Optimizing coordinate choice for locomotion systems with toroidal shape spaces

Lin, Benyao; Chong, Baxi; Ozkan-Aydin, Yasemin; Aydın, Enes; Choset, Howie; Goldman, Daniel I.; Blekherman, Grigoriy

doi:10.1109/iros45743.2020.9341476

Cited by 5 publications

(6 citation statements)

References 13 publications

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“…Several circular clustering algorithms have been proposed to address this issue, but they also have disadvantages, such as being angle-focused or lacking generality [2,3,14,29,30]. Our proposed method addresses these problems by adapting the cylindrical coordinate system [43,44] and taking advantage of fundamental mathematical properties of polar coordinates that have been observed and successfully applied in phase-controlled coordinate choice optimization [34,45].…”

Section: Discussionmentioning

confidence: 99%

“…In this example, the appropriate distance to generate the correct clustering result is D2(A, B2), so it is essential to locate the accurate distance that moves clockwise or counterclockwise in a circle. Inspired by the coordinate optimization approach in phase-controlled robotics [34], we can take advantage of the periodic nature of the polar coordinate system. Specifically, we address the circularity problem by leveraging its periodic nature through period repetition and explore three different clustering methods to demonstrate how this technique can be used.…”

Section: Solving For Circularitymentioning

confidence: 99%

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Circular Clustering With Polar Coordinate Reconstruction

Sun,

Sajda

2024

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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There is a growing interest in characterizing circular data found in biological systems. Such data are wide-ranging and varied, from the signal phase in neural recordings to nucleotide sequences in round genomes. Traditional clustering algorithms are often inadequate due to their limited ability to distinguish differences in the periodic component θ. Current clustering schemes for polar coordinate systems have limitations, such as being only angle-focused or lacking generality. To overcome these limitations, we propose a new analysis framework that utilizes projections onto a cylindrical coordinate system to represent objects in a polar coordinate system optimally. Using the mathematical properties of circular data, we show that our approach always finds the correct clustering result within the reconstructed dataset, given sufficient periodic repetitions of the data. This framework is generally applicable and adaptable to most state-of-the-art clustering algorithms. We demonstrate on synthetic and real data that our method generates more appropriate and consistent clustering results than standard methods. In summary, our proposed analysis framework overcomes the limitations of existing polar coordinate-based clustering methods and provides an accurate and efficient way to cluster circular data. We provide the code as open-source on GitHub.

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Section: Discussionmentioning

confidence: 99%

Section: Solving For Circularitymentioning

confidence: 99%

Circular Clustering With Polar Coordinate Reconstruction

Sun,

Sajda

2024

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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“…Each of the three integrals of equation (4) can be approximated to the first order as follows.where A x , A y , A θ are the three rows of the local connection, respectively. The accuracy of the approximation in equation (5) can be optimized by properly choosing the body frame (Hatton and Choset, 2015; Lin et al, 2020). According to Stokes’ theorem, the line integral along a closed curve ∂ϕ is equal to the surface integral of the curl of A ( r ) over the surface enclosed by ∂ϕ :where ϕ denotes the surface enclosed by ∂ϕ .…”

Section: Background On Geometric Mechanicsmentioning

confidence: 99%

Optimizing contact patterns for robot locomotion via geometric mechanics

Chong,

Wang,

et al. 2023

The International Journal of Robotics Research

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Contact planning is crucial to the locomotion performance of robots: to properly self-propel forward, it is not only important to determine the sequence of internal shape changes (e.g., body bending and limb shoulder joint oscillation) but also the sequence by which contact is made and broken between the mechanism and its environment. Prior work observed that properly coupling contact patterns and shape changes allows for computationally tractable gait design and efficient gait performance. The state of the art, however, made assumptions, albeit motivated by biological observation, as to how contact and shape changes can be coupled. In this paper, we extend the geometric mechanics (GM) framework to design contact patterns. Specifically, we introduce the concept of “contact space” to the GM framework. By establishing the connection between velocities in shape and position spaces, we can estimate the benefits of each contact pattern change and therefore optimize the sequence of contact patterns. In doing so, we can also analyze how a contact pattern sequence will respond to perturbations. We apply our framework to sidewinding robots and enable (1) effective locomotion direction control and (2) robust locomotion performance as the spatial resolution decreases. We also apply our framework to a hexapod robot with two back-bending joints and show that we can simplify existing hexapod gaits by properly reducing the number of contact state switches (during a gait cycle) without significant loss of locomotion speed. We test our designed gaits with robophysical experiments, and we obtain good agreement between theory and experiments.

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“…The accuracy of the approximation in ( 11) can be optimized by properly choosing the body frame (Hatton and Choset, 2015;Lin et al, 2020). According to Stokes' theorem, the line integral along a closed curve ∂x is equal to the surface integral of the curl of A(r) over the surface enclosed by ∂x:…”

Section: Geometric Mechanicsmentioning

confidence: 99%

Frequency modulation of body waves to improve performance of sidewinding robots

Chong

Wang

Rieser

et al. 2021

The International Journal of Robotics Research

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Sidewinding is a form of locomotion executed by certain snakes and has been reconstructed in limbless robots; the gait is beneficial because it is effective in diverse terrestrial environments. Sidewinding gaits are generated by coordination of horizontal and vertical traveling waves of body undulation: the horizontal wave largely sets the direction of sidewinding with respect to the body frame while the vertical traveling wave largely determines the contact pattern between the body and the environment. When the locomotor’s center of mass leaves the supporting polygon formed by the contact pattern, undesirable locomotor behaviors (such as unwanted turning or unstable oscillation of the body) can occur. In this article, we develop an approach to generate desired translation and turning by modulating the vertical wave. These modulations alter the distribution of body–environment contact patches and can stabilize configurations that were previously statically unstable. The approach first identifies the spatial frequency of the vertical wave that statically stabilizes the locomotor for a given horizontal wave. Then, using geometric mechanics tools, we design the coordination between body waves that produces the desired translation or rotation. We demonstrate the effectiveness of our technique in numerical simulations and on experiments with a 16-joint limbless robot locomoting on flat hard ground. Our scheme broadens the range of movements and behaviors accessible to sidewinding locomotors at low speeds, which can lead to limbless systems capable of traversing diverse terrain stably and/or rapidly.

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Optimizing coordinate choice for locomotion systems with toroidal shape spaces

Cited by 5 publications

References 13 publications

Circular Clustering With Polar Coordinate Reconstruction

Circular Clustering With Polar Coordinate Reconstruction

Optimizing contact patterns for robot locomotion via geometric mechanics

Frequency modulation of body waves to improve performance of sidewinding robots

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