Date of Award


Document Type


Degree Name

Master of Science in Engineering (MSE)


Mechanical Engineering

Committee Chair/Advisor

Umesh Vaidya

Committee Member

Ardalan Vahidi

Committee Member

Ian Walker


Safe navigation of mission-critical systems is of utmost importance in many modern autonomous applications. Over the past decades, the approach to the problem has consisted of using probabilistic methods, such as sample-based planners, to generate feasible, safe solutions to the navigation problem. However, these methods use iterative safety checks to guarantee the safety of the system, which can become quite complex. The navigation problem can also be solved in feedback form using potential field methods. Navigation function, a class of potential field methods, is an analytical control design to give almost everywhere convergence properties, but under certain topological constraints and mapping onto a sphere world.

Alternatively, the navigation problem can be formulated in the dual space of density. Recent works have shown the use of linear operator theory on density to convexly approach the navigation problem. Inspired by those works, this work uses the physical-based interpretation of occupation through density to synthesize a safe controller for the navigation problem. Moreso, by using this occupation-based interpretation of density, we design a feedback density-based controller to solve the almost everywhere navigation problem.

Furthermore, due to the recent popularity of legged locomotion for the navigation problem, we integrate this analytical feedback density-based controller into the quadruped navigation problem. By devising a density-based navigation architecture, we show in simulation and hardware the results of the density-based navigation.

Author ORCID Identifier




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