Applied Control Theory Research

Caltech has an outstanding program in control and dynamical systems . However, several problems in robotics (in particular, locomotion) involve significant problems in control theory. Hence, even non-specialists in control must occasionally get involved in control theory research. Currently, our efforts are focused in the following areas:

Control on Stratified Sets.

We are working on the extension of standard notions of nonlinear controllability, trajectory generation, and feedback to stratified systems. Systems, such as legged robots, have a configuration space that has a naturally stratified structure. Unfortunately, nonlinear control theory results do not hold for the systems because of the discontinuous nature of their dynamics. We term this work "applied" because the basic notions of nonlinear controllability have already been established. However, this work is categorized as control "theory" because the convential notions need a new theoretical framework in order for them to be successfully extended to these new domains.

People working in this area:


Motion Planning on Principal Bundles.

Many interesting mechanical systems, such as most locomotion systems, have governing equations that evolve on a principle fiber bundle. We are using tools from differential geometry and nonlinear control theory to develop local motion planning techniques for this class of systems. The key idea is to exploit the geometric structure inherent in this problem.

People working in this area:


Hybrid Control Theory.

Broadly speaking, hybrid systems have properties that can be characterized by both continuous (o.d.e. and p.d.e) and discrete (finite state machine, finite automata) dynamical systems. For example, the stratified systems described above are one example of a hybrid system. Due to the widespread use of computers to control physical devices, hybrid systems abound. The analysis of such systems lies at the boundary of computer science and control theory. Successful hybrid system must robustly combine high-level planning (planning of the finite automaton transitions) with feedback control (evolution of the dynamic equations). While the planning and control problems have been addressed separately by computer scientists and control theorists, the interaction of the discrete and continuous worlds is largely left to the ingenuity of engineers. As the complexity of the computer controlled physical systems grows, such methods break down and there is a need for rigorous theory to design, build, and evaluate hybrid systems. With the support of a National Science Foundation post-doctoral fellowship and a MURI grant, we hope to contribute to the emerging hybrid control literature in the area of control design for systems whose physical dynamics are hybrid and whose desired behavior can be defined by a hybrid system. For more on hybrid systems, see this page .

People working in this area:

Selected Papers in applied nonlinear control


Switched Systems.

Switched systems are a special class of hybrid systems. Switching in a control system can occur in the physics of the problem (i.e., a system changes contact state), or in the design of the controller. We focus on problems where the switching occurs in the basic physical system that is being modelled and controlled. For example, one can show that overconstrained wheeled vehicles (such as the Sojourner vehicle of the Mars Pathfinder mission) and distributed manipulation systems inherently have switching mechanics. Our goal

People working in this area:

Selected Papers in applied nonlinear control