Stability and Optimality Properties of Sequential Action Control for Nonlinear and Hybrid Systems

非线性和混合系统顺序动作控制的稳定性和最优性

基本信息

批准号：
1662233
负责人：
Todd Murphey
金额：
$ 37.5万
依托单位：
Northwestern University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1662233&HistoricalAwards=false
关键词：
Stability Optimality Properties Sequential Action

项目摘要

This project will greatly extend a powerful new method for control of robots and vehicles, called sequential action control (SAC). One widely used approach to controlling complicated systems is to solve a real-time numerical optimization problem for the magnitude of the next few control pulses, where the all the pulses have a constant width. However even with powerful processors it can be difficult to compute these values fast enough. SAC addresses this challenge by instead computing the optimal width and relative start time of the next control pulse. For many problems of interest, this change in control strategy greatly simplifies computation, to the point that infeasible control problems become tractable. SAC allows analytical solutions to some problems, and speeds computations by up to eight orders of magnitude for others. SAC is naturally compatible with common features of modern control design, including hybrid systems that switch discretely between a collection of continuous dynamic behaviors; quantized systems where inputs, states, and outputs may take only a finite set of constant values; and systems with nonlinear dynamics. SAC can be shown to recover the globally optimal control signal in a number of analytically solvable cases. In other representative test cases, the computed SAC input provides performance that is numerically indistinguishable from the optimum. Optimal or near-optimal input signals are of no value if small disturbances cause the system to rapidly diverge from the desired behavior. Therefore practical controllers must also ensure that small disturbances to the controlled system cause only small deviations in the system response -- a property known as stability. This project seeks to rigorously derive SAC performance guarantees for a broad class of systems, as well as to show conditions under which SAC ensures stability. The Darwin humanoid robot will be used as a high-dimensional, nonlinear, hybrid testbed for this research. Control of the Darwin robot may be implemented in the open-source Robot Operating System (ROS), allowing a robust and verifiable SAC distribution for dissemination. The results of this project will enable greatly improved and verifiable control over systems such as rehabilitation robots, assistive devices, rotor vehicles, and driverless cars, using widely available and low-cost computing platforms such as mobile phones. Benefits to society from this project include enhanced safety and performance of these automated infrastructure systems. The project also includes classroom innovation, international collaboration, outreach activities through the Museum of Science and Industry in Chicago, and dissemination of open-source software.The twofold purpose of this project is to develop sequential action control (SAC) into an actionable, near-universal method for synthesizing embedded real-time control as well as to provide foundational results on optimality, stability, and geometry. The method is computationally efficient and scales to high dimensional problems. Moreover, SAC extends naturally to Lie groups, common in applications such as robotics and automation. The project will address three fundamental questions. First, it will identify conditions under which SAC can be applied directly or iteratively to achieve optimal control. Second, it will derive conditions for stability. Third, it will adapt SAC to systems evolving on Lie groups, to achieve global performance for multibody mechanical systems. The broader impacts for this work include outreach, technology transfer to rehabilitation, the development of online courses in dynamics and analysis, and international collaboration. The PI is currently working with the Museum of Science and Industry, and as part of the project the PI, and graduate and undergraduates involved in the PI's laboratory, will participate in a National Robotics Week exhibit in the main rotunda of the museum with an estimated viewership of over ten thousand on-site visitors.

该项目将极大地扩展一种强大的机器人和车辆控制新方法，称为顺序动作控制（SAC）。控制复杂系统的一种广泛使用的方法是解决接下来几个控制脉冲幅度的实时数值优化问题，其中所有脉冲都具有恒定的宽度。然而，即使使用强大的处理器，也很难足够快地计算这些值。 SAC 通过计算下一个控制脉冲的最佳宽度和相对开始时间来解决这一挑战。对于许多感兴趣的问题，控制策略的这种变化极大地简化了计算，使得不可行的控制问题变得易于处理。 SAC 允许对某些问题进行分析解决，并将其他问题的计算速度提高多达八个数量级。 SAC 自然地兼容现代控制设计的常见特征，包括在一系列连续动态行为之间离散切换的混合系统；量化系统，其中输入、状态和输出只能采用一组有限的常量值；以及具有非线性动力学的系统。 SAC 可以在许多分析可解的情况下恢复全局最优控制信号。在其他代表性测试案例中，计算出的 SAC 输入提供的性能在数值上与最佳性能没有区别。如果小的干扰导致系统迅速偏离所需的行为，那么最佳或接近最佳的输入信号就没有任何价值。因此，实际控制器还必须确保对受控系统的小干扰仅导致系统响应出现小偏差，这种特性称为稳定性。该项目旨在严格推导 SAC 对各种系统的性能保证，并展示 SAC 确保稳定性的条件。达尔文人形机器人将用作这项研究的高维、非线性、混合测试平台。达尔文机器人的控制可以在开源机器人操作系统（ROS）中实现，从而允许强大且可验证的 SAC 分发进行传播。该项目的成果将利用移动电话等广泛使用的低成本计算平台，极大地改进和验证对康复机器人、辅助设备、转子车辆和无人驾驶汽车等系统的控制。该项目给社会带来的好处包括增强这些自动化基础设施系统的安全性和性能。该项目还包括课堂创新、国际合作、通过芝加哥科学与工业博物馆的外展活动以及开源软件的传播。该项目的双重目的是将顺序动作控制 (SAC) 开发成一种可操作的、近乎可操作的方法。 -用于综合嵌入式实时控制以及提供优化性、稳定性和几何形状的基础结果的通用方法。该方法计算效率高，并且可以扩展到高维问题。此外，SAC 自然地扩展到李群，这在机器人和自动化等应用中很常见。该项目将解决三个基本问题。首先，它将确定可以直接或迭代应用 SAC 以实现最优控制的条件。二是为稳定创造条件。第三，它将使 SAC 适应在李群上演化的系统，以实现多体机械系统的全局性能。这项工作的更广泛影响包括外展、康复技术转让、动力学和分析在线课程的开发以及国际合作。 PI 目前正在与科学与工业博物馆合作，作为该项目的一部分，PI 以及参与 PI 实验室的研究生和本科生将参加在博物馆主圆形大厅举行的国家机器人周展览，预计现场观众人数超万人次。

项目成果

期刊论文数量（8）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Feedback synthesis for underactuated systems using sequential second-order needle variations

使用顺序二阶针变化的欠驱动系统的反馈合成

DOI：
10.1177/0278364918776083
发表时间：
2018-04-24
期刊：
The International Journal of Robotics Research
影响因子：
0
作者：
Giorgos Mamakoukas;M. A. MacIver;T. Murphey
通讯作者：
T. Murphey

Efficient Computation of Higher-Order Variational Integrators in Robotic Simulation and Trajectory Optimization

机器人仿真和轨迹优化中高阶变分积分器的高效计算

DOI：
10.1007/978-3-030-44051-0_40
发表时间：
2020-05
期刊：
Workshop on the Algorithmic Foundations of Robotics
影响因子：
0
作者：
Fan, T.;Schultz, J.;Murphey, T.
通讯作者：
Murphey, T.

Efficient and Guaranteed Planar Pose Graph optimization Using the Complex Number Representation

使用复数表示进行高效且有保证的平面位姿图优化

DOI：
10.1109/iros40897.2019.8968044
发表时间：
2019-11
期刊：
2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS
影响因子：
0
作者：
Fan, Taosha;Wang, Hanlin;Rubenstein, Michael;Murphey, Todd
通讯作者：
Murphey, Todd

Superlinear Convergence Using Controls Based on Second-Order Needle Variations

使用基于二阶针变体的控制的超线性收敛