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

• 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

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新方法来控制机器人和车辆，称为顺序动作控制（SAC）。一种广泛使用的控制复杂系统的方法是解决接下来几个对照脉冲的大小的实时数值优化问题，其中所有脉冲都具有恒定的宽度。但是，即使使用功能强大的处理器，也可能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启动时间来应对这一挑战。对于许多感兴趣的问题，控制策略的这种变化大大简化了计算，以至于无法可行的控制问题变得可行。 SAC允许解决某些问题的分析解决方案，并且对其他问题的计算速度最多八个数量级。 SAC自然与现代控制设计的共同特征兼容，包括混合系统在连续的动态行为集合之间离散地切换；量化输入，状态和输出的系统可能只有一组有限的恒定值集；和具有非线性动力学的系统。可以证明SAC可以在许多可分析解决的情况下恢复全球最佳控制信号。在其他代表性的测试用例中，计算出的SAC输入提供了与最佳最佳不同区分的性能。如果微小的干扰导致系统与所需的行为迅速差异，则最佳或近乎最佳的输入信号是无价值的。因此，实用控制器还必须确保对受控系统的小干扰仅导致系统响应中的小偏差 - 一种称为稳定性的属性。该项目试图严格地为广泛的系统提供SAC性能保证，并显示SAC确保稳定性的条件。 Darwin类人生物机器人将用作这项研究的高维，非线性，混合测试床。对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，从而允许进行稳健且可验证的SAC分布以进行传播。该项目的结果将对诸如康复机器人，辅助设备，转子车和无人驾驶汽车等系统进行大大改进和可验证的控制，并使用广泛可用的和低成本的计算平台，例如移动电话。该项目对社会的好处包括增强的安全性和这些自动化基础设施系统的性能。该项目还包括课堂创新，国际合作，通过芝加哥的科学和工业博物馆进行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的行动控制（SAC）开发为可行的，近乎婚姻的方法，用于合成嵌入实时控制以及嵌入了最佳成果以及对最佳性能的基础性结果，并稳定性，稳定性。该方法在计算上是有效的，并扩展到高维问题。此外，SAC自然而然地扩展到谎言组，在机器人技术和自动化等应用中常见。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以实现最佳控制的条件。其次，它将得出稳定性的条件。第三，它将适应SAC在谎言组上发展的系统，以实现多体机械系统的全球性能。这项工作的更广泛影响包括外展，康复技术转移，动态和分析中的在线课程的发展以及国际合作。 PI目前正在与科学和工业博物馆合作，作为PI项目的一部分，涉及PI实验室的研究生和本科生将参加博物馆主要圆形大厅的全国机器人周展览，估计有超过一万个现场访问者的观看率。

项目成果

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

• DOI: 10.1177/0278364918776083
• 发表时间: 2018-04
• 期刊: The International Journal of Robotics Research
• 作者: Giorgos Mamakoukas;M. A. MacIver;T. Murphey

CPL-SLAM: Efficient and Certifiably Correct Planar Graph-Based SLAM Using the Complex Number Representation

• DOI: 10.1109/tro.2020.3006717
• 发表时间: 2020-12-01
• 期刊: IEEE TRANSACTIONS ON ROBOTICS
• 影响因子: 7.8
• 作者: Fan, Taosha;Wang, Hanlin;Murphey, Todd
• 通讯作者: Murphey, Todd

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
• 期刊: Workshop on the Algorithmic Foundations of Robotics
• 作者: Fan, T.;Schultz, J.;Murphey, T.
• 通讯作者: Murphey, T.

Superlinear Convergence Using Controls Based on Second-Order Needle Variations

• DOI: 10.1109/cdc.2018.8619405
• 发表时间: 2018-12
• 期刊: 2018 IEEE Conference on Decision and Control (CDC)
• 作者: Giorgos Mamakoukas;M. A. MacIver;T. Murphey

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
• 期刊: 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS
• 作者: Fan, Taosha;Wang, Hanlin;Rubenstein, Michael;Murphey, Todd
• 通讯作者: Murphey, Todd