Related papers: Geometric Algebra for Optimal Control with Applica…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
Robotic manipulation demands precise control over both contact forces and motion trajectories. While force control is essential for achieving compliant interaction and high-frequency adaptation, it is limited to operations in close…
We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting…
This work presents a new evolutionary optimization algorithm in theoretical mathematics with important applications in scientific computing. The use of the evolutionary algorithm is justified by the difficulty of the study of the…
This paper presents a new class of adaptive filters, namely Geometric-Algebra Adaptive Filters (GAAFs). They are generated by formulating the underlying minimization problem (a deterministic cost function) from the perspective of Geometric…
We present a diffusion-based model recipe for real-world control of a highly dexterous humanoid robotic hand, designed for sample-efficient learning and smooth fine-motor action inference. Our system features a newly designed 16-DoF…
In the limited workspace model, we consider algorithms whose input resides in read-only memory and that use only a constant or sublinear amount of writable memory to accomplish their task. We survey recent results in computational geometry…
Control systems are at the core of every real-world robot. They are deployed in an ever-increasing number of applications, ranging from autonomous racing and search-and-rescue missions to industrial inspections and space exploration. To…
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
A Geometric programming (GP) is a type of mathematical problem characterized by objective and constraint functions that have a special form. Many methods have been developed to solve large scale engineering design GP problems. In this paper…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
Soft robots can safely interact with environments because of their mechanical compliance. Self-collision is also employed in the modern design of soft robots to enhance their performance during different tasks. However, developing an…
This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each…
In this paper, we study mechanical optimal control problems on a given Riemannian manifold $(Q,g)$ in which the cost is defined by a general cometric $\tilde{g}$. This investigation is motivated by our studies in robotics, in which we…
The availability of low cost sensors has led to an unprecedented growth in the volume of spatial data. However, the time required to evaluate even simple spatial queries over large data sets greatly hampers our ability to interactively…
We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example…
We investigate systems of equations, involving parameters from the point of view of both control theory and computer algebra. The equations might involve linear operators such as partial (q-)differentiation, (q-)shift, (q-)difference as…
Geometric algebra (GA) is a mathematical tool for geometric computing, providing a framework that allows a unified and compact approach to geometric relations which in other mathematical systems are typically described using different more…
The design (shape) of a robot is usually decided before the control is implemented. This might limit how well the design is adapted to a task, as the suitability of the design is given by how well the robot performs in the task, which…