论文标题
用于最佳控制的几何代数，并在操纵任务中应用
Geometric Algebra for Optimal Control with Applications in Manipulation Tasks
论文作者
论文摘要
机器人技术中的许多问题从根本上是几何问题，这导致近年来机器人技术的研究工作增加。结果是使用螺丝理论，谎言代数和双重四元素的各种框架的算法。这些流行形式主义的统一和概括可以在几何代数中找到。本文的目的是展示当应用于机器人操纵任务时几何代数的功能。特别是，可以在不同的几何原语上统一地进行最佳控制成本函数的建模，从而导致所得表达式的符号复杂性低和几何直觉。我们证明了使用Franka Emika机器人的几种实验中几何代数的有用性，简单性和计算效率。提出的算法在C ++ 20中实现，并导致公开可用的库\ textit {gafro}。基准比最先进的机器人库显示了运动学的计算速度。
Many problems in robotics are fundamentally problems of geometry, which lead to an increased research effort in geometric methods for robotics in recent years. The results were algorithms using the various frameworks of screw theory, Lie algebra and dual quaternions. A unification and generalization of these popular formalisms can be found in geometric algebra. The aim of this paper is to showcase the capabilities of geometric algebra when applied to robot manipulation tasks. In particular the modelling of cost functions for optimal control can be done uniformly across different geometric primitives leading to a low symbolic complexity of the resulting expressions and a geometric intuitiveness. We demonstrate the usefulness, simplicity and computational efficiency of geometric algebra in several experiments using a Franka Emika robot. The presented algorithms were implemented in c++20 and resulted in the publicly available library \textit{gafro}. The benchmark shows faster computation of the kinematics than state-of-the-art robotics libraries.
