Related papers: Four-dimensional Gait Surfaces for A Tilt-rotor --…

Gait recognition is an important biometric technique for video surveillance tasks, due to the advantage of using it at distance. In this paper, we present a persistent homology-based method to extract topological features (the so-called…

Maximal planar graph refers to the planar graph with the most edges, which means no more edges can be added so that the resulting graph is still planar. The Four-Color Conjecture says that every planar graph without loops is 4-colorable.…

In this paper we exploit some interesting properties of a class of bipedal robots which have an inertial disc. One of this properties is the ability to control every position and speed except for the disc position. The proposed control is…

For a two-dimensional surface in the four-dimensional Euclidean space we introduce an invariant linear map of Weingarten type in the tangent space of the surface, which generates two invariants k and kappa. The condition k = kappa = 0…

We prove that a uniformly chosen proper $3$-coloring of the $d$-dimensional discrete torus has a very rigid structure when the dimension $d$ is sufficiently high. We show that with high probability the coloring takes just one color on…

During learning trials, systems are exposed to different failure conditions which may break robotic parts before a safe behavior is discovered. Humans contour this problem by grounding their learning to a safer structure/control first and…

Geometric motion planning offers effective and interpretable gait analysis and optimization tools for locomoting systems. However, due to the curse of dimensionality in coordinate optimization, a key component of geometric motion planning,…

We study the motion of surfaces in an intrinsic formulation in which the surface is described by its metric and curvature tensors. The evolution equations for the six quantities contained in these tensors are reduced in number in two cases:…

Using experimental techniques, we study properties of the "circumcenter map", which, upon $n$ iterations sends an $n$-gon to a scaled and rotated copy of itself. We also explore the topology of area-expanding and area-contracting regions…

The attitude of a rigid body evolves on the three-dimensional special orthogonal group, and it is often estimated by measuring reference directions, such as gravity or magnetic field, using an onboard sensor. As a single direction…

This research aims to evaluate the performance of the rotors and study the behavior of the human driver in interacting with the rotors. In recent years, rotors have been increasingly used between countries due to their safety, capacity, and…

In character animation, direction invariance is a desirable property. That is, a pose facing north and the same pose facing south are considered the same; a character that can walk to the north is expected to be able to walk to the south in…

In this report, we present the theory on aerodynamics of quadrotors using the well established momentum and blade element theories. From a robotics perspective, the theoretical development of the models for thrust and horizontal forces and…

General rotational surfaces as a source of examples of surfaces in the four-dimensional Euclidean space have been introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the base of our…

At any point of a surface in the four-dimensional Euclidean space we consider the geometric configuration consisting of two figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We show…

A tilting phase transition is predicted for systems comprising rod like molecules which are irreversibly grafted to a flat surface, so that the non interacting rods are perpendicularly oriented. The transition is controlled by the grafting…

The goal of gait recognition is to extract identity-invariant features of an individual under various gait conditions, e.g., cross-view and cross-clothing. Most gait models strive to implicitly learn the common traits across different gait…

Soft robotics aims to develop robots able to adapt their behavior across a wide range of unstructured and unknown environments. A critical challenge of soft robotic control is that nonlinear dynamics often result in complex behaviors hard…

Let $S$ be a smooth projective surface on a smooth threefold $X$ such that $X$ has Picard rank 1 and NS$(S)$ is generated by the restriction of divisors from X. We show that if $X$ satisfies the Bogomolov-Gieseker type inequality for tilt…

We study the stable pairs theory of local curves in 3-folds with descendent insertions. The rationality of the partition function of descendent invariants is established for the full local curve geometry (equivariant with respect to the…