Workshop on 21st Century Kinematics; Washington, DC; 27-28 August 2011

该奖项的目的是支持21世纪运动学研讨会，该研讨会将专家和新手聚集在一起，展示使用数值代数几何来解决当前对推进运动学至关重要的领域的研究问题。这些领域是由解决更大的多项式系统的挑战联合起来的，特别是机构和机器人的分析和综合，柔性机构，张拉整体和电缆驱动系统。在每种情况下，表述和求解这些多项式系统的挑战都是一个重大障碍。研讨会将探索数值代数几何和改进计算的新结果，这些结果有可能为复杂多项式系统的快速推导、分析和解决提供工具。这对21世纪机械和机器人研究的进步至关重要。本次研讨会的智力价值集中在通过向机构和机器人研究界引入先进的数值代数几何技术来推进复杂和创新机械系统设计的研究能力。如果成功，这次研讨会将提供一个机会，利用新的数学公式，在机器人系统、兼容和微机电系统发展方面取得过去的成功。在21世纪，信息驱动系统和机电一体化的进步要求在机械和机器人方面进行更多的创新，以便将“信息比特”转化为操作、运输和交付货物和服务所需的“身体活动比特”。这些报告将被整合到课程笔记中，形成全国大学研究生课程的基础，以平衡理论与实践，基础科学与设计创新。这次研讨会有可能迅速将数值代数几何的计算工具传播给大量的研究人员，并重新设定对日益复杂的机械系统设计的可能性的期望。

The purpose of this award is to support a workshop on 21st Century Kinematics, which will bring together experts and novices together to demonstrate the use of numerical algebraic geometry to solve current research problems in areas that are fundamental to advancing Kinematics. These areas are united by the challenge of solving even larger systems of polynomials, specifically the analysis and synthesis of mechanisms and robots, compliant mechanisms, and tensegrity and cable-driven systems. In each case, the challenge of formulating and solving these polynomial systems is a significant obstacle. The workshop will explore new results in numerical algebraic geometry and improved computation that have the potential to provide tools for rapid derivation, analysis and solution of complex polynomial systems. This is critical to the advancement of mechanisms and robotics research into the 21st century. The intellectual merit of this workshop award centers on advancing the capabilities for research into the design of complex and innovative mechanical systems by introducing advanced techniques of numerical algebraic geometry to the mechanisms and robotics research community.If successful, this workshop will provide an opportunity to build on past successes in the development of robotic systems, compliant and micro-electromechanical systems by using new mathematical formulations. In the 21st century, advances in information-driven systems and mechatronics demand even more innovation in mechanisms and robotics, in order to transform 'bits of information' into the 'bits of physical activity' needed to manipulate, transport and deliver goods and services. The presentations will be assembled into course notes to form the foundation of graduate courses in universities around the country that will balance theory with practice, and fundamental science with design innovation. This workshop has the potential to rapidly disseminate the computational tools of numerical algebraic geometry to a large number of researchers, and reset the expectations of what is possible in the design of increasingly complex mechanical systems.