74,464 research outputs found
The rolling problem: overview and challenges
In the present paper we give a historical account -ranging from classical to
modern results- of the problem of rolling two Riemannian manifolds one on the
other, with the restrictions that they cannot instantaneously slip or spin one
with respect to the other. On the way we show how this problem has profited
from the development of intrinsic Riemannian geometry, from geometric control
theory and sub-Riemannian geometry. We also mention how other areas -such as
robotics and interpolation theory- have employed the rolling model.Comment: 20 page
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Geometric configuration in robot kinematic design
A lattice of geometries is presented and compared for representing some geometrical aspects of the kinematic design of robot systems and subsystems. Three geometries (set theory, topology and projective geometry) are briefly explored in more detail in the context of three geometric configurations in robotics (robot groupings, robot connectivities and robot motion sensor patterns)
DeepFactors: Real-time probabilistic dense monocular SLAM
The ability to estimate rich geometry and camera motion from monocular imagery is fundamental to future interactive robotics and augmented reality applications. Different approaches have been proposed that vary in scene geometry representation (sparse landmarks, dense maps), the consistency metric used for optimising the multi-view problem, and the use of learned priors. We present a SLAM system that unifies these methods in a probabilistic framework while still maintaining real-time performance. This is achieved through the use of a learned compact depth map representation and reformulating three different types of errors: photometric, reprojection and geometric, which we make use of within standard factor graph software. We evaluate our system on trajectory estimation and depth reconstruction on real-world sequences and present various examples of estimated dense geometry
On Centroidal Dynamics and Integrability of Average Angular Velocity
In the literature on robotics and multibody dynamics, the concept of average
angular velocity has received considerable attention in recent years. We
address the question of whether the average angular velocity defines an
orientation framethat depends only on the current robot configuration and
provide a simple algebraic condition to check whether this holds. In the
language of geometric mechanics, this condition corresponds to requiring the
flatness of the mechanical connection associated to the robotic system. Here,
however, we provide both a reinterpretation and a proof of this result
accessible to readers with a background in rigid body kinematics and multibody
dynamics but not necessarily acquainted with differential geometry, still
providing precise links to the geometric mechanics literature. This should help
spreading the algebraic condition beyond the scope of geometric
mechanics,contributing to a proper utilization and understanding of the concept
of average angular velocity.Comment: 8 pages, accepted for IEEE Robotics and Automation Letters (RA-L
Geometry of wave propagation on active deformable surfaces
Fundamental biological and biomimetic processes, from tissue morphogenesis to
soft robotics, rely on the propagation of chemical and mechanical surface waves
to signal and coordinate active force generation. The complex interplay between
surface geometry and contraction wave dynamics remains poorly understood, but
will be essential for the future design of chemically-driven soft robots and
active materials. Here, we couple prototypical chemical wave and
reaction-diffusion models to non-Euclidean shell mechanics to identify and
characterize generic features of chemo-mechanical wave propagation on active
deformable surfaces. Our theoretical framework is validated against recent data
from contractile wave measurements on ascidian and starfish oocytes, producing
good quantitative agreement in both cases. The theory is then applied to
illustrate how geometry and preexisting discrete symmetries can be utilized to
focus active elastic surface waves. We highlight the practical potential of
chemo-mechanical coupling by demonstrating spontaneous wave-induced locomotion
of elastic shells of various geometries. Altogether, our results show how
geometry, elasticity and chemical signaling can be harnessed to construct
dynamically adaptable, autonomously moving mechanical surface wave guides.Comment: text changes abstract and intro, new results on self-propelled
elastic shells added; 5 pages, 3 figures; videos available on reques
Riemannian geometry as a unifying theory for robot motion learning and control
Riemannian geometry is a mathematical field which has been the cornerstone of
revolutionary scientific discoveries such as the theory of general relativity.
Despite early uses in robot design and recent applications for exploiting data
with specific geometries, it mostly remains overlooked in robotics. With this
blue sky paper, we argue that Riemannian geometry provides the most suitable
tools to analyze and generate well-coordinated, energy-efficient motions of
robots with many degrees of freedom. Via preliminary solutions and novel
research directions, we discuss how Riemannian geometry may be leveraged to
design and combine physically-meaningful synergies for robotics, and how this
theory also opens the door to coupling motion synergies with perceptual inputs.Comment: Published as a blue sky paper at ISRR'22. 8 pages, 2 figures. Video
at https://youtu.be/XblzcKRRIT
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