Control and Stabilization of Mechanical Systems with Broken Symmetry via Symmetry Recovery

University Of Texas At Dallas, Richardson TX

Investigators

Abstract

Many mechanical or robotic systems are designed to operate in a specific configuration or position. For example, an underwater vehicle must maintain a certain attitude to carry out its missions such as underwater surveillance or an offshore wind turbine must maintain its upright position under various disturbances created by waves and gusts in the ocean. However, such a configuration tends to be naturally unstable under external disturbances, and hence must be controlled properly to stay in a desired configuration. The main objective of this project is to innovate new control strategies to stabilize and control such difficult-to-control systems, exploiting some inherent dynamic characteristics of these systems. The new control strategies will be applicable to a wide class of mechanical and robotic systems as opposed to ad-hoc techniques that are currently used which are designed for a specific system. The project involves a group of students from diverse backgrounds and academic levels, and integrates research with outreach activities using a simple and easy to understand robotic system. Mechanical and robotic systems under the influence of gravity or buoyancy can be seen as systems with broken symmetry: The presence of the external forces introduces a particular direction along which the force applies to the system, thereby breaking the symmetry that the system would otherwise possess. Balancing or stabilizing such systems by applying controls to them has been one of the main challenges in control theory. The project develops a new paradigm of control and stabilization of mechanical systems with broken symmetry. Building on the differential-geometric formulation of Lagrangian/Hamiltonian systems with broken symmetry, the project aims to develop a general theory of stabilization that applies to mechanical and robotic systems under the influence of gravity/buoyancy. The project broadens the scope of applications of stabilization techniques developed for mechanical systems by systematically extending the method of controlled Lagrangians/Hamiltonians to systems with broken symmetry. The methods will also be generalized to those mechanical systems under nonholonomic constraints as well, further extending the scope of applications to those robotic systems with rolling and sliding constraints as well as underwater vehicles with velocity constraints. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.