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

Project: Research project

Project Details

Description

Efficient computation of optimal controllers for general systems is still largely an unrealized objective. The proposed work focuses on developing sequential action control (SAC), a new model-based form of control applicable to nonlinear and hybrid/impulsive systems. The method is computationally efficient and scales to high dimensional problems. Most importantly, SAC computationally coincides with global optimizers for a variety of well-known benchmarks with nonlinearities, hybrid mechanics, and control saturation. The twofold purpose of the proposed work is to develop SAC into an actionable, near-universal method for synthesizing embedded real-time control as well as provide foundational results about optimality, stability, and geometry.

SAC is very general and is applicable to a large range of applications, often coincides with optimizers obtained by other (more computationally intensive) means, and enables policy-based synthesis of feedback laws in high dimensional, nonlinear/nonsmooth systems with input saturation. More importantly, SAC is well-posed as a closed form feedback law for these systems without modification, so it can be automated in software. Moreover, SAC extends naturally to Lie groups, common in applications such as robotics and automation. SAC is based on optimizing a finite number of infinitesimal control actions over a continuum of potential application times rather than optimizing a continuum of control actions. As a result, SAC is likely not as general as the classical theory of optimal control, but rather creates a new class of easily addressable control problems (like linear systems or differentially flat systems). What is not known is when SAC can be expected to apply to a system or perform well. The proposed work will address three fundamental questions. First, under what conditions is SAC optimal, or under what situations will it be optimal after iteration? Second, when is SAC stable? Third, how can SAC be applied to Lie groups to achieve global performance for multibody mechanical systems?

An experimental testbed, the Darwin humanoid robot, will support this research. The Darwin is a high dimensional, nonlinear, nonsmooth dynamical system. Moreover, it can be controlled in the Robot Operating System (ROS), and will provide a range of dynamic tasks appropriate for developing, verifying, and stressing SAC as a controller.

The broader impacts for this work will 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 proposed work the PI and supported students 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. Graduate students, undergraduates, and high school students involved in the PI's laboratory will all be involved in the exhibit. The algorithms and software that are part of the proposed work are also in use at the Rehabilitation Institute of Chicago in ongoing research. Outcomes of this work will have immediate impact on those projects. The PI is involved in significant classroom innovations, and the proposed work will include complementary online courses in analysis and dynamics in the form of a massive open online course. Lastly, the project will include a collaboration with Prof. Sina Ober-Bloebaum of Oxford University. Her expertise in optimal control and mechanics will be a key element
StatusActive
Effective start/end date8/1/177/31/21

Funding

  • National Science Foundation (CMMI-1662233)

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