Related papers: The south-pointing chariot on a surface
Due to possibly changing pose of a movable object and nonholonomic constraint of a differential-drive robot, it is challenging to design an object servoing scheme for the differential-drive robot to asymptotically park at a predefined…
A small sphere placed on the top of a big static frictionless sphere, slips until it leaves the surface at an angle $\theta_{l}=\cos^{-1}{2/3}$. On the other extreme, if the surface of the big sphere has coefficient of static friction,…
This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…
Consider the Euclidean space $\mathbb{R}^3$ endowed with a canonical semi-symmetric non-metric connection determined by a vector field $\mathsf{C}\in\mathfrak{X}(\mathbb{R}^3)$. We study surfaces when the sectional curvature with respect to…
We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The classification is also suitable for a hyperboloid and a…
Accurate maps are a prerequisite for virtually all mobile robot tasks. Most state-of-the-art maps assume a static world; therefore, dynamic objects are filtered out of the measurements. However, this division ignores movable but non-moving…
In the present paper, the geometric properties of a soliton surface $\Psi=\Psi(s,t)$ associated with the Betchov-Da Rios (B-DR) equation using the parallel transport frame field in four-dimensional Euclidean space are examined. We obtain…
We develop a semi-analytic deterministic framework for charged-particle transport with continuous slowing-down in energy and angular scattering. Directed transport and energy advection are treated by method-of-characteristics integration,…
This paper addresses the question: given a scalar group, can we determine all the additions that transform this scalar group into a (near-)field? A key approach to addressing this problem involves transporting (near-)field structures via…
Physical reasoning is a core aspect of intelligence in animals and humans. A central question is what model should be used as a basis for reasoning. Existing work considered models ranging from intuitive physics and physical simulators to…
In the field of bioimaging, an important part of analyzing the motion of objects is tracking. We propose a method that applies the Sinkhorn distance for solving the optimal transport problem to track objects. The advantage of this method is…
By observing their environment as well as other traffic participants, humans are enabled to drive road vehicles safely. Vehicle passengers, however, perceive a notable difference between non-experienced and experienced drivers. In…
If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by…
Stabilizing multi-steered articulated vehicles in backward motion is a complex task for any human driver. Unless the vehicle is accurately steered, its structurally unstable joint-angle kinematics during reverse maneuvers can cause the…
The variational problem of the least uncomfortable journey between two locations on a straight line is simplified by a choice of the dependent variable. It is shown that taking the position, instead of the velocity, as the optimal function…
Robotic pick and place tasks are symmetric under translations and rotations of both the object to be picked and the desired place pose. For example, if the pick object is rotated or translated, then the optimal pick action should also…
A new closed-form solver is proposed minimizing the algebraic error optimally, in the least-squares sense, to estimate the relative planar motion of two calibrated cameras. The main objective is to solve the over-determined case, i.e., when…
Our goal is to forecast the near future given a set of recent observations. We think this ability to forecast, i.e., to anticipate, is integral for the success of autonomous agents which need not only passively analyze an observation but…
There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles…
In recent years, autonomous driving algorithms using low-cost vehicle-mounted cameras have attracted increasing endeavors from both academia and industry. There are multiple fronts to these endeavors, including object detection on roads,…