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1. Moving sidewinding forward: optimizing contact patterns for limbless robots via geometric mechanics

   https://doi.org/10.15607/RSS.2021.XVII.031  

   Chong, Baxi; Wang, Tianyu; Lin, Bo; Li, Shengkai; Choset, Howie; Blekherman, Grigoriy; Goldman, Daniel (July 2021, Robotics: Science and Systems)

   Chong, Baxi; Wang, Tianyu; Lin, Bo; Li, Shengkai; Choset, Howie; Blekherman, Grigoriy; Goldman, Daniel (Ed.)

   Abstract—Contact planning is crucial to the locomotion per-formance of limbless robots. Typically, the pattern by which contact is made and broken between the mechanism and its environment determines the motion of the robot. The design of these patterns, often called contact patterns, is a difficult problem. In previous work, the prescription of contact patterns was derived from observations of biological systems or determined empirically from black-box optimization algorithms. However, such contact pattern prescription is only applicable to specific mechanisms, and is challenging to generalize. For example, the stable and effective contact pattern prescribed for a 12-link limbless robot can be neither stable nor effective for a 6-link limbless robot. In this paper, using a geometric motion planning scheme, we develop a framework to design, optimize, and analyze contact patterns to generate effective motion in the desired directions. Inspired by prior work in geometric mechanics, we separate the configuration space into a shape space (the internal joint angles), a contact state space, and a position space; then we optimize the function that couples the contact state space and the shape space. Our framework provides physical insights into the contact pattern design and reveals principles of empirically derived contact pattern prescriptions. Applying this framework, we can not only control the direction of motion of a 12-link limbless robot by modulating the contact patterns, but also design effective sidewinding gaits for robots with fewer motors (e.g., a 6-link robot). We test our designed gaits by robophysical experiments and obtain excellent agreement. We expect our scheme can be broadly applicable to robots which make/break contact. 

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2. Motion Comparator: Visual Comparison of Robot Motions

   https://doi.org/10.1109/LRA.2024.3430649  

   Wang, Yeping; Peseckis, Alexander; Jiang, Zelong; Gleicher, Michael (September 2024, IEEE Robotics and Automation Letters)

   Roboticists compare robot motions for tasks such as parameter tuning, troubleshooting, and deciding between possible motions. However, most existing visualization tools are designed for individual motions and lack the features necessary to facilitate robot motion comparison. In this letter, we utilize a rigorous design framework to develop Motion Comparator , a web-based tool that facilitates the comprehension, comparison, and communication of robot motions. Our design process identified roboticists' needs, articulated design challenges, and provided corresponding strategies. Motion Comparator includes several key features such as multi-view coordination, quaternion visualization, time warping, and comparative designs. To demonstrate the applications of Motion Comparator, we discuss four case studies in which our tool is used for motion selection, troubleshooting, parameter tuning, and motion review. 

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3. A nanoscale reciprocating rotary mechanism with coordinated mobility control

   https://doi.org/10.1038/s41467-021-27230-7  

   Bertosin, Eva; Maffeo, Christopher M.; Drexler, Thomas; Honemann, Maximilian N.; Aksimentiev, Aleksei; Dietz, Hendrik (December 2021, Nature Communications)

   Abstract Biological molecular motors transform chemical energy into mechanical work by coupling cyclic catalytic reactions to large-scale structural transitions. Mechanical deformation can be surprisingly efficient in realizing such coupling, as demonstrated by the F 1 F O ATP synthase. Here, we describe a synthetic molecular mechanism that transforms a rotary motion of an asymmetric camshaft into reciprocating large-scale transitions in a surrounding stator orchestrated by mechanical deformation. We design the mechanism using DNA origami, characterize its structure via cryo-electron microscopy, and examine its dynamic behavior using single-particle fluorescence microscopy and molecular dynamics simulations. While the camshaft can rotate inside the stator by diffusion, the stator’s mechanics makes the camshaft pause at preferred orientations. By changing the stator’s mechanical stiffness, we accelerate or suppress the Brownian rotation, demonstrating an allosteric coupling between the camshaft and the stator. Our mechanism provides a framework for manufacturing artificial nanomachines that function because of coordinated movements of their components. 

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4. Longitudinal shock waves in a class of semi-infinite stretch-limited elastic strings

   https://doi.org/10.1177/10812865211025582  

   Rodriguez, Casey (March 2022, Mathematics and Mechanics of Solids)

   In this paper, we initiate the study of wave propagation in a recently proposed mathematical model for stretch-limited elastic strings. We consider the longitudinal motion of a simple class of uniform, semi-infinite, stretch-limited strings under no external force with finite end held fixed and prescribed tension at the infinite end. We study a class of motions such that the string has one inextensible segment, where the local stretch is maximized, and one extensible segment. The equations of motion reduce to a simple and novel shock front problem in one spatial variable for which we prove existence and uniqueness of local-in-time solutions for appropriate initial data. We then prove the orbital asymptotic stability of an explicit two-parameter family of piece-wise constant stretched motions. If the prescribed tension at the infinite end is increasing in time, our results provide an open set of initial data launching motions resulting in the string becoming fully inextensible and tension blowing up in finite time. 

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5. Design of dissipative multimaterial viscoelastic‐hyperelastic systems at finite strains via topology optimization

   https://doi.org/10.1002/nme.6083  

   Zhang, Guodong; Khandelwal, Kapil (May 2019, International Journal for Numerical Methods in Engineering)

   Summary This study focuses on the topology optimization framework for the design of multimaterial dissipative systems at finite strains. The overall goal is to combine a soft viscoelastic material with a stiff hyperelastic material for realizing optimal structural designs with tailored damping and stiffness characteristics. To this end, several challenges associated with incorporating finite‐deformation viscoelastic‐hyperelastic materials in a multimaterial design framework are addressed. This includes consideration of a thermodynamically consistent finite‐strain viscoelasticity model for simulating energy dissipation together with F‐bar finite elements for handling material incompressibility. Moreover, an effective multimaterial interpolation scheme is proposed, which preserves the physics of material mixtures in the context of density‐based topology optimization. A numerically accurate analytical design sensitivity calculation is also presented using a path‐dependent adjoint method. Furthermore, both prescribed‐load and prescribed‐displacement boundary conditions are considered in the optimization formulations, together with various strategies for controlling stiffness. As demonstrated by the numerical examples, the use of the stiffer hyperelastic material phase in a design not only improves stiffness but also increases energy dissipation capacity. Moreover, with the finite‐deformation theory, the effect of the loading magnitude on the optimized designs can be observed. 

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