This research program aims at introducing new methodologies for the design of navigation systems for autonomous robotic vehicles to meet stringent stability and performance requirements.

1) Using simple kinematics relationships, the problem of estimating the velocity and position of an autonomous vehicle can be solved by resorting to special bilinear time-varying filters. These are the natural generalization of linear time-invariant complementary filters that are commonly used to properly merge sensor information available at low frequency with that available in the complementary region. Complementary filters lend themselves to frequency domain interpretations that provide valuable insight into the filter design process. The main purpose of the research program initiated is to extend those properties to the time-varying setting by resorting to the theory of linear differential inclusions and by converting the problem of weighted filter performance analysis into that of determining the feasibility of a related set of linear matrix inequalities. Using this set-up, the stability of the resulting filters as well as their “frequency-like” performance characteristics may be assessed using efficient numerical tools that borrow from convex optimization theory. Applications are being made to the design of navigation systems for air and underwater vehicles.

2) The problem of estimating the position and velocity of an autonomous vehicle by relying on inertial and vision sensors has received considerable attention over the past few years. Classical solutions rely on the use of Extended Kalman Filters. However, the resulting filters lack performance and stability guarantees. The main objective of the research effort undertaken in the course of this project is the extension of complementary filtering to a full non-linear setting by resorting to the theory of linear parametrically varying systems. The resulting filters are stable and exhibit a structure that exploits the complementarity of vision and inertial sensor data at low and high frequencies, respectively. Applications are being made to the design of navigation systems for air vehicles for automatic landing on aircraft carriers.