Abstract The mechanical response of a knot tied in elastic rods strongly depends on the frictional force due to rod–rod contact. The behavior of a knot can be qualitatively different based on the frictional coefficient of the elastic rod. Systematic variation of friction during rod–rod contact is a crucial component of any experimental design to uncover the underlying ingredients behind the mechanics of knots. In this paper, we demonstrate a novel process of controlling the friction of a continuous rod by adhering non-spherical inorganic micro-particles. Polymeric binder is used to deliver the particles as asperities over the rod substrate and by controlling their size and distribution the coefficient of friction of the rod is determined. In parallel, numerical simulations with the discrete elastic rods algorithm are used to reproduce the experimental observations. Tabletop experiments are performed where overhand knots with a variety of unknotting numbers are pulled tight. The force–extension curve of these experiments shows that the proposed process can successfully tune the friction between rods.
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This content will become publicly available on May 1, 2025
Sim2Real Neural Controllers for Physics-Based Robotic Deployment of Deformable Linear Objects
Deformable linear objects (DLOs), such as rods, cables, and ropes, play important roles in daily life. However, manipulation of DLOs is challenging as large geometrically nonlinear deformations may occur during the manipulation process. This problem is made even more difficult as the different deformation modes (e.g., stretching, bending, and twisting) may result in elastic instabilities during manipulation. In this paper, we formulate a physics-guided data-driven method to solve a challenging manipulation task—accurately deploying a DLO (an elastic rod) onto a rigid substrate along various prescribed patterns. Our framework combines machine learning, scaling analysis, and physical simulations to develop a physics-based neural controller for deployment. We explore the complex interplay between the gravitational and elastic energies of the manipulated DLO and obtain a control method for DLO deployment that is robust against friction and material properties. Out of the numerous geometrical and material properties of the rod and substrate, we show that only three non-dimensional parameters are needed to describe the deployment process with physical analysis. Therefore, the essence of the controlling law for the manipulation task can be constructed with a low-dimensional model, drastically increasing the computation speed. The effectiveness of our optimal control scheme is shown through a comprehensive robotic case study comparing against a heuristic control method for deploying rods for a wide variety of patterns. In addition to this, we also showcase the practicality of our control scheme by having a robot accomplish challenging high-level tasks such as mimicking human handwriting, cable placement, and tying knots.
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- NSF-PAR ID:
- 10524073
- Publisher / Repository:
- Sage Journals
- Date Published:
- Journal Name:
- The International Journal of Robotics Research
- Volume:
- 43
- Issue:
- 6
- ISSN:
- 0278-3649
- Page Range / eLocation ID:
- 791 to 810
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Changing the surface properties (i.e., roughness or friction) can be instrumental for many applications but can be a complex and resource-intensive process. In this paper, we demonstrate a novel process of controlling the friction of a continuous rod by delivering inorganic microparticles. A standardized continuous particle transfer protocol has been developed in our laboratory for depositing particles from a liquid carrier system (LCS) to the cylindrical rod substrate. The particle transfer process can produce controllable and tunable surface properties. Polymeric binder is used to deliver the particles as asperities over the rod substrate and by controlling their size, shape, and distribution, the coefficient of friction of the rod is determined. Tabletop experiments are designed and performed to measure the friction coefficient following the Capstan equation. The entrained particles on the substrate will create size- and shape-based asperities, which will alter the surface morphology toward the desired direction. Both oblique and direct quantitative measurements are performed at different particles and binder concentrations. A systematic variation in the friction coefficient is observed and reported in the result section. It is observed from the capstan experiment that adding only 1% irregular shaped particles in the suspension changes the friction coefficient of the rods by almost 115%. The proposed friction control technique is a simple scale-up, low-cost, low-waste, and low-energy manufacturing method for controlling the surface morphology.
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This work experimentally investigates the pressure-driven flow of a pure Newtonian fluid through three-dimensional (3D) porous media models. The porous media model consists of square arrays of rods that also could be interpreted as a periodic tandem rod arrangement. We employed a time-resolved three-dimensional particle tracking velocimetry (3D Shake-the-Box) technique for a range of Reynolds numbers [Formula: see text] to observe flow structures and vortex formation between the rods in porous media structures with different porosities of [Formula: see text] which corresponds to the spacing ratio of [Formula: see text], where L is the distance between the centers of the rods, and D is the diameter of the rods. For all the examined cases, we further analyzed the effect of the Reynolds number and the spacing ratio on the instantaneous and averaged patterns of velocity, vorticity, and the other flow parameters after obtaining the two-dimensional velocity fields using the bin-averaging method. We observed both symmetrical and asymmetrical patterns of structure and recirculation regions between the rods depending on the Reynolds number and spacing ratio. Increasing the Reynolds number reduced the symmetrical patterns of flow structures with respect to the centerline of the gap region, while the spacing ratio was randomly affecting the symmetry degree. Vortex shedding was considerable for the two examined high Reynolds numbers of Re = 444 and Re = 890 behind the upstream rod as the porosity increased. The backward movement of the reattachment point has been observed by increasing the Reynolds number.more » « less
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Abstract Purpose To assess biomechanics of a lumbar PSO stabilized with different multi-rod constructs (4-, 5-, 6-rods) using satellite and accessory rods.
Methods A validated spinopelvic finite element model with a L3 PSO was used to evaluate the following constructs: 2 primary rods T10-pelvis (“Control”), two satellite rods (4-rod), two satellite rods + one accessory rod (5-rod), or two satellite rods + two accessory rods (6-rod). Data recorded included: ROM T10-S1 and L2-L4, von Mises stresses on primary, satellite, and accessory rods, factor of safety yield stress, and force across the PSO surfaces. Percent differences relative to Control were calculated.
Results Compared to Control, 4-rods increased PSO flexion and extension. Lower PSO ROMs were observed for 5- and 6-rods compared to 4-rods. However, 4-rod (348.6 N) and 5-rod (343.2 N) showed higher PSO forces than 2-rods (336 N) and 6-rods had lower PSO forces (324.2 N). 5- and 6-rods led to the lowest rod von Mises stresses across the PSO. 6-rod had the maximum factor of safety on the primary rods.
Conclusions In this finite element analysis, 4-rods reduced stresses on primary rods across a lumbar PSO. Although increased rigidity afforded by 5- and 6-rods decreased rod stresses, it resulted in less load transfer to the anterior vertebral column (particularly for 6-rod), which may not be favorable for the healing of the anterior column. A balance between the construct’s rigidity and anterior load sharing is essential.
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null (Ed.)Choosing a kinematic model for a continuum robot typically involves making a tradeoff between accuracy and computational complexity. One common modeling approach is to use the Cosserat rod equations, which have been shown to be accurate for many types of continuum robots. This approach, however, still presents significant computational cost, particularly when many Cosserat rods are coupled via kinematic constraints. In this work, we propose a numerical method that combines orthogonal collocation on the local rod curvature and forward integration of the Cosserat rod kinematic equations via the Magnus expansion, allowing the equilibrium shape to be written as a product of matrix exponentials. We provide a bound on the maximum step size to guarantee convergence of the Magnus expansion for the case of Cosserat rods, compare in simulation against other approaches, and demonstrate the tradeoffs between speed and accuracy for the fourth and sixth order Magnus expansions as well as for different numbers of collocation points. Our results show that the proposed method can find accurate solutions to the Cosserat rod equations and can potentially be competitive in computation speed.more » « less
