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1. A Method for Constraint Inference Using Pose and Wrench Measurements

   https://doi.org/arXiv:2010.15916  

   Subramani, Guru; Hagenow, Michael; Gleicher, Michael; Zinn, Michael (October 2020, ArXivorg)

   null (Ed.)

   Many physical tasks such as pulling out a drawer or wiping a table can be modeled with geometric constraints. These geometric constraints are characterized by restrictions on kinematic trajectories and reaction wrenches (forces and moments) of objects under the influence of the constraint. This paper presents a method to infer geometric constraints involving unmodeled objects in human demonstrations using both kinematic and wrench measurements. Our approach takes a recording of a human demonstration and determines what constraints are present, when they occur, and their parameters (e.g. positions). By using both kinematic and wrench information, our methods are able to reliably identify a variety of constraint types, even if the constraints only exist for short durations within the demonstration. We present a systematic approach to fitting arbitrary scleronomic constraint models to kinematic and wrench measurements. Reaction forces are estimated from measurements by removing friction. Position, orientation, force, and moment error metrics are developed to provide systematic comparison between constraint models. By conducting a user study, we show that our methods can reliably identify constraints in realistic situations and confirm the value of including forces and moments in the model regression and selection process. 

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2. In-Situ Calibration of Six-Axis Force/Torque Transducers on a Six-Legged Robot

   https://doi.org/10.1115/1.4066455  

   Wu, Ziyou; Revzen, Shai (May 2025, Journal of Dynamic Systems, Measurement, and Control)

   Ground contact modeling for multilegged locomotion is challenging due to the possibility of multiple slipping legs. To understand the interplay of contact forces among multiple legs, we integrated a robot with six high-precision 6 degree-of-freedom (DoF) force-torque sensors, and measured the wrenches (forces and torques) produced in practice. Here, we present an in situ calibration procedure for simultaneously measuring all foot contact wrenches of a hexapod using 6-DoF load cells installed at the hips. We characterized transducer offset, leg gravity offset, and the wrench transformation error in our calibration model. Our calibration reduced the root-mean-square-error (RSME) by 63% for forces and 90% for torques in the residuals of the robot standing in different poses, compared with naive constant offset removal. 

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3. Flight Dynamics of a Flying Wing Aircraft Featuring the Bell Spanload

   https://doi.org/10.2514/6.2023-2610  

   Robb, Caleb S; Vuppala, Rohit; Paul, Ryan C; Kara, Kursat (January 2023, American Institute of Aeronautics and Astronautics)

   Results of a previous aerodynamics study conducted over a wing that exhibits the Prandtl Bell Spanload were implemented into a simulation environment with the intent of studying unique flight characteristics that are theorized to be presented by this spanload. However, early simulations over the dynamics show that the yawing moment due to roll rate is of higher effect than the yaw moment due to aileron deflection angle. This over-prediction of the roll-yaw coupling term has been called into question. A new method is to be tested, which implements a compact vortex-lattice (CVLM) formulation, to show the difference between the flight dynamics predicted by this new method and the stability derivative method currently in use. The analysis utilizes two initial conditions to test the differences as the dynamics propagate through time. The first, a large initial bank angle, leads to the stabiltiy derivative method diverging while the CVLM results show this to not be the case. The second condition, a wind-field representative of a stable nocturnal boundary layer over the ground, leads to much more agreement between methods before divergence occurs due to a velocity higher than that of the stability derivative linearization point. It is then agreed that, since CVLM cannot predict stall effects and other nonlinear flight regions, a hybrid approach is proposed that takes advantage of the roll-yaw coupling prediction of the CVLM and the range of condition available to the stability derivative method. 

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4. Balance Recoverability and Control of Bipedal Walkers With Foot Slip

   https://doi.org/10.1115/1.4053098  

   Mihalec, Marko; Trkov, Mitja; Yi, Jingang (May 2022, Journal of Biomechanical Engineering)

   Abstract Low-friction foot/ground contacts present a particular challenge for stable bipedal walkers. The slippage of the stance foot introduces complexity in robot dynamics and the general locomotion stability results cannot be applied directly. We relax the commonly used assumption of nonslip contact between the walker foot and the ground and examine bipedal dynamics under foot slip. Using a two-mass linear inverted pendulum model, we introduce the concept of balance recoverability and use it to quantify the balanced or fall-prone walking gaits. Balance recoverability also serves as the basis for the design of the balance recovery controller. We design the within- or multi-step recovery controller to assist the walker to avoid fall. The controller performance is validated through simulation results and robustness is demonstrated in the presence of measurement noises as well as variations of foot/ground friction conditions. In addition, the proposed methods and models are used to analyze the data from human walking experiments. The multiple subject experiments validate and illustrate the balance recoverability concept and analyses. 

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5. Improved Spectral Density Estimation via Explicit and Implicit Deflation

   Bhattacharjee, Rajarshi; Jayaram, Rajesh; Musco, Cameron; Musco, Christopher; Ray, Archan (January 2025, ACM-SIAM Symposium on Discrete Algorithms)

   We study algorithms for approximating the spectral density (i.e., the eigenvalue distribution) of a symmetric matrix A ∈ ℝn×n that is accessed through matrix-vector product queries. Recent work has analyzed popular Krylov subspace methods for this problem, showing that they output an ∈ · || A||2 error approximation to the spectral density in the Wasserstein-1 metric using O (1/∈ ) matrix-vector products. By combining a previously studied Chebyshev polynomial moment matching method with a deflation step that approximately projects off the largest magnitude eigendirections of A before estimating the spectral density, we give an improved error bound of ∈ · σℓ (A) using O (ℓ log n + 1/∈ ) matrix-vector products, where σℓ (A) is the ℓth largest singular value of A. In the common case when A exhibits fast singular value decay and so σℓ (A) « ||A||2, our bound can be much stronger than prior work. We also show that it is nearly tight: any algorithm giving error ∈ · σℓ (A) must use Ω(ℓ + 1/∈ ) matrix-vector products. We further show that the popular Stochastic Lanczos Quadrature (SLQ) method essentially matches the above bound for any choice of parameter ℓ, even though SLQ itself is parameter-free and performs no explicit deflation. Our bound helps to explain the strong practical performance and observed ‘spectrum adaptive’ nature of SLQ, and motivates a simple variant of the method that achieves an even tighter error bound. Technically, our results require a careful analysis of how eigenvalues and eigenvectors are approximated by (block) Krylov subspace methods, which may be of independent interest. Our error bound for SLQ leverages an analysis of the method that views it as an implicit polynomial moment matching method, along with recent results on low-rank approximation with single-vector Krylov methods. We use these results to show that the method can perform ‘implicit deflation’ as part of moment matching. 

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