The Compass That Steered Robotics
The Compass That Steered Robotics
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引导机器人的指南针
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发表时间：
2012
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通讯作者：
B. Donald
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作者：
B. Donald
机器人研究人员将会意识到德克斯特·科岑对代数算法的贡献，这些算法使实闭域理论和多项式运算在运动规划中得到了广泛应用。然而，Dexter也对信息不变量理论做出了几项重要贡献，并在这一领域产生了一些最深刻的结果。这些第一次体现在他1978年与曼努埃尔·布鲁姆合著的论文《指南针的力量》中。这项工作对机器人学和纳米科学产生了广泛的影响。
从德克斯特的见解开始，机器人学研究人员利用信息不变量的概念，探索了确定执行机器人任务的信息需求的问题。这代表了一种尝试，即描述与测量机器人任务复杂性有关的一系列复杂和微妙的问题。
在这方面，已经提出了几种措施来衡量任务的信息复杂性：(A)机器人应该保留多少内部状态？(B)需要多少个协作机器人，它们之间需要多少通信？(C)机器人如何改变(副作用)环境以记录执行任务所需的状态或感觉信息？(D)传感器提供了多少信息？以及(E)机器人需要多少计算量？我们已经考虑了如何在(A)-(E)上开发一种“微积分”，以便从分析上比较传感器系统的能力。为此，信息不变量是一种理论，在这种理论中，通过在协作的自主机器人之间添加、删除和重新分配(A)-(E)，一个传感器可以“减少”到另一个传感器(很大程度上是在计算理论上减少的精神)。如下所示，这项工作使用的是德克斯特的指南针。
Robotics researchers will be aware of Dexter Kozen's contributions to algebraic algorithms, which have enabled the widespread use of the theory of real closed fields and polynomial arithmetic for motion planning. However, Dexter has also made several important contributions to the theory of information invariants, and produced some of the most profound results in this field. These are first embodied in his 1978 paper On the Power of the Compass , with Manuel Blum. This work has had a wide impact in robotics and nanoscience.
Starting with Dexter's insights, robotics researchers have explored the problem of determining the information requirements to perform robot tasks, using the concept of information invariants. This represents an attempt to characterize a family of complicated and subtle issues concerned with measuring robot task complexity.
In this vein, several measures have been proposed [14] to measure the information complexity of a task: (a) How much internal state should the robot retain? (b) How many cooperating robots are required, and how much communication between them is necessary? (c) How can the robot change (side-effect) the environment in order to record state or sensory information to perform a task? (d) How much information is provided by sensors? and (e) How much computation is required by the robot? We have considered how one might develop a kind of "calculus" on (a) --- (e) in order to compare the power of sensor systems analytically. To this end, information invariants is a theory whereby one sensor can be "reduced" to another (much in the spirit of computation-theoretic reductions), by adding, deleting, and reallocating (a) --- (e) among collaborating autonomous robots. As we show below, this work steers using Dexter's compass.