Source-linked AI summary
System Identification of Admittance Models for Large Real-World Objects
Nathan I. Baum, Nathaniel G. Luttmer, Mark A. Minor
TL;DR
Admittance-type haptic interfaces need physically consistent models of real-world objects, but accurate models of commercial objects are rarely available. This paper presents a workflow for identifying such models without joint-level torque sensors and successfully applies it to a hydraulic door and a wheelbarrow, with physically consistent estimates and reported residual errors across handle and body estimation.
Problem
Accurate physically consistent dynamic models of commercially available objects are rarely available, although admittance-type haptic interfaces require models of both object components and physically consistent inertia matrices.
Method
The workflow identifies handle and body models in stages, using force/torque sensing, motion capture, and an IMU without joint-level instrumentation; it models the door with four-bar kinematics and four fluid-damping zones and the wheelbarrow with a 3D spherical-wheel, no-slip model.
Results
The workflow produced physically consistent door and wheelbarrow models, with handle RMS residuals below 0.64 N and 0.042 Nm, door body RMS residual of 2.19 Nm, and wheelbarrow results below 4.2% of signal range.
Takeaways & Limitations
Physically consistent admittance models can be identified for large, constrained real-world objects without detailed CAD models or torque sensors at constrained joints.
Takeaways & Limitations
The sensor-module adapters impose a lower bound on applicable object mass and may introduce compliance because the handle, sensor module, and body are assumed to form a rigid chain.
Abstract
from arXiv · showhide
Simulation of admittance-type models requires physically consistent dynamic models that are rarely available for off-the-shelf, everyday objects, limiting the fidelity of haptic interfaces that rely on such simulations. This paper presents the first complete workflow for producing physically consistent models of large real-world objects with various constraints and mechanisms, guaranteeing physical consistency of inertia and friction parameters. The workflow separates each object and identifies the handle and body in two stages, requiring no torque sensors at hinges, axles, or other constrained joints. Models are produced for a heavy, closer-actuated door and a wheelbarrow, representing objects of differing constraint types and model complexity. The door is modeled using four-bar linkage kinematics and a fluid dynamics-based lumped parameter model including opening, backcheck, swing, and latch zones. The wheelbarrow is modeled as a rigid body with a spherical wheel and no slip during rolling. Handle estimation RMS errors were below 0.64 N and 0.042 Nm across both objects. Door body estimation had RMS error of 2.19 Nm and wheelbarrow body estimation had RMS error of 6.77 Nm.
I. INTRODUCTION
Admittance haptic interfaces need physically consistent models for both the virtual object's body and handle, but accurate models of everyday objects are rarely available. The paper presents a workflow that identifies these components separately using force/torque sensing, motion capture, and an IMU.
- Motivation: Admittance interfaces require models of both pre-sensor object bodies and post-sensor handles, with physically consistent inertia matrices for stable motion.The workflow targets commercially available objects whose accurate models are rarely available.
- Workflow: The workflow separates handles from bodies and estimates them in two stages using force/torque sensing, motion capture, and inertial measurements.Payload estimation identifies handle inertial parameters before body dynamics are estimated.
- Contribution: The paper presents a complete workflow for constrained real-world objects while guaranteeing physically consistent inertia and friction parameters.It identifies models for a hydraulic door and a wheelbarrow without joint-level torque instrumentation.
- Object models: The workflow addresses objects with different constraint types and model complexity, including a four-bar door model and a full 3D wheelbarrow model.The wheelbarrow uses a spherical wheel contact model with no-slip rolling.
- Related work: Prior work has modeled doors using dynamics, optimization, lookup tables, and recorded torque profiles, while wheelbarrow models remain less studied.This work extends wheelbarrow identification to a full 3D model with physically consistent inertia and friction parameters.
B. Handles
The handles are separated from their objects, connected to the force/torque sensor through adapters, and identified from dynamic excitation data. Angular acceleration is obtained from filtered IMU angular velocity.
- Handle identification: Handle inertial parameters are estimated after separating each handle and mounting it to the force/torque sensor with an adapter.The sensor measures the handle during manually excited orientations and angular velocities.
- Signal processing: Angular acceleration is computed by differentiating IMU angular velocity with a fourth-order Savitzky-Golay filter using a 101 ms window.The filter is implemented with MATLAB's sgolay routine.
C. Door
The door is modeled as a hinged rigid body coupled to a hydraulic closer through a four-bar linkage. The closer dynamics are represented by four operating zones governed by direction and door angle.
- C. Door: The door rotates about its hinge by θd, while the closer pinion rotates by ϕd through a four-bar linkage.The linkage contains links L1, L2, L3, and L4.
- C. Door: Freudenstein’s equation determines the absolute angle γd of linkage link L3 from the door and linkage geometry.The resulting positive root corresponds to the physical assembly of the door closer linkage.
- C. Door: The hydraulic closer contains a spring, piston, and valves that control fluid flow and generate rack force on the output pinion.The piston is driven by hydraulic pressure and spring forces.
- C. Door: The closer exhibits opening, backcheck, swing, and latch zones determined by the sign of ϕ̇d and thresholds θbc and θl.Opening permits free flow, backcheck limits overextension, and sweep or latch valves restrict closing flow.
1) Physics Model:
The door physics model balances measured and predicted wrenches while separating spring identification from dynamic parameter estimation. Its scalar constrained model includes inertia, damping, friction, and closer torques.
- 1) Physics Model:: The body wrench model combines the measured sensor wrench with predicted handle, hinge-friction, closer-damping, and closer-spring wrenches.The sensor-to-body transmission matrix maps measurements into the body frame.
- 1) Physics Model:: Closer damping uses a laminar approximation in which torque is proportional to pinion velocity.Backcheck, sweep, and latch damping coefficients parameterize the corresponding closing and opening behavior.
- 1) Physics Model:: The damping and friction parameters are grouped with smooth transition weights that control the widths of transitions between operating zones.The transition functions use tanh-based smoothing.
- 1) Physics Model:: The door spring torque is modeled with a polynomial.This spring model is part of the closer torque parameterization.
- 1) Physics Model:: Separating identification into two steps creates smaller regression problems: a quasi-static test identifies the spring model, followed by a dynamic test for inertia, damping, and friction.The identified spring model is then used in the dynamic estimation stage.
- 1) Physics Model:: Because the door is constrained about zB, the wrench regression is reduced to scalar equations using the sixth basis vector.The resulting scalar model includes hinge inertia, velocity-dependent damping, Coulomb friction, and closer damping torque.
2) Experimental Setup:
The experiment instruments a freestanding heavy door with motion-capture markers and a sensor module placed between the door and its handle.
- 2) Experimental Setup:: A wooden frame makes the door freestanding and visible to motion-capture cameras, while a bottom weight creates the feel of a heavy door.Sixteen markers were used in the Kabsch algorithm, and part of the door panel was removed to improve marker visibility.
- 2) Experimental Setup:: The sensor module, containing an IMU and force/torque sensor, is positioned between the door and the door handle.This placement supports measurement of the handle and body interaction wrenches.
3) Body Kinematics:
The door body frame is reconstructed from hinge and panel markers, and the door angle is obtained relative to the closed configuration. Velocity and acceleration are then filtered derivatives of that angle.
- 3) Body Kinematics:: The body-frame origin is placed at the mean of six hinge markers, with zB aligned to the hinge markers and xB directed toward the panel marker bPL.The yB axis follows from the cross product, completing the body frame.
- 3) Body Kinematics:: The door angle θd is computed from the rotation of xB relative to its closed-position direction.This defines the angular coordinate used in the door dynamics.
- 3) Body Kinematics:: Door velocity and acceleration are obtained by differentiating θd and filtering with a fourth-order Savitzky-Golay filter using a 310 ms window.The filtered derivatives provide the dynamic quantities for model estimation.
4) Body Dynamics:
The wheelbarrow body model combines rigid-body wrench balance, spherical-wheel contact, rolling friction, and physically constrained parameter estimation. Its formulation includes no-slip kinematics and a regularized regression using measured handle wrenches and motion data.
- Wheelbarrow body model: The wheelbarrow body is modeled with handle, contact, and axle wrenches acting on a frame centered at the axle.The wheel inertia is lumped with the bucket inertia, while bearing friction acts through the axle wrench.
- Wheel contact: The spherical wheel model projects the contact point downward from the axle midpoint to capture lateral shift under camber.The approximation is intended for small camber angles within ±7.5° and avoids the limitation of a rigid disc model.
- Wheel contact: No-slip wheel kinematics relate wheel angular velocity to contact-point motion, while the contact wrench includes rolling resistance and scrubbing friction.The friction formulation also includes viscous and Coulomb friction terms.
- Parameter estimation: The body regression combines measured handle wrenches and model terms into a six-component residual, then uses weighted, regularized least squares.The regression is constrained to wrench components available without force-plate measurements, and a CAD prior supports the inertial parameters.
- Parameter estimation: The workflow additionally estimates leg-contact geometry and penetration depth for possible future surface-contact simulation.The left-foot penetration depth can be used in a future haptic contact model.
2) Experimental Setup:
The wheelbarrow experiment used a full instrumented setup with handle sensors, motion-capture markers, and a secured payload. These measurements support wrench transmission and body-frame estimation.
- Experimental setup: A static 50 lb payload was secured inside the wheelbarrow bucket during the experiment.The setup included motion-capture markers on both sensor modules and nine additional bucket markers for robust point-cloud matching.
- Experimental setup: Motion-capture markers provide the geometry needed to compute wrench transmission matrices from the handles and body to the contact frame.The aligned markers establish the body-frame axes and the corresponding transmission quantities.
3) Body Kinematics:
Body kinematics are reconstructed from motion-capture markers by aligning sensor and bucket marker sets and computing the body, handle, and contact frames. The resulting frame signals are differentiated for dynamic estimation.
- Marker-based kinematics: Fixed offsets between each sensor housing and its markers provide sensor rotations and positions directly from motion capture.These measurements supply W R_R, W R_L, W r_W,R, and W r_W,L.
- Marker-based kinematics: The contact-frame rotation is determined from axle markers and the body-frame direction vectors.The construction uses the body and contact z-axis relationship to define the contact orientation.
- Marker-based kinematics: The body-frame transmission matrix is computed from contact and body geometry, with body y- and z-axes obtained directly from motion capture.The corresponding left-handle derivation follows by symmetry from the right-hand case.
- Signal processing: A fourth-order Savitzky-Golay filter with a 110 ms window differentiates the reconstructed frame to obtain velocities and accelerations.These filtered kinematic quantities support subsequent dynamic identification.
4) Body Dynamics:
The body experiments dynamically excited the wheelbarrow while enforcing physically consistent parameter estimates. Door and wheelbarrow test sets then showed low residuals, with manual excitation limiting identification of difficult-to-excite directions.
- Body estimation: The wheelbarrow body was excited by pushing, rolling side to side, yawing to scrub the tire, and lifting the bucket.Handles were removed and sensors zeroed before the body-only data collection.
- Body estimation: All estimated inertial and damping parameters were positive and physically consistent, with every effective condition number below 100.The regularization parameter λ was increased until this conditioning threshold was met.
- Results: 0.64 N and 0.042 Nm were the maximum RMS residuals for handle estimation, with all signal-range percentages below 3% except the wheelbarrow handle nz component at 13.7%.The nz direction aligns with the cylindrical handle length and is difficult to excite manually.
2) Door:
The identified door and wheelbarrow models achieve low residual errors while using physically consistent parameters, but the workflow remains bounded by hysteresis, adapter compliance, and instrumentation assumptions.
- Door: 2.19 Nm RMS residual was obtained for the door model, with 1.54 mm average marker error.The residual was 5.2% of the torque reference range.
- Door: The door spring model exhibited hysteresis because one polynomial coefficient set was fit to both opening and closing trajectories.Independent opening and closing coefficients are identified as a next step.
- Wheelbarrow: All wheelbarrow RMS residuals were below 4.2% of the signal range, with 2.1 mm average marker error.The spherical wheel approximation appeared valid according to the model results.
- Dynamics and Object Compliance: Motion-capture-derived kinematic quantities produced better results for the larger bodies than the IMU-based approach.The lower IMU performance may have resulted from compounded sensor-frame estimation errors.
- Dynamics and Object Compliance: The workflow requires 1–2 kg adapters and assumes a rigid handle–sensor–body chain, limiting applicability to sufficiently massive objects.Adapter compliance can manifest as additional error and may noticeably affect interaction with lighter objects such as a cane.
- Conclusion: The identified models were produced with physically consistent inertial and friction estimates without joint-level instrumentation or detailed CAD models.The workflow uses force/torque sensing, motion capture, and an IMU, and future work includes deployment in a real admittance robot.