### Robot Sensing and Planning

We pursue research on sensing of, and planning in large, spatially distributed uncertain environments, using distributed mobile sensor platforms. This research is at the confluence of control theory, robotics, AI and information theory. Imagine a mobile robot that has to build a map of an unknown area without the help of GPS, and it has to accomplish this in an optimal fashion, and in real time: this is the problem of Simultaneous Planning, Localization and Mapping (SPLAM). Solving the SPLAM problem might one day enable the autonomous operation of systems in disaster affected areas, planetary exploration, submarine exploration and homeland security among myriad other applications of great practical interest. As with any practical real-world Control problem, it involves an estimation-theoretic and a control theoretic problem. The estimation theoretic problem being one of estimating a model of the environment using only relative measurements while the planning problem is that of adaptively controling the robotic platform based on the current model of the environment so as to accomplish some objective. The problem is made very hard because of the extreme high dimensionality of the environment and hence, the estimation and control methods have to be both robust to uncertainties as well as computationally, i.e., the methods need to be implementable in real-time. We are developing robust and computationally efficient hybrid Bayesian Frequentist methods for solving the SLAM problem with guaranteed performance. We are also developing generalized sampling based feedback planners for the planning of high DOF robotic systems under process and sensing uncertainty, these methods being termed the Generalized Probabilistic Roadmap (GPRM) and the Feedback Aware Information Roadmap (FIRM) respectively.

### Stochastic Dynamical Systems and Nonlinear Filtering

In this work , we pursue the problem of uncertainty propagation in complex nonlinear dynamical systems, specifically through the design of robust computational methods for the solution of the Fokker-Planck-Kolmogorov Equation. The Fokker-Planck-Kolmogorov equation is at the core of any stochastic analysis and design problem. Specific applications of these methods are to the control of morphing wing aircraft and to the Air Traffic Control problem. We also pursue research on nonlinear filtering, in particular, we are very interested in the problem of space situational awareness and how advanced nonlinear filtering techniques based on the FPK equation can be applied to this problem. We are also very interested in the nonlinear filtering of very high dimensional systems, for instance, systems governed by PDEs as opposed to ODEs, that routinely have states in the order of millions. Such problems pose very unique and difficult challenges to conventional nonlinear filtering techniques such as the Kalman Filter. This work is at the intersection of this broad research thrust and that of robotic mapping and planning above.

### Space Based High Resolution Imaging Systems

In this field, we have researched the design of space based imaging systems that are capable of imaging earth and space-based objects at heretofore unheard of resolutions. Such systems combine the light from smaller telescopes that are space apart to form a synthetic aperture that is euivalent to a much larger monolithic aperture. Such systems have application in the field of space situational awareness, for the protection of space-based assets and in Science missions such as the detection and imaging of distant exo-solar planets and other such interesting distant astronomical phenomenon.