Geometric reduction in optimal control theory with symmetries

A Discrete Geometric Optimal Control Framework for Systemts with Symmetries

This paper studies the optimal motion control of mechanical systems through a discrete geometric approach. At the core of our formulation is a discrete Lagrange-d’AlembertPontryagin variational principle, from which are derived discrete equations of motion that serve as constraints in our optimization framework. We apply this discrete mechanical approach to holonomic systems with symmetries and...

A Discrete Geometric Optimal Control Framework for Systems with Symmetries

This paper studies the optimal motion control of mechanical systems through a discrete geometric approach. At the core of our formulation is a discrete Lagrange-d’AlembertPontryagin variational principle, from which are derived discrete equations of motion that serve as constraints in our optimization framework. We apply this discrete mechanical approach to holonomic systems with symmetries and...

Geometric Optimal Control with Applications

Symmetries in Motion: Geometric Foundations of Motion Control

Some interesting aspects of motion and control for systems such as those found in biological and robotic locomotion, attitude control of spacecraft and underwater vehicles, and steering of cars and trailers, involve geometric concepts. When an animal or a robot moves its joints in a periodic fashion, it can move forward or rotate in place. When the amplitude of the motion increases, the resulti...

On Quantization and Optimal Control of Dynamical Systems with Symmetries

This paper outlines some progress in the study of quantized control systems. We consider the dynamical systems arising from robotics and autonomous vehicles applications and describe a procedure to transcribe their dynamics into finite-state automata. The transcription procedure extends known previous results. We consider optimal control problems and present conditions under which linear progra...