Related papers: The CR geometry of the three-segment snake
We compute the chains associated to the left-invariant CR structures on the three-sphere. These structures are characterized by a single real modulus $a$. For the standard structure $a=1$, the chains are well-known and are closed curves. We…
Answering connectivity queries in semi-algebraic sets is a long-standing and challenging computational issue with applications in robotics, in particular for the analysis of kinematic singularities. One task there is to compute the number…
The tree spanner problem for a graph $G$ is as follows: For a given integer $k$, is there a spanning tree $T$ of $G$ (called a tree $k$-spanner) such that the distance in $T$ between every pair of vertices is at most $k$ times their…
This letter considers control of a radially symmetric tripedal friction-driven robot. The robot features 3 servo motors mounted on a 3-D printed chassis 7 cm from the center of mass and separated 120 degrees. These motors drive limbs, which…
Contact-rich problems, such as snake robot locomotion, offer unexplored yet rich opportunities for optimization-based trajectory and acyclic contact planning. So far, a substantial body of control research has focused on emulating snake…
This paper presents a bio-inspired central pattern generator (CPG)-type architecture for learning optimal maneuvering control of periodic locomotory gaits. The architecture is presented here with the aid of a snake robot model problem…
We introduce the Study variety of conformal kinematics and investigate some of its properties. The Study variety is a projective variety of dimension ten and degree twelve in real projective space of dimension 15, and it generalizes the…
We introduce a compactification of the group of rigid motions in 3-space derived from the Study model for this group. We use this compactifi-cation in robot kinematics, by considering the boundary of the configuration space of a robot. We…
The geometry of spinning codimension-two branes in AdS spacetime is analyzed in three and higher dimensions. The construction of non-extremal solutions is based on identifications in the covering of AdS space by isometries that have fixed…
The goal of this paper is to study the family of snake polyominoes. More precisely, we focus our attention on the class of partially directed snakes. We establish functional equations and length generating functions of two dimensional,…
The intrinsic geometry of the Kerr ergosurface on constant Boyer-Lindquist (BL), Kerr, and Doran time slices is characterized. Unlike the BL slice, which had been previously studied, the other slices (i) do not have conical singularities at…
Social robots are becoming increasingly diverse in their design, behavior, and usage. In this chapter, we provide a broad-ranging overview of the main characteristics that arise when one considers social robots and their interactions with…
Nature suggests that exploiting the elasticities and natural dynamics of robotic systems could increase their locomotion efficiency. Prior work on elastic snake robots supports this hypothesis, but has not fully exploited the nonlinear…
A special approach to examine spinor structure of 3-space is proposed. It is based on the use of the concept of a spatial spinor defined through taking the square root of a real-valued 3-vector. Two sorts of spatial spinor according to…
A novel kinematically redundant (6+3)-DoF parallel robot is presented in this paper. Three identical 3-DoF RU/2-RUS legs are attached to a configurable platform through spherical joints. With the selected leg mechanism, the motors are…
The paper derives the inverse and forward kinematic equations of a spatial three-degree-of-freedom parallel mechanism, which is the parallel module of a hybrid serial-parallel 5-axis machine tool. This parallel mechanism consists of a…
The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direct construction of the Brownian sphere is via a continuous…
For almost all tendon-driven continuum robots, a segment is actuated by three or four tendons constrained by its mechanical design. For both cases, methods to account for the constraints are known. However, for an arbitrary number of…
We provide a classification of the homogeneous 3-dimensional permutation structures, i.e. homogeneous structures in a language of 3 linear orders, partially answering a question of Cameron. We also arrive at a natural description of all…
The understanding of mobile hexapods, i.e., parallel manipulators with six legs, is one of the driving questions in theoretical kinematics. We aim at contributing to this understanding by employing techniques from algebraic geometry. The…