Stiffness Modulation

This letter investigates how the parameters of a slope-aware variable-admittance filter influence user preferences in force-based interaction with a robotic guide dog for visually impaired individuals. The proposed system consists of a quadruped robot equipped with a sensor-free rigid handle for physical guidance. The framework combines path following, momentum-based interaction-wrench estimation, and a variable-admittance filter whose stiffness and damping are adapted online from slope information extracted by the robot's depth camera. The adaptation policies are evaluated through high-fidelity simulations and a human-subject study involving blindfolded sighted participants. Multiple strategies are compared using a Taguchi L9 design of experiments. Preliminary main-effect results suggest that increasing stiffness uphill and decreasing it downhill improves both objective and subjective metrics, whereas damping shows no significant main effect.

Reinforcement learning has produced capable controllers across a broad range of legged-robot tasks, but a subset of these tasks fail to converge under standard training: those for which most exploration trajectories terminate before producing useful gradient signal. To address such tasks we introduce the \emph{Actuator Dynamics Curriculum}, a procedure that initializes joint stiffness at a high value and anneals it toward the system-identified value as completed episode lengths grow. Using a cart-pole system as a representative example, we show that higher closed-loop joint natural frequency under critical damping enlarges the viability kernel of the underlying Markov Decision Process, increasing the fraction of initial states from which the task is feasible. We validate the kernel monotonicity on the cart-pole and apply the curriculum to a quadrupedal-to-handstand transition on the Boston Dynamics Spot, a narrow-viability task where training under fixed identified stiffness plateaus at a policy that never completes the transition. The trained policy executes the transition in simulation across 10 seeds and transfers to hardware. More broadly, our results suggest that simulated actuator dynamics is a useful axis along which to design curricula for tasks in which exploration is bottlenecked by termination conditions rather than by reward signal.

We use tools from nonlinear algebra to study the equilibria of small linear translational spring networks. Specifically we use the techniques of homotopy continuation, monodromy, and parameter homotopy (a.k.a. cheater homotopy) to solve all rigid linear translational spring networks up to $5$ nodes in both $2$ and $3$ dimensions. We describe a method of implementing parameter homotopy that arises naturally from the physical structure of the system. We give precise total degree bounds on the maximum number of solutions for general planar spring networks. We discuss further efficiency gains obtained from polyhedral homotopy methods. We compare the computation efficiency of these techniques against a baseline of Newton's method.

To improve torque capacity and energy efficiency of humanoid ankles, this paper proposes a 2-DoF parallel elastic actuator (PEA). The main novelty of the proposed design lies in its dual-cam, single-gas-spring architecture, which enables torque compensation in both pitch and roll using a shared elastic element, thereby improving structural compactness compared with conventional multi-element compensation schemes. By leveraging parallel gas springs and customized cam modules, the proposed architecture provides dual-axis torque assistance tailored to specific task requirements. The second key contribution is the formulation of a coupled 2-DoF mathematical model that explicitly captures the interdependence between the two compensation units through the shared spring. Based on this model, an optimization-based design framework is developed to synthesize customized cam profiles from prescribed torque references, establishing a systematic link from task requirements to hardware realization. The complete lower-leg CAD integration is presented in detail. Static FEA and kinematic simulations confirm the design's feasibility and torque-relief effectiveness. The results highlight the proposed design as a compact, customizable solution for 2-DoF humanoid ankle torque compensation.

Soft robotic systems are well suited for developing devices for biomedical applications. A bio-mimicking robotic soft esophagus (RoSE) is developed as an in vitro testing device of endoprosthetic stents for dysphagia management. Endoprosthetic stent placement is an immediate and cost-effective therapy for dysphagia caused by malignant esophageal strictures from esophageal cancer. However, later stage complications, like stent migration, could weaken swallow efficacy in the esophagus. The stent radial force (RF) on the esophageal wall is pivotal in avoiding stent migration. Due to limited randomized controlled trials in patients, stent design and stenting guidelines remain incomplete. To address this knowledge deficit, we investigate RoSE by implanting two stents (A and B) of different radial stiffness characteristics, to measure stent RF and its effect on migration. Endoscopic manometry under peristalsis is also performed to study the impact of stenting and stent dysfunction on intra-bolus pressure signatures (IBPSs) and swallowing efficacy. Each implanted stent undergoes experiments with varied peristalsis velocity, wavelength, and bolus concentrations. The results show that stiffer stent B has a higher RF, whereas stent A maintains a lower RF profile due to lesser stiffness. High RF is necessary to minimize migration under prolonged peristaltic contractions in RoSE. For manometry, stent A slightly increases IBPS, but stiffer stent B significantly decreases IBPS, especially for higher-concentration boluses. If a stiffer stent buckles, it can reduce swallow efficacy and cause recurrent dysphagia. RoSE is therefore an innovative soft robotic platform for testing endoprosthetic stents and addressing clinical challenges in stent evaluation.

Reconstructing objects with mechanical properties from video observations enables physically consistent dynamic prediction, benefiting robotics planning and interaction. Existing spring--mass based physical driven reconstruction approaches offer efficient and differentiable physical reconstruction, but they typically rely on axial springs alone. Such formulations oversimplify the underlying structural mechanics and can become mechanically under-constrained when the physical graph is coarsened, limiting their ability to preserve stable local deformation. We present BendTwin, a bending-aware differentiable spring--mass framework for video-based reconstruction and future prediction of deformable objects. BendTwin introduces bending stiffness and damping over local surface triplets, penalizing deviations from rest angles and regularizing higher-order deformation. These bending constraints improve mechanical stability while preserving the simplicity of spring--mass system. Experiments show that BendTwin consistently outperforms the axial-only PhysTwin baseline. Ablation studies further demonstrate that the bending constraints maintain system stability across different downsampling ratios and consistently improve upon the original PhysTwin formulation. Overall, BendTwin provides an effective approach for constructing mechanically faithful digital twins from sparse-view RGB-D videos.

Supervised training of finite-element (FE) surrogate models requires reference solutions, and each reference solution is obtained by solving the system that the surrogate is intended to replace. The assembled discrete potential energy provides a training signal that requires no reference solution. This note records, with proofs, the identities that make this signal exact for linear elastostatics: the difference between the energy of a prediction and the energy of the reference solution equals one half of the squared stiffness-norm error, and the gradient of the energy equals the stiffness-weighted error. Label-free discrete-energy minimisation and supervised regression in the stiffness norm therefore have the same unique minimiser and identical gradients at every point. Around this central result, the note states a conditioning lemma that bounds the displacement error by the energy gap, a modewise contraction identity that explains why the Euclidean displacement error is an unsuitable primary metric, the Chebyshev bound that governs conjugate-gradient post-processing of surrogate predictions, and a conditional latent-separation proposition for joint-embedding predictive architecture (JEPA) pretraining on a shared stiffness operator, with an explicit numerical counterexample that delimits its scope. Every claim with numeric content is implemented as an executable falsification check; the checks were executed twice, on synthetic test problems and on a probe set of 16 instances from the validation split of a pre-registered experimental run, and every inequality holds, with the measured tightness reported. A closing section explains why the construction does not extend to elastodynamics through direct minimisation of the action functional, and which time-discrete formulation restores exactness.

Supportive continuum robots (SCRs) enhance the load-bearing capability of an operative continuum robot by mechanically coupling it with a supportive arm. However, their passive stiffness is determined by the mechanical configuration and cannot be adjusted online for varying payloads or interaction forces. Active stiffness control is therefore needed to regulate the load response and maintain positioning accuracy. Meanwhile, the closed-chain structure introduces kinematic constraints that complicate task-space regulation and stiffness control. This paper presents an active task-space stiffness control framework for a tendon-driven SCR. An existing geometric variable strain model describes the closed-chain dynamics, which are projected onto the constraint-consistent motion subspace. A projected sliding mode controller regulates the operative arm tip while preserving the constraints, and closed-loop stability is established through Lyapunov analysis. After position regulation, active apparent stiffness is introduced through a virtual Cartesian spring based on position-error feedback to shape the force--displacement response. The framework is evaluated in simulation and experimentally validated under prescribed external loads and different desired configurations. Results show that increasing the commanded stiffness gain reduces load-induced tip deflection and increases apparent directional stiffness, thereby improving load resistance and positioning robustness under external loading.

Realistic palpation training requires reliable rendering of soft tissue stiffness changes in real time, which is difficult to achieve with conventional simulators. This paper presents a compact, variable-stiffness tactile interface (VSTaI) based on vacuum-induced jamming of 3D-printed structured fabrics. A vacuum-sealed fabric layer is sandwiched between two silicone layers, and stiffness is tuned by regulating internal pressure. Four fabric patterns with different geometric parameters were fabricated and evaluated using force-indentation tests under atmospheric and vacuum conditions. Across the tested pattern and geometry combinations, vacuum jamming increased stiffness significantly, producing an effective modulus from sub-megapascal to megapascal levels. Specifically, one configuration exhibited a stiffness increase of up to 140% under the jammed state. Circular chainmail patterns provided the most spatially uniform distribution of tactile stiffness, while denser geometries reached higher peak stiffness. VSTaI was also shown to exhibit excellent conformability to the underlying geometry. These results support structured-fabric jamming as a practical approach for shape-conformable, tunable-stiffness displays aimed at physical examination training.

Many ceiling construction tasks still rely on heavy serial manipulators that are difficult to deploy in cluttered interiors, motivating lightweight, field-ready alternatives that reach ceiling height while maintaining millimeter-level accuracy and the stiffness demanded by overhead tool loads. We introduce Tripody, a wheeled 3-DoF parallel robot for high-reach tasks that replaces the base spherical joints of a classical 3-SPR (3 legs; S: base spherical joint; P: actuated prismatic joint; R: end-effector revolute joint) morphology with universal joints, intentionally overconstraining the mechanism; small, distributed elastic deflections absorb the resulting incompatibilities, preserving predominantly translational motion. The 33kg system extends from 1.7m to 3.4m in height, supports a continuous 32kg payload, and offers a modular end-effector interface for ceiling operations. We detail the mechanical design - including custom linear actuators and a kinematic-compatibility analysis - and a control stack for accurate positioning that combines SE(3) state estimation, forward kinematics, and task-space control. In experiments, Tripody exhibits similar in-plane stiffness to a spherical-base variant but substantially higher torsional stiffness - an increase of 67% at 1.7m, 196% at 2.6m, and 454% at 3.4m - while maintaining negligible cross-axis coupling. Closed-loop positioning with a total station converges below 0.6mm across the entire workspace; pure model extrapolation achieves a 95th-percentile error of 2.7mm (max 3.6mm). Finally, we demonstrate task-level ceiling-drilling feasibility in an open-loop study by drilling a 15-hole pattern with 4.5mm maximum relative hole-position error after rigid alignment. These results support overconstrained, compliance-absorbing 3-SPR-like architectures as a practical path to lightweight, high- reach, millimeter-accurate construction robots.

The paper proposes a robot-agnostic compliant-control framework that extends the ROS control ecosystem with standardized joint and Cartesian command interfaces. It addresses a key limitation of existing control software: no reusable infrastructure for implementing compliant-control algorithms across different manipulators while preserving a common interface to higher-level applications. A plugin-based architecture separates controller infrastructure from control-law implementation. Generic wrappers use existing hardware abstractions to interface with different manipulators, while runtime-loaded plugins implement only the control law. Command interfaces support joint- and Cartesian-space references, stiffness and damping gains, nullspace targets, and feedforward terms, enabling variable impedance and diverse compliant-control formulations. Robot kinematics and dynamics are computed from URDF models using Pinocchio. The architecture facilitates the development of compliant-control strategies and enables the same implementation to be deployed across platforms unchanged. The complete framework, including reference controllers, high-level task interfaces, and example configurations for various manipulators, is open-sourced. The reference Cartesian impedance controller supports task-dependent compliance by rotating translational and rotational stiffness and damping, allowing the principal compliance directions to be updated online according to local task geometry rather than remaining fixed in the robot base or TCP frame. This is particularly important in contact-rich manipulation, where the desired directions of motion, constraints, and compliance directions may vary throughout task execution. Real-robot experiments demonstrate task-dependent compliance in contact-rich manipulation, while simulations show portability across manipulators with distinct kinematic and dynamic characteristics.

In this paper, we present a generalized temporal-difference (TD) reinforcement learning framework based on the theory of conditional expectations. The value and action-value (Q-value) functions are treated as uncertain quantities, and their estimation is formulated as a stochastic inference problem. Unlike classical Kalman-based temporal-difference learning, which relies on linear-Gaussian assumptions, the proposed formulation is derived directly from the conditional expectation framework and naturally extends to nonlinear models and non-Gaussian probability distributions. The proposed method recursively estimates not only the conditional expectation of the value function but also its second probabilistic moment, thereby quantifying the uncertainty associated with the learned value function throughout the learning process. To obtain a computationally tractable algorithm, the stochastic problem is discretized using either polynomial chaos expansions or ensemble-based approximations, providing efficient representations of the underlying random variables. The proposed framework is demonstrated on two optimal control problems: a linear mass--spring--damper system and a nonlinear heat conduction problem in a closed cavity. The numerical examples illustrate the capability of the proposed method to accurately estimate both the value function and its associated uncertainty, while extending classical Kalman-based temporal-difference learning to a broader class of stochastic systems.

Model-based control of flexible joint robots with position-controlled actuators relies on accurate knowledge of the joint compliance. In practice, precise stiffness models are often unavailable as the properties of physical elastic elements vary with operating conditions and slowly change over time due to wear and aging. To improve model-based control of these systems, we propose an adaptive control approach in this work, which updates an estimate of the uncertain, nonlinear torque-deflection relation of each joint. As opposed to classical adaptive control approaches for non-elastic robots, we rely on an implicit control law and a control-input-dependent regressor matrix to account for the uncertain joint stiffness. We analyze robustness of the approach against errors induced by the motor position controller. Experimental results on a flexible joint with nonlinear stiffness characteristics demonstrate the effectiveness of the proposed approach.

Simulating deformable objects is essential for a wide range of robotic manipulation applications, yet accurately predicting their dynamics remains challenging. We propose Physics-Guided Residual Dynamics (PGRD), a hybrid simulation framework that combines the advantages of physics-based and learning-based approaches. Specifically, PGRD combines an optimizable spring-mass simulator as a backbone with a learned neural network that predicts residual corrections to the physics-based predictions. We adopt a velocity-based formulation to ensure stable simulation and a sliding-window transformer architecture to capture temporal dependencies. We show that PGRD produces more accurate results than both purely physics-based and learning-based methods on a set of diverse real-world deformable objects. We further demonstrate the utility of PGRD in two applications: manipulation planning via Model Predictive Control, including a language-conditioned setting with a generated goal image; and interactive simulation via action-conditioned video prediction by 3D Gaussian Splatting.

Robot-environment interactions in dynamic or unstructured settings are often degraded by impact shocks, vibrations, and uncertainties in contact geometry and mechanical properties. This paper proposes an interaction architecture that combines feedback-linearized hybrid position-force control with a passive compliant degree of freedom embedded at the end-effector. Unlike conventional hybrid position-force control, which relies mainly on active feedback, force sensing, and gain tuning, the proposed architecture uses a physical spring-damper interface to store and dissipate impact energy at the contact point before high-frequency shocks propagate to the actuated joints and force-control loop. The approach is evaluated in MATLAB/Simulink on a 2-DOF planar manipulator with three end-effector configurations: rigid, spring-only, and spring-damper. Results under fixed and time-varying interaction conditions show that the spring-damper configuration provides stronger attenuation of contact-induced oscillations, lower force and velocity error variance, and smoother joint-torque response. Representative reductions include 36.5% in fixed-environment tangential force-error standard deviation, 25.4% in variable-environment normal force-error standard deviation, and 41.1% in variable-environment normal velocity-error standard deviation.

Compliant joints can embed safety and adaptability into dexterous hands, but achieving large-stroke anthropomorphic motion while maintaining joint-specific, directiondependent stiffness and reliable proprioception remains challenging. This paper presents the PDS joint, a parametric doublespiral (PDS) compliant joint that enables systematic shaping of directional stiffness across multiple deformation modes, including flexion/extension, abduction/adduction, and pronation/supination. We instantiate the joint using Archimedean and logarithmic spiral templates for different hand joints and introduce an asymmetry ratio to tailor stiffness distributions for both grasp stability and hyperextension resistance. To make the joint practically usable under large deformation, we co-design embedded inductive proprioception and propose a learningbased calibration pipeline that maps raw inductive signals to joint states using ArUco-marker tracking. Experiments characterize the stiffness landscapes across geometric parameters and demonstrate a non-monotonic dependence of lateral support on asymmetry, indicating the importance of principled parameter tuning. For joint-state estimation in the most challenging abduction/adduction motion, a learned multilayer-perceptron (MLP) mapping reduces the error compared with conventional curve fitting by 41.6%. Finally, we integrate the proposed joints into an open-source dexterous hand as a demonstration platform, on which the hand grasps a set of nine everyday objects and performs safe, contact-rich human-involved interactions.

Woven structures exhibit rich mechanical behaviors including anisotropic stiffness, shear-induced locking, and crimp interchange that emerge purely from the geometric arrangement of individual weavers rather than from constituent material properties. Existing models either homogenize these interactions or resolve them at prohibitive computational cost. We introduce a reduced-order model that bridges this gap by representing individual weaver interactions through a system of nodes and four physically interpretable stiffness elements capturing axial deformation, in-plane uncrimping, inter-weaver shear, and frictional slip. Eigenvalue analysis of the unit cell confirms that the lowest-energy deformation modes correspond directly to known weave-specific phenomena, and that each element is necessary for a complete kinematic and mechanistic description. Element stiffness parameters are calibrated against empirical three-point bending and shear data, achieving agreement within 5% across varied weaver widths and spacings. The validated model is then applied to demonstrate capabilities beyond the reach of continuum approaches including: the emergent Poisson's response arising from crimp interchange, stepwise force reduction during progressive weaver pullout, stress localization under three distinct tearing configurations, and programmable mechanical anisotropy through spatially graded weaver stiffness. The physical transparency and computational efficiency of the framework position it as a practical tool for the analysis and design of woven architected materials with programmable mechanical response.

Compliant mechanisms are important in robotics because they can improve adaptability, safety, and energy efficiency while reducing hardware complexity. This paper presents SPiralRoll, a novel torsion-spring-based underactuated compliant mechanism for rolling robots and compliant robotic actuation. The mechanism uses arc-distributed elastic members and two motor inputs to realize three physically observable output motions: rotational motion, radial expansion/contraction, and axial spin induced by nonlinear compliant deformation. Two configurations, namely full-arc and single-arc designs, are developed and experimentally evaluated. Beyond benchtop validation, the mechanism is integrated into a spherical rolling robot, where proof-of-concept experiments demonstrate forward rolling and turning. The results show that the full-arc design provides better structural support and smoother deformation, whereas the single-arc design yields larger deformation and stronger inertial excitation, making it more suitable for pendulum-driven rolling locomotion. Overall, SPiralRoll provides a low-cost, compact, and fully 3D-printable solution for underactuated compliant rolling robots and adaptive robotic joints.

Co-design of legged robots with elastic elements is challenging due to the non-differentiability of contact dynamics and mechanism engagement. This paper presents SurGE, a framework that computes surrogate gradients of the design objective through a differentiable pipeline consisting of a kinodynamic single-rigid-body (Kino-SRB) model and a design-aware control policy, and injects them into CMA-ES via mean shift with cosine-annealed step decay. On a 4-DOF design space of a hopping robot with unidirectional parallel spring, SurGE achieves 6 times lower cross-seed standard deviation and 18% tighter population concentration compared to vanilla CMA-ES, while matching or improving the best objective. Hardware experiments on a 2D design subspace show that, starting from a hand-tuned initial design, SurGE reduces the design objective by 37.65% on hardware, with the improvement trend identified in simulation transferring consistently to the physical system. SurGE provides the potential to accelerate non-differentiable co-design problems in legged robots via surrogate model gradients.

Fish achieve efficient swimming across varied speeds through active modulation of their body flexibility. To explore the effects of tunable stiffness on swimming performance, we present a bio-inspired freely swimming fish robot with a rapidly tunable particle-jamming body. This design enables rapid stiffness adjustments with negligible changes in shape or volume, achieving a 54% variation in flexural rigidity across vacuum pressures of 0 to -40 kPa. We visualize the midline of the oscillating body under both low- and high-stiffness conditions, and the comparison confirms that the body curvature varies with stiffness. We further experimentally evaluate the tunable stiffness body's effects on swimming performance using velocity and cost of transport (CoT) measurements obtained via a motion tracking system. Results show that active stiffness tuning is essential for sustaining efficient and high-speed swimming across beating frequencies of 1-3 Hz. At low frequencies (1-1.5 Hz), a softer body (0 kPa) maximizes velocity and minimizes CoT, whereas at high frequencies (2.5-3 Hz), a stiffer body (-40 kPa) delivers superior velocity and reduced transport cost. These findings highlight stiffness modulation as a key strategy for adaptive and efficient propulsion in bio-inspired robotic swimmers.

Load transportation with quadruped robots is strongly affected by the dynamics of the physical interface between the robot and the load. Passive spring-based arms reduce weight and complexity compared to active manipulators, but their spring-damper dynamics can introduce oscillatory forces that degrade locomotion stability. This paper derives an extended Zero Moment Point (ZMP) formulation that includes passive payload-interface dynamics, relating stiffness, damping, and payload mass to the stability margin. The analysis shows that underdamped configurations can resonate with locomotion harmonics. Based on this insight, we augment a Single Rigid Body Dynamics model with passive subsystem dynamics and integrate it into a Model Predictive Control framework. In simulation, the proposed controller reduces stability violations by up to $10\times$, from $7.0\%$ to $0.7\%$, and increase locomotion efficiency by lowering horizontal ground reaction force effort by up to $15\%$ compared to a nominal baseline. Hardware experiments with a $2\,\mathrm{kg}$ payload show stable locomotion under pull-release disturbances where the nominal controller fails. The same model also enables end-effector tracking through passive arm dynamics without direct arm actuation.

This work presents a transparent and reproducible benchmark study of a direct dual-network Physics-Informed Neural Network (PINN) formulation for the optimal control of a mass-spring-damper system. The classical linear-quadratic optimal control problem is solved by two independent classical methods -- Pontryagin's Minimum Principle with single shooting, and direct transcription through trapezoidal collocation -- and recast as a constrained optimization problem solved by two feedforward neural networks: a state network whose boundary conditions are enforced exactly through a composite cubic-and-mask ansatz, and an unconstrained control network. The composite loss combines the physics residual at the collocation points with a trapezoidal approximation of the cost functional, weighted by a single scalar hyperparameter. On the benchmark considered, the PINN reproduces the classical optimal cost to four significant digits, satisfies the terminal state constraints exactly by construction, and produces pointwise state and control errors that fall within the spread of the two classical references. Training is approximately two orders of magnitude slower than classical shooting on this benchmark, which is honestly reported. The contribution is methodological clarity rather than methodological novelty: the formulation and the accompanying Google Colab implementation are intended to lower the barrier to entry for practitioners exploring PINN-based optimal control without prior exposure to adjoint methods or two-point boundary value problems.

Dexterous manipulation is fundamentally a problem of interaction dynamics: the hand must track precise finger trajectories, regulate the contact force exchanged with grasped objects, respect actuation and safety limits, and remain predictable when contact persists -- objectives in tension for any fixed-gain controller. A sustained contact torque $τ_{\text{ext}}$ through a joint stiffness $K_d$ produces the structural bias $e_\infty=τ_{\text{ext}}/K_d$, so stiffening for accuracy sacrifices contact safety while softening yields by design. We make these interaction dynamics explicit and actuator-agnostic through a constant-$A_d$ double-integrator backbone, instantiating the offset-free architecture established for physical human-robot interaction (pHRI) and preserving its modeling assumptions on the reduced residual dynamics. An algebraic feedforward reduces the tendon transmission -- hydraulic, cable, pneumatic, twisted-string, or series-elastic -- to a constant-coefficient double integrator, so the QP cost inverse is precomputed offline and a 10-step receding-horizon QP runs at 500,Hz under contact-force (ISO/TS 15066), actuation, and jerk constraints. An encoder-only augmented-Kalman disturbance state drives steady-state error to zero under constant contact loads in the nominal detectable case. In simulation, a hydraulically actuated finger -- the worked example, adding pressure and cavitation constraints -- attains 0.6,mrad RMS, 0.1,mrad steady-state, and 7.3,mrad peak deflection under 1.5,Nm contact: 153$\times$, 1500$\times$, and 21$\times$ better than classical impedance. The realized first-move stiffness (18$\to$323,Nm/rad with update rate) is independently verified, and the architecture scales to a 16-DOF LEAP Hand MuJoCo model, recovering from 2.5,N grasp disturbances within 0.7,s.

Physical human-robot interaction requires yielding transiently to contact yet recovering the commanded reference under sustained load. Finite-stiffness impedance control retains a static deflection there, while predictive alternatives typically optimize a nonlinear robot or impedance model online. Operational-space cancellation instead exposes a translational error double integrator with a fixed transition matrix and a configuration-scheduled input map, making interaction a predictive quantity rather than a property re-derived per configuration. We build on it a compact offset-free interaction-error MPC for torque-controlled manipulators: a force-domain random-walk state estimates persistent interaction and model error, and a 30-variable convex QP maps the correction through the current task inertia while constraining the applied joint torque. Conditional results establish impedance equivalence of the unconstrained passive feedback, offset-free regulation at feasible frozen configurations, and quadratic stabilizability of the scheduled backbone. In a 1kHz MuJoCo simulation of a 7-DOF Franka FR3, the estimator cuts steady-state error under a repeated 15N step from 2.77mm to 0.042mm when added to the otherwise identical 100Hz MPC. A stiffness-and-damping-calibrated impedance baseline attains 2.59mm but briefly saturates and needs 3.3x the peak positive joint power. Adding ideal measured-force cancellation to that baseline gives 1.39mm, so constant-load rejection is not unique to MPC; the sensorless controller still reaches 0.042mm in the moving task, a 65x reduction without force sensing and without the baseline's saturation or power cost. Demonstrated in simulation under a shared actuator budget, the contribution is an efficient operational-space realization complementing rather than replacing broader interaction-control architectures.

Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complementary strategies. First, we develop a matrix-free update step that uses Jacobian-vector products, iterative linear solvers, and stochastic covariance estimation to enable linear scaling, all while retaining stability. Second, we propose iterative re-linearization to further improve stability without sacrificing scalability, turning probabilistic ODE solvers into fully implicit methods. We evaluate the proposed approaches on a range of stiff and high-dimensional problems and demonstrate improved stability and scalability over established probabilistic solvers.

Haptic guidance in teleoperation enhances operator performance through force feedback. This paper presents guidelines to select the most appropriate model considering the task, the environment and the operator. We define a unified formulation expressing most common models (spring-damper, potential field, and guiding tube) as variations of a stiffness-damping system with model-specific guiding functions. We conducted a user study comparing the three classical models across six scenarios with varying environmental conditions in a vertical farming task. Results show no universally superior model: spring-damper excels in cluttered environments, potential field in free spaces (but it shows risks near obstacles), and guiding tube offers a balanced compromise. We propose novel objective metrics to evaluate the interaction, and show that guiding force magnitude correlates with comfort and trust scores. These findings provide practical model selection guidelines through environmental characteristics and real-time evaluation metrics.

The effectiveness of a soft wearable back-support device in enhancing postural stability was investigated under trip-like perturbations using two experimental paradigms: perturbed standing and perturbed walking. Healthy subjects completed trials under three different back-support conditions: no device, device worn with low stiffness, and device activated with high stiffness. Whole-body stability was quantified using the minimum Margin of Stability (MOS) at the point of maximal instability. Results demonstrated increased MOS during device use, indicating enhanced postural stability. In standing, MOS increased significantly with device stiffness, whereas in walking, both device conditions improved MOS relative to no device but did not differ significantly from each other. These findings highlight the potential of soft wearable back-support devices with adjustable stiffness to improve reactive balance control against external perturbations, with important implications for fall prevention. Future research should explore personalized stiffness optimization and evaluate efficacy in populations at elevated risk of falls.

A passive monolithic compliant grasping mechanism that works based on the eversion of an elastically deformable bistable shell is conceptualized. It comprises grasping arms made of beam segments that work in conjunction with the everting shell. The grasper is capable of picking up a stiff object of any shape up to a maximum size and weight. The bistable shell everts upon contact with the object to enable the grasping arms envelop the object forming an enclosure. The mechanism then stays in that configuration until it is actuated again to turn the shell back to its original configuration and thereby opening the enclosure to release the object. The stiffness of the arms decides the payload of the mechanism. The size of the arms decides the largest object that can be grasped and held. The arms have distributed compliance so that they can conform to the shape of the object without applying undue force on it.

Soft robotics is increasingly explored in artistic contexts, where tactile interaction provides audiences with embodied engagement beyond visual or auditory signals. This work presents an interactive installation that maps semantic emotion analysis of narrative text into variable stiffness of soft pneumatic modules. A natural language model identifies two dominant emotions from a predefined set of six, driving the inflation of seven hexagonally arranged soft actuators. The central actuator represents the primary emotion, while the surrounding ones express the secondary. We develop and mechanically characterize silicone actuators, called soft modules, featuring a thin membrane layer, demonstrating how this morphological control expands the achievable stiffness range while preserving simplicity and low-cost fabrication. A user study with ten participants further evaluates how multisensory coupling of stiffness and LEDs intensity influences emotional perception. The results suggest that stiffness modulation accompanied by color change can support emotionally meaningful and engaging tactile interaction in soft robotic installations.

Soft wearable robotic systems have emerged as a promising solution for assisting individuals with reduced hand function. This paper presents SoFiE, a modular soft finger exoskeleton designed to assist index-finger flexion during grasping tasks. The proposed system is primarily fabricated using 3D-printed flexible materials, enabling a lightweight, low-profile, and modular design. Actuation is achieved through a tendon-driven mechanism powered by a compact DC motor, while passive extension is provided by a compliant conductive spring. This element, termed StretchSense, also functions as a proprioceptive sensor by exhibiting resistance changes under deformation. Furthermore, a novel tactile sensing approach, MagSense, is introduced, using a magnet and magnetometer pair embedded in a soft fingertip structure to estimate contact force and object compliance. The system is fully untethered and controlled by an embedded microcontroller. In addition, actuator-level sensing through motor encoder feedback enables estimation of the system state, providing a foundation for safe and adaptive control strategies. Experimental validation demonstrates the capability of the system to provide reliable pose estimation, distinguish between materials with different stiffness, and generate distinct sensor signatures across different grasping tasks. This paper details the design, fabrication, and sensing concepts of the proposed exoskeleton as a proof of concept toward modular, soft, and assistive wearable robotics.

Achieving both efficient pushability (propulsion transmission) and proximally concentrated bending for steerability is challenging for magnetically actuated soft catheters: higher axial/bending stiffness improves force transmission but reduces steerability, whereas lower stiffness enables large, proximally concentrated bending yet increases kinking/buckling risk under compressive push loads. To address this trade-off, we propose a stiffness-optimized multi-segment magnetically actuated catheter (SO-MAC) that integrates a decoupled steering-advancement mechanism with a gradient-stiffness architecture. The SO-MAC concentrates bending about a stable proximal pivot during advancement while the distal section passively self-straightens to transmit propulsion, aided by the optimized stiffness distribution and elastic recovery of the spring backbone against friction-induced kinking/buckling. Over $0{-}180^{\circ}$ combined steering and advancement, the pivot remained stable and the distal tip advanced near-straight toward the target direction. A 1.5 mm-diameter SO-MAC achieved up to $180^{\circ}$ steering with a 3 mm bending radius at its 10 mm tip, with an average shape error of $1.39 \pm 0.56$ mm and a steering-pivot error of $0.35 \pm 0.10$ mm. Visual feedback control in a bronchial phantom further confirmed robust navigation through highly curved, bifurcating paths.

Advanced driver assistance systems (ADAS) play an important role in modern automotive intelligence, significantly enhancing vehicle safety and stability. The performance of ADAS critically relies on accurate and reliable vehicle state estimation, particularly from vehicle dynamic sensors. Among these signals, wheel load is a key variable for chassis control and safety-critical functions, yet it remains difficult to estimate robustly due to complex suspension geometry, nonlinear dynamics, and measurement noise. To address this issue, we propose DBPnet, a Bayesian physics-informed neural network (PINN) with a physics-aware embedding module inspired by damper characteristics. First, this paper presents a suspension linkage-level modeling (SLLM) approach that constructs a nonlinear instantaneous dynamic model by explicitly considering the complex geometric structure of the suspension. Building upon SLLM, Bayesian inference is integrated into the PINN to effectively cope with noise and uncertainty in the vehicle chassis system, thereby improving the model's robustness. Then, a physics-informed loss function is employed to ensure consistency with fundamental physical principles, while the damper characteristics-inspired embedding module extracts temporal variation features of input signals and incorporates them into each layer of the PINN, ensuring that physical observations guide the neural network without being constrained by fixed physical models. Extensive evaluations on high-fidelity simulations and real-world experiments demonstrate that our DBPnet consistently achieves lower RMSE and MaxError than baseline methods. These results highlight the potential of our DBPnet to advance wheel load estimation and contribute to the development of more reliable ADAS actuator functions.

In robotic applications, actuators are typically designed to be stiff with minimal backlash to ensure precision and repeatability. However, this limits compliance, leading to potential damage and poor force control in uncertain environments. Series Elastic Actuation (SEA) introduces compliance to enhance disturbance rejection and enable force measurement via Hooke's Law but reduces system bandwidth. A custom Series Elastic (SE) element was retrofitted to a black-box actuator to mitigate non-linearities like backlash and static friction. Integrating the SE element enabled high-fidelity force measurements, improving force control bandwidth and performance. A torsional SE element was designed through Finite Element (FE) analysis, yielding a stiffness of 2155.4 Nm/rad. Open-loop force control bandwidth was measured for the original motor and the SEA-integrated configuration, while closed-loop bandwidth was assessed using feedback from the SEA and a commercial force sensor. The SEA module increased bandwidth from 10.32 Hz to 30.32 Hz, a 2.93X improvement. Additionally, it outperformed the commercial sensor by 7.63% despite costing 25 GBP, a fraction of the price.

Soft sleeve actuators (SSAs) have recently been developed as a pneumatic actuation approach for wearable and assistive robotic systems. By integrating the actuation structure into a sleeve-like geometry, these actuators can reduce reliance on external attachment layers and transmission mechanisms while maintaining compliance with limb-shaped surfaces. However, the force-generation behavior of SSAs remains insufficiently explained, particularly with respect to the variation of output force during extension, the influence of external loading, and the mechanical role of axial stiffness. This paper presents an analytical and experimental force analysis of a linear soft sleeve actuator (LSSA). A quasi-static analytical model was developed by expressing the net axial force as the pressure-generated contribution from the cap and folded walls, reduced by the force associated with axial stiffness. The model incorporates internal pressure, projected pressure areas, folded wall geometry, axial displacement, and an experimentally fitted axial stiffness relation. Prescribed-extension and static-load experiments were conducted to evaluate the actuator response. At 125 kPa, the generated force decreased from approximately 112 N at zero extension to nearly zero at 40 mm. Static loading delayed measurable force generation and reduced force output, particularly at low and intermediate pressures. The results show that LSSA force generation is governed by coupled effects of pressure, geometry, displacement, loading, and axial stiffness.

Differentiable simulation of soft bodies is a foundation for system identification, trajectory optimization, and Real2Sim transfer. Yet, existing methods such as the differentiable Projective Dynamics (DiffPD) struggle when faced with heterogeneous materials with extreme stiffness contrasts, hyperelasticity under large deformations, and contact-rich interactions, which are common scenarios in the real world. We present DiffPhD, a unified GPU-accelerated differentiable Projective Dynamics framework for heterogeneous materials that tackles these intertwined challenges simultaneously. Our key insight is a careful integration of: (i) stiffness-aware projective weights to embed heterogeneity into the global system; (ii) trust-region eigenvalue filtering lifted to the backward pass for stable hyperelastic gradients and a type-II Anderson Acceleration scheme with dual-gate convergence to stabilize forward iteration under large stiffness contrasts; and (iii) a unified GPU pipeline that reuses a single sparse factor across forward, backward, and contact computations, with stiffness-amplified Rayleigh damping folded into the same factor for heterogeneity-aware dissipation at zero recurring cost. DiffPhD achieves strict gradient accuracy while delivering up to an order-of-magnitude speedup over prior differentiable solvers on heterogeneous, hyperelastic, contact-rich benchmarks. Crucially, this speedup does not come at the cost of stability: DiffPhD remains convergent on stiffness contrasts up to 100x where prior PD solvers degrade. This unlocks end-to-end gradient-based optimization on regimes previously bottlenecked by either solver fragility or per-iteration cost -- shell--joint composite creatures, soft characters wielding stiff weapons, and soft-gripper robotic manipulation -- all handled within a single forward--backward pass.

Quadruped robots are often designed with rigid feet to simplify control and maintain stable contact during locomotion. While this approach is straightforward, it limits the ability of the legs to absorb impact forces and reuse stored elastic energy, leading to higher energy expenditure during locomotion. To explore whether compliant feet can provide an advantage, we integrate foot compliance into a reinforcement learning (RL) locomotion controller and study its effect on walking efficiency. In simulation, we train eight policies corresponding to eight different spring stiffness values and then cross-evaluate their performance by measuring mechanical energy consumed per meter traveled. In experiments done on a developed quadruped, the energy consumption for the intermediate stiffness spring is lower by ~ 17% when compared to a very stiff or a very flexible spring incorporated in the feet, with similar trends appearing in the simulation results. These results indicate that selecting an appropriate foot compliance can improve locomotion efficiency without destabilizing the robot during motion.

Physics-based digital twins aim to predict the dynamics of real-world objects under interaction, enabling real-to-sim-to-real applications in robotics. Current approaches reconstruct such twins as explicit physical models (such as spring-mass systems) to predict the dynamics, but the resulting models often inherit the resolution of the visual reconstruction rather than being reduced to the physical complexity required to reproduce task-relevant dynamics. This mismatch introduces redundant topology, making repeated forward-dynamics rollouts unnecessarily expensive. To address this challenge, we present PhySPRING, an fully differentiable GNN-based method to reduce complexity in spring--mass digital twins. PhySPRING jointly learns a hierarchy of coarsened graph topologies and their mechanical parameters from observations. At each reduction level, PhySPRING merges nodes with similar learned dynamic responses to optimize the topology, while maintaining every reduced layer as an explicit spring--mass system. On the PhysTwin benchmark, PhySPRING improves dense reconstruction and prediction accuracy over PhysTwin, while reduced models retain stable physical and visual fidelity with up to a 2.30 times speed-up. We further demonstrate the effectiveness of PhySPRING in a Real2Sim robot policy-evaluation pipeline, where the reduced models are substituted zero-shot into ACT and $π_0$ evaluations, maintaining comparable manipulation success rates across downsampling levels while improving action-sampling effectiveness. Together, PhySPRING enables efficient and structure-preserving spring--mass reduction without sacrificing fidelity or robotic utility.

Physics-Informed Neural Networks (PINNs) often struggle to train reliably on stiff and oscillatory dynamical systems due to poor optimization conditioning. While prior work has emphasized representational remedies such as spectral parameterizations, the optimization implications of initial-condition (IC) embeddings in adaptive spectral PINNs have not been well characterized. In this work, we show that the choice of IC gating function induces explicit time-dependent gradient scaling, which interacts with spectral representations during training. Using a nonlinear stiff spring-pendulum ODE as a controlled benchmark, we compare exponential and linear IC gates in combination with fixed and adaptive Fourier spectral trunks. We observe stiffness-dependent changes in relative dominance for adaptive PINNs: at moderate stiffness ($k=20$), exponential gating often yields lower error but exhibits heterogeneous behavior across random seeds, whereas at higher stiffness ($k=60$), linear gating becomes preferable, with additional reversals observed at larger $k$. These trends hold for both relative $L^2$ error and maximum pointwise error and are confirmed by paired Wilcoxon signed-rank tests with Holm correction. Overall, our results demonstrate that IC embeddings are not a neutral design choice in PINNs: the induced gradient scaling materially shapes optimization conditioning in stiff regimes, with distinct sensitivity patterns in baseline and adaptive spectral models.

Purpose: Six million people use crutches as mobile aids in the US. Rigid designs with no axial mobility limit sensory feedback and lead to secondary injury on the upper joints. Spring-loaded designs offer compliance but may compromise stability. We designed a biologically inspired tensegrity crutch with a compliant module aiming to achieve favorable mechanical properties. The terminal module was a pre-stressed self-tensile two-cell tensegrity structure. We compared the tensegrity crutch to commercial rigid and spring-loaded crutches in mechanical tests using axial loading, in overground straight and turning walking, and in participant experience. Methods: In human trials, healthy young adults (N=18) with no recent lower-body injury performed straight walking and turning trials at a comfortable self-selected pace. A knee blocker simulated unilateral injury of the dominant leg. After using each type of crutch, participants reported their perceived levels of effort, comfort, pain, stability, and usability. Results: Compared to the rigid design, both spring-loaded and tensegrity conditions reduced peak loading rates. The tensegrity design improved effort, comfort, pain, and usability. Spring-loaded crutches reduced perceived stability and walking speed. Conclusion: The biologically inspired tensegrity crutches were an overall improvement to existing designs. Simulations and mechanical testing suggest that nonlinear stiffness, ground-following, and force feedback are among the beneficial mechanical properties that underlie this improvement.

Variable impedance model predictive control (MPC) formulations often treat joint stiffness as an instantaneous decision variable. The resulting feasible set strictly contains the physically realizable set under first-order actuator dynamics. We identify this as a formulation error rather than a modeling approximation, formalize the distinction between the parameter-based feasible set F_param and the realizable set F_real, and characterize the regime of mismatch via the dimensionless parameter α = ωsT (actuator bandwidth times task timescale). For the 1D hopping monoped, we prove that below an analytical threshold α_crit derived in closed form from task physics, no admissible stiffness command realizes the parameter-based prediction. Numerical validation in 1D shows monotonic deviation growth as α decreases, with the predicted scaling holding across ten parameter combinations (log-log R2 = 0.986). Mechanism transfer to planar spring-loaded inverted pendulum dynamics confirms center-of-mass and stance-timing deviation as the primary consequence, with regime-dependent friction effects as a tertiary observable. A second threshold α_infeas < α_crit establishes a floor below which restricting the admissible stiffness range cannot repair realizability, closing the conservative-tuning objection. Augmenting the prediction state with stiffness closes the mismatch by construction.

Shared Control methods often use impedance control to track target poses in a robotic manipulator. The guidance behavior of such controllers is shaped by the used stiffness gains, which can be varying over time to achieve an adaptive guiding. When multiple target poses are tracked at the same time with varying importance, the corresponding output wrenches have to be arbitrated with weightings changing over time. In this work, we study the stabilization of both variable stiffness in impedance control as well as the arbitration of different controllers through a scaled addition of their output wrenches, reformulating both into a holistic framework. We identify passivity violations in the closed loop system and provide methods to passivate the system. The resulting approach can be used to stabilize standard impedance controllers, allowing for the development of novel and flexible shared control methods. We do not constrain the design of stiffness matrices or arbitration factors; both can be matrix-valued including off-diagonal elements and change arbitrarily over time. The proposed methods are furthermore validated in simulation as well as in real robot experiments on different systems, proving their effectiveness and showcasing different behaviors which can be utilized depending on the requirements of the shared control approach.

Human softness perception in haptics has mainly been studied using mechanically homogeneous objects, despite the fact that many real-world objects exhibit heterogeneous layered structures with nonuniform stiffness. This study examined how layered heterogeneity modulates haptic softness perception. Sixteen lattice-structured stimuli were fabricated by 3D printing, with the stiffness of the upper four layers systematically varied while the bottom two layers remained fixed. Twenty-two participants evaluated the softness of the stimuli in a psychophysical task, and compression tests were conducted to quantify their mechanical properties. Perceived softness was significantly predicted by displacement under load, however, perceptual ranking did not fully coincide with the physical ranking. Linear mixed-effects analyses showed that the softness of the outermost layer had the greatest impact on the perceived softness. Perceived softness also increased as the number of soft subsurface layers increased, although this contribution decreased with depth. Layers 2 and 3 showed significant effects, whereas Layer 4 did not. These findings suggest that haptic softness perception depends not only on the overall stiffness but also on the depth-dependent distribution of compliance within layered structures.

Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff integrators. We introduce an extended Newton implicit layer that enforces algebraic constraints exactly and reduces fast dynamics to their quasi-steady-state values in a single differentiable solve. Embedded in a physics-informed DeepONet, the layer recovers all fast and algebraic states exactly from slow-state predictions, removes the per-window stiffness-amplification pathway, and yields a stiffness-scaled Implicit Function Theorem gradient absent from penalty methods. Cascaded implicit layers extend this to multi-component systems with provable convergence. On a grid-forming inverter (stiffness ratio of about 4712), extended Newton attains 1.42% error versus 39.3% (penalty) and 57.0% (standard Newton); augmented Lagrangian and feedback linearization diverged. Two independently trained models compose without retraining (0.72% to 1.16% error, exact constraint satisfaction). Cross-domain validation on the Robertson stiff DAE (stiffness ratio up to $10^5$) confirms generalization. Conformal prediction provides 90% coverage with automatic out-of-distribution detection.

Wrist exoskeletons play a vital role in rehabilitation and assistive applications, yet conventional actuation mechanisms such as electric motors or pneumatics often introduce undesirable weight, friction, and complexity. This paper presents a novel single-cable (tendon), torsional-spring-assisted actuation mechanism for wrist abduction-adduction, and a simulation-based method for selecting its stiffness parameters. The mechanism employs a single Bowden cable passively tensioned by a spiral torsional spring (clock spring) to maintain continuous cable tension without antagonistic actuation. Kinematic and dynamic modeling of the mechanism was performed to estimate the required torque and identify optimal spring parameters. These simulation-derived parameters guided the design of a functional prototype, which was experimentally evaluated with five participants with no motor disabilities (NMD) under varying arm positions and loading conditions using three spring configurations to account for user variability and modeling uncertainties. Experimental results show consistent agreement with simulation-derived trends, with the nominal spring configuration achieving balanced motion range, torque demand, and repeatability. The results demonstrate that simulation-informed stiffness selection can effectively guide the design of compact, cable-driven wrist exoskeletons while reducing reliance on empirical tuning.

Nature suggests that exploiting the elasticities and natural dynamics of robotic systems could increase their locomotion efficiency. Prior work on elastic snake robots supports this hypothesis, but has not fully exploited the nonlinear dynamic behavior of the systems. Recent advances in eigenmanifold theory enable a better characterization of the natural dynamics in complex nonlinear systems. This letter investigates if and how the nonlinear natural dynamics of a kinematic elastic snake robot can be used to design efficient gaits. Two types of gaits based on natural dynamics are presented and compared to a state-of-the-art approach using dynamics simulations. The results reveal that a gait generated by switching between two nonlinear normal modes does not improve the locomotion efficiency of the robot. In contrast, gaits based on non-brake periodic trajectories (non-brake orbits) are perfectly efficient in the energy-conservative case. Further simulations with friction reveal that, in a more realistic scenario, non-brake orbit gaits achieve higher efficiency compared to the baseline gait on the rigid system. Overall, the investigation offers promising insights into the design of gaits based on natural dynamics, fostering further research.

Vine-inspired robots achieve large workspace coverage through tip eversion, enabling safe navigation in confined and cluttered environments. However, their deployment in free space is fundamentally limited by low axial stiffness, poor load-bearing capacity, and the inability to retain shape during and after steering. In this work, we propose a reconfigurable pneumatic joint (RPJ) architecture that introduces discrete, pressure-tunable stiffness along the robot body without compromising continuous growth. Each RPJ module comprises symmetrically distributed pneumatic chambers that locally increase bending stiffness when pressurized, enabling decoupling between global compliance and localized rigidity. We integrate the RPJs into a soft growing robot with tendon-driven steering and develop a compact base station for mid-air eversion. System characterization and experimental validation demonstrate moderate pressure requirements for eversion, as well as comparable localized stiffening and steering performance to layer-jamming mechanisms. Demonstrations further show that the proposed robot achieves improved shape retention during bending, reduced gravitational deflection under load, cascading retraction, and reliable payload transport up to 202 g in free space. The RPJ mechanism establishes a practical pathway toward structurally adaptive vine robots for manipulation-oriented tasks such as object sorting and adaptive exploration in unconstrained environments.

Precision reducers couple contact geometry, bearing support, structural deformation, and loading history. This paper presents a dynamic toolkit connecting distributed local contacts to the complete mechanical reaction path. Work-conjugate maps transfer displacement, reaction, and tangent contributions between contacts and rigid or reduced coordinates, with explicit allocation of contact and body elasticity. An implicit generalized-alpha solution distinguishes trial evaluations from accepted history. Contact records then support performance protocols and configured geometric or constitutive feedback. The numerical studies focus on mechanical coupling and pressure recovery. An idealized annular housing retains physical interfaces while its structural coordinates are reduced. Two reductions with similar static errors have cross-port response errors of 24.975 and 0.312 percent over the same frequency band relative to a common parent model. In a shared-pin example, a 20 micrometer radial displacement of one wheel changes the load on a second, fixed wheel by approximately 75 N. Removing cross-station compliance removes this incremental transfer on the tested sleeve-seating branch. A double-wheel cycloidal assembly relates torsional branch response to aggregate contact-load variation and normalized pressure fields. The pressure maxima remain sensitive to resolution despite small discrete force residuals. Further formulations specify how motion and contact records support precision, vibration, heat, wear, and durability models with their required inputs. The framework separates model representation and numerical resolution while retaining common definitions of motion, force, and observation.