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Quadrotors have gained popularity over the last decade, aiding humans in complex tasks such as search and rescue, mapping and exploration. Despite their mechanical simplicity and versatility compared to other types of aerial vehicles, they…

Humans are efficient, yet expressive in their motion. Human walking behaviors can be used to walk across a great variety of surfaces without falling and to communicate internal state to other humans through variable gait styles. This…

A rotor configuration on a graph contains in every vertex an infinite ordered sequence of rotors, each is pointing to a neighbor of the vertex. After sampling a configuration according to some probability measure, a rotor walk is a…

This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…

This article is devoted to the properties of the planar triangulations. The conjugated planar triangulation will be introduced and on the base of the properties, which were achieved by the other authors there will be proved some theorems,…

Recent quadrotors have transcended conventional designs, emphasizing more on foldable and reconfigurable bodies. The state of the art still focuses on the mechanical feasibility of such designs with limited discussions on the tracking…

The proof uses the property that the vertices of a triangulated planar graph can be four coloured if the triangles can have a +1 or -1 orientation so that the sum of the triangle orientations around each vertex is a multiple of 3. Such…

We propose a 12-dimensional, global, continuous, and exponentially convergent observer for gyro bias and attitude of a rigid body. Any attitude observer developed on the special orthogonal group suffers from the topological restriction that…

In 1880, P. G. Tait showed that the four colour theorem is equivalent to the assertion that every 3-regular planar graph without cut-edges is 3-edge-colourable, and in 1891, J. Petersen proved that every 3-regular graph with at most two…

We study the computational power of the Full-Tilt model of motion planning, where slidable polyominos are moved maximally around a board by way of a sequence of directional ``tilts.'' We focus on the deterministic scenario in which the…

In this paper, we deal with the gluing of two surfaces, where the gluing locus is assumed to be a curve. We consider a moving frame along the gluing locus, and define developable surfaces with respect to the frame. Considering geometric…

A topological space is introduced in this paper. Just liking the plane, it's continuous, however its $n+1$ regions couldn't be mutually adjacent. Some important phenomenon about its cross-section are discussed. The geometric generating…

In this paper we give an elementary treatment of the dynamics of skew tent maps. We divide the two-parameter space into six regions. Two of these regions are further subdivided into infinitely many regions. All of the regions are given…

Legged robot locomotion is hindered by a mismatch between applications where legs can outperform wheels or treads, most of which feature deformable substrates, and existing tools for planning and control, most of which assume flat, rigid…

Obstacle avoidance of quadrotors in dynamic environments is still a very open problem. Current works commonly leverage traditional static maps to represent static obstacles and the detection and tracking of moving objects (DATMO) method to…

We study the problem of bipedal robot navigation in complex environments with uncertain and rough terrain. In particular, we consider a scenario in which the robot is expected to reach a desired goal location by traversing an environment…

Navigating mobile robots through environments shared with humans is challenging. From the perspective of the robot, humans are dynamic obstacles that must be avoided. These obstacles make the collision-free space nonconvex, which leads to…

The choice of the representations is essential for deep gait recognition methods. The binary silhouettes and skeletal coordinates are two dominant representations in recent literature, achieving remarkable advances in many scenarios.…

Planning whole-body motions while taking into account the terrain conditions is a challenging problem for legged robots since the terrain model might produce many local minima. Our coupled planning method uses stochastic and…

During the wear process of surfaces in sliding friction, there is a running-in period during which the topography of surfaces changes with time before reaching the steady wear regime. In the steady wear regime, the statistical parameters…