cannot converge before the next surface change. The standard remedy: increase normal force to maintain traction through brute margin. This works, but at the cost of energy, wear, and mechanical stress. A Q_A-based system responds differently. It does not need to estimate the new friction coefficient before acting. It measures interaction features (impedance, microvibration spectrum, dielectric response) that respond to surface changes within a single sampling interval. Q_A shifts immediately. The system actuates — adjusts ultrasonic stimulation frequency or electrostatic field — and the effective friction is regulated within the same closed-loop cycle. No convergence delay. No force increase. No estimation lag. The architectural reason is simple: Q_A is formed from interaction features, not from model identification. Interaction features are measured directly. Model identification requires fitting parameters over time. When the environment changes faster than the model can converge, the estimator fails. Q_A does not. A possible objection: "But φ(z̃) still requires calibration — so Q_A is just a faster estimator". The distinction matters. Calibration of φ is a one-time static mapping — setting w, b, or α during system setup. It does not adapt at runtime to track a changing surface. Model identification in LuGre or adaptive friction compensation is a continuous parameter fitting process that must converge before the estimate is useful. Static mapping versus dynamic convergence: the former has zero convergence delay; the latter has convergence delay proportional to the rate of environmental change. Under fast-switching surfaces, the convergence delay is the failure mode. Q_A eliminates it by construction. In some embodiments, the system–medium interaction exhibits a rotational component — a torsional mismatch that manifests as directional drift. This is directly related to what I call "spin" in the broader NC2.5 framework: the non-potential divergence-free component of adaptive dynamics that prevents stagnation under bounded resources. Here, spin enters the alignment charge as a correction: Q_A(t) = φ(z̃(t)) − γ · τ(t), γ ≥ 0 where τ(t) = Ψ(z̃(t)) is a rotational-component signal extracted from interaction features. Meaning: if the system–medium pair exhibits torsional mismatch, the alignment charge decreases, and the interaction regime shifts toward more conservative, stable contact. Spin does not destabilize — it provides the signal that triggers stabilization. This block is optional but extends the method's applicability to drifting, rotating, and unstable-contact media. The alignment charge alone is sufficient for contact control. But in systems that interact with humans — wearables, haptic interfaces, orthoses, prosthetics — there is a second layer that changes everything. The human is not a constant. The same hand gripping the same handle at 2 PM and 3 AM operates in radically different physiological regimes. Fatigue, stress, arousal, sleep stage — all of these alter the contact conditions, not because the surface changed, but because the system's other half changed. For this, I introduce a second formally defined variable: the Moment-State Charge Q_M(t). Q_M(t) is a bounded scalar (or low-dimensional vector) summarizing the instantaneous state of the system/user in context. It is computed from multi-modal sensor inputs — motion, temperature, heart rate, heart rate variability, electrodermal activity, respiration, impedance, audio features, optical features — combined with a context vector c(t) that includes sleep stage, circadian phase, activity regime, environmental conditions, and task type. Q_M(t) = φ_M(s̃(t), c(t)) The system does not diagnose emotions. It classifies measurable state regimes: calm vs. activated, stable vs. unstable, recovered vs. fatigued, focused vs. scattered. These classifications are inferred from signals, not from psychological models. The coupling to contact control is direct: µ_eff(t) = µ₀ · g(Q_A^stab(t), Q_M(t), c(t)) A_eff(t) = A₀ · h(Q_A^stab(t), Q_M(t), c(t)) When Q_M indicates stress or high activation, or when the coherence metric C(t) indicates low stability relative to context-dependent normative bands, the system selects conservative contact regimes: less chatter, less jerk, safer adhesion margins — without increasing mechanical force. Sleep/REM context gating deserves special attention. During REM, physiological variability patterns differ fundamentally from wakefulness. A wearable device that uses the same thresholds during sleep as during active use will either miss important state changes or generate false alarms. The normative bands N(c(t)) switch based on sleep stage: sleep_stage(t) ∈ {wake, NREM, REM} and thresholds, hysteresis criteria, dwell times, and allowed actuation modes all shift accordingly. A robot on a changing surface — wet tile to carpet to gravel — no longer needs to increase normal force when traction drops. Instead, it regulates Q_A through ultrasonic stimulation of its sole, or electrostatic modulation of its contact pad, or thermal adjustment of the contact zone. The same robot can stabilize an unstable object on fabric by locally increasing A_eff through alignment — achieving a "stable on edge" effect that would otherwise require mechanical clamping. A gripper holding an object with uncertain contact properties does not need to squeeze harder when slip is detected. It measures interaction features, computes Q_A, and adjusts its contact regime — through microvibration, electrostatic modulation, or compliance modulation — to increase adhesion without increasing grip force. Less force means less damage, less energy, and more precision. A haptic device on a user's wrist measures skin impedance, temperature, microperspiration, and microvibration response. From these, it computes Q_A for the device–skin contact and Q_M for the user's physiological state. During high-stress moments, the device automatically shifts to a more conservative adhesion regime — gentler, less jittery, with wider hysteresis bands. During sleep, thresholds change entirely. The user feels nothing change. The device simply works better when they need it most. The claim "without increasing mechanical effort" requires an honest qualification: Q_A-based actuation does not increase normal force, but it is not free. Ultrasonic vibration requires electrical power to drive the piezoelectric element. Electrostatic modulation requires voltage supply. Thermal adjustment requires heat input and dissipation time. Active microtexture requires mechanical or pneumatic infrastructure. The trade-off is between mechanical energy (pressing harder) and electrical/thermal energy (modulating the contact regime). In many practical cases this trade-off is favorable: piezoelectric actuators operating at ultrasonic frequencies consume milliwatts to low watts, while the mechanical force savings — reduced wear, lower actuator load, less structural stress — can be substantial. But the trade-off is not universal. On surfaces where the medium does not respond to available actuation channels (e.g., a dry rigid metal-on-metal contact with no dielectric gap), Q_A-based modulation may offer no advantage. The architecture applies where at least one non-mechanical actuation channel exists that can modify contact conditions. Additional constraints include: acoustic noise from ultrasonic actuation in human-proximate applications, thermal limits in wearable devices, electromagnetic interference from electrostatic fields, and long-term degradation of piezoelectric elements or surface coatings under sustained operation. These are implementation constraints, not architectural ones — they define the boundary of applicability, not a flaw in the control topology. The Alignment Charge is not a replacement for force control, PID, or adaptive regulation. It is a new layer — a formally defined interaction variable that makes the system–medium contact regime an explicit object of control for the first time. In the broader architecture of Navigational Cybernetics 2.5, Q_A occupies a specific position: it is the control primitive for the boundary between the system and the world. ΔE provides coherence-driven stabilization of internal dynamics. UTAM provides direction and curvature of the adaptive trajectory. The alignment charge provides the point of contact — the surface where the system meets the medium, where theory touches physics. This is where admissibility becomes engineering. Max Barzenkov / MxBv Originally filed: December 20, 2025 · Published: February 27, 2026 CC BY-NC-ND 4.0 The alignment charge is one node of Navigational Cybernetics 2.5 — an architectural theory of long-horizon adaptive systems. The broader framework, including ΔE, UTAM, CAS-T, structural burden, spin, admissibility, and meta-revision, is available at petronus.eu. Templates let you quickly answer FAQs or store snippets for re-use. Are you sure you want to hide this comment? It will become hidden in your post, but will still be visible via the comment's permalink. Hide child comments as well For further actions, you may consider blocking this person and/or reporting abuse - Projection form: Q_A(t) = tanh(wᵀz̃(t) + b), where w and b are calibration parameters. - Distance form: Q_A(t) = 1 / (1 + α‖z̃(t) − z̃₀‖), where z̃₀ is the baseline aligned state and α > 0 is a sensitivity coefficient. - The alignment mapping φ is bounded by construction (e.g., tanh or inverse-distance form), so Q_A(t) ∈ [Q_min, Q_max] for all t. - The sampling interval Δ is chosen above the dominant sensor-noise timescale. - Derivative terms are either bandwidth-limited by sensor physics or explicitly bounded via clipping or filtering: Q̇_A^b(t) = clip(Q̇_A(t), [−d₁, d₁]), Q̈_A^b(t) = clip(Q̈_A(t), [−d₂, d₂]). - Interaction features z(t): contact impedance (drops during separation), microvibration spectrum (shows harmonic peaks at f), phase delay between commanded and measured vibration. - Alignment charge Q_A: increases as the vibration parameters approach optimal separation conditions — i.e., as the system achieves better ultrasonic alignment with the surface. - Actuation: adjusting A and f to drive Q_A^stab toward Q_A^target. - µ_eff as function of Q_A^stab: the sigmoidal g(Q) maps the alignment state to the effective friction reduction achievable at that operating point. - Measure interaction features z(t) - Compute Q_A(t) and stabilize to Q_A^stab(t) - Compute µ_eff(t) and A_eff(t) - Evaluate current contact regime (stick / slip / transitional) - Actuate — change at least one interaction parameter to drive Q_A^stab(t) toward a target Q_A^target - Friction estimator: sensor → estimate µ̂ → adjust controller gains → apply more/less force → observe result. The loop goes through the controller. - Alignment Charge: sensor → compute Q_A → actuate interaction parameter (not force) → contact physics change → new sensor reading. The loop goes through the physics of the interaction.