Geometric Approaches to Control in the Presence of Magnitude and Rate Saturations

This paper gives a survey of some recent results on control of systems with magnitude and rate limits, motivated by problems in real-time trajectory generation and tracking for unmanned aerial vehicles. Two problems are considered: stabilization using “nonlinear wrappers” to rescale a given control law and real-time trajectory generation using differential flatness. For both problems, simplified versions of the general problem are studied using tools from differential geometry and nonlinear control to give insights into the limitations imposed by magnitude and rate limits and provide insights into constructive solutions to the trajectory generation and tracking problems.