Related papers: Motion, Unit Dual Quaternion and Motion Optimizati…
In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In Part I, we presented the mathematical…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass,…
In this note, we generalize the classical optimal partial transport (OPT) problem by modifying the mass destruction/creation term to function-based terms, introducing what we term ``generalized optimal partial transport'' problems. We then…
Mapping operator motions to a robot is a key problem in teleoperation. Due to differences between workspaces, such as object locations, it is particularly challenging to derive smooth motion mappings that fulfill different goals (e.g.…
Retargeting human kinematic reference motion onto a robot's morphology remains a formidable challenge. Existing methods often produce physical inconsistencies, such as foot sliding, self-collisions, or dynamically infeasible motions, which…
The paper surveys topological problems relevant to the motion planning problem of robotics and includes some new results and constructions. First we analyse the notion of topological complexity of configuration spaces which is responsible…
Simultaneous Localization And Mapping (SLAM) is a fundamental problem in mobile robotics. While point-based SLAM methods provide accurate camera localization, the generated maps lack semantic information. On the other hand, state of the art…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
The quantum rotor represents, after the harmonic oscillator, the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum. Proper quantification of…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…
We consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
Precise collaboration in vision-based dual-arm robot systems requires accurate system calibration. Recent dual-robot calibration methods have achieved strong performance by simultaneously solving multiple coordinate transformations.…
We introduce a total order and the absolute value function for dual numbers. The absolute value function of dual numbers are with dual number values, and have properties similar to the properties of the absolute value function of real…
Expressions for variables of the center of mass and relative motions for two-body system with different and equal masses in three-dimensional spaces of constant curvature are introduced in the terms of biquaternions. The problem of the…
MAVs have great potential to assist humans in complex tasks, with applications ranging from logistics to emergency response. Their agility makes them ideal for operations in complex and dynamic environments. However, achieving precise…