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Bill Goodwine |
Research
Cyber Physical Systems
My research focuses primarily on theoretical nonlinear control with recent emphasis on Cyber Physical Systems. Cyber physical systems are systems with highly integrated physical and computational components (often involving the complication of networked communication). They tend to be very large and complex in scale. While many CPS systems exist in the real world, to date there are few general theoretical results available to guide both the design of such systems and the control of such systems. Most existing CPS systems are designed and controlled based upon accumulated real-world industrial knowledge that tends to be industry- or application-specific. My recent work has focused particularly on so-called symmetric systems. A symmetric system is comprised of many components with the restriction that the components be very closely related and connected together in a "regular" manner. With such restrictions, it is possible to formulate general models and then consider what types of properties remain invariant as components are added to or removed from the system. A related question is how the system behaves as components fail, which is a question of robustness.
Stratified Systems
Many interesting and important control systems evolve on stratified configuration spaces. Roughly speaking, we will call a configuration manifold stratified if it contains submanifolds upon which the system is subjected to additional constraints or has different equations of state. For such systems, the equations of motion on each submanifold may change in a non-smooth, or even discontinuous manner, when the system moves from one submanifold to another. In such cases, traditional nonlinear control methodologies are inapplicable because they generally rely upon differentiation in one form or another. Yet it is the discontinuous nature of such systems that is often their most important characteristic because the system must cycle through different submanifolds to effectively be controlled. Therefore, it is necessary to incorporate explicitly into control methodologies the non-smooth or discontinuous nature of these systems.
Robotic systems, in particular, are of this nature. A legged robot has discontinuous equations of motion near points in the configuration space where each of its ``feet come into contact with the ground, and it is precisely the ability of the robot to lift its feet off of the ground that enables it to move about. Similarly, a robotic hand grasping an object often cannot reorient the object without lifting its fingers off of the object. Despite the obvious utility of such systems, however, a comprehensive framework in which to consider control issues for such systems does not exist.
The fundamental approach of this work has been to exploit the physical geometric structure present in such problems to address control issues such as nonlinear controllability, trajectory generation and stabilization. The fundamental philosophy is to generate general results, i.e., results independent of a particular robot's number of legs, fingers or morphology.
Courses
Course Blog
In order to be able to interactively answer questions online, I've maintained a course blog for all courses since 2002.
AME 30315, Differential Equations, Vibrations and Control II
AME 40590, Intellectual Property for Engineers
- AME 44590 Course Syllabus, Summer 2011
- AME 44590 Homework, Summer 2011
- AME 40590 Course Content
- AME 40590 Homeworks, Spring 2011
Book
Engineering Differential Equations: Theory and Applications, Springer 2010
