In this talk I will consider the questions of observability and design of observers for position estimates of an object moving in 3D space.
The scenario considered assumes a possibly biased measurement of velocity along with bearing or direction measurements to one or multiple fixed points in the environment. The motivating example is a robot moving in either two- or three-dimensional space with a sensor, such as a camera, capable of providing bearing but not distance to observed fixed points in the environment. I provide a comprehensive observability analysis, and discuss stability and convergence of the observer design and observer error dynamics, under persistence of excitation conditions on the vehicle motion. Interestingly, I can show uniform observability even for a single direction measure and with unknown velocity bias as long as the vehicle trajectory is persistently exciting. Some extensions to the case of multiple directions with known or unknown observed point location or to the case of pose estimation are addressed and observers endowed with exponential stability of error dynamics are derived.
Biography: Tarek Hamel is Professor at the University of Nice Sophia Antipolis since 2003. He received his Ph.D. degree in Robotics from the University of Technology of Compiègne (UTC), France, in 1996. After two years as a research assistant at the UTC, he joined the Centre d'Etudes de Mécanique d'Ile de France in 1997 as an associate professor. His research interests include nonlinear control theory, estimation and vision-based control with applications to Unmanned Aerial Vehicles. Prof. T. Hamel is senior member of the Institut Universitaire de France. He served as Associate Editor for IEEE Transactions on Robotics and for Control Engineering Practice.
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