Games, control and optimization with coupled constriants
Source Department of Science and Technology, Government of India
Project duration 2013 - 2018
Principal Investigator Ankur Kulkarni
Amount 35 lakhs
Objective This proposal envisions research from a system theoretic viewpoint with a focus on decision problems that involve multiple decision makers. Each decision maker (or player) has his objective, the decision makers are faced with a dynamic and uncertain environment, they exchange information in complex ways and their decisions are coupled in a nontrivial manner. The research explores questions such as, how does one obtain clarity on emergent behaviour in such settings? How does one design conditions so that a desireable behaviour emerges? And, how does one efficiently compute the emergent behaviour offline and ex ante? The resulting contributions will advance the theory of games and the theory of control and optimization. They have relevance and application to fields such as economics, engineering and biology.

Approximation of High Dimensional Optimization and Control Problems
Source Science and Engineering Research Board, Department of Science and Technology, Government of India
Project duration 2015 - 2018
Principal Investigator Ankur Kulkarni
Co-Principal Investigator Vivek Borkar (Electrical Engg)
Amount 30 lakhs
Objective The project addresses issues thrown up by high dimensionality in optimization and con- trol problems, with special focus on variational inequalities, convex optimization, particle filters and learning control. The aim will be to develop provably effective computational schemes and substantiate them through numerical experimentation. Specific directions to be pursued include: dimensionality reduction via random projections, characterizing random projection of sets such as polyhedra, function approximation, approximation to high dimensional filtering problems and applications of the above to network analytics.

Vision based motion planning for a 3D crane
Source Konecranes Pvt. Ltd.
Project duration Jan 2016 - July 2017
Principal Investigator Leena Vachhani
Co-Principal Investigator Srikant Sukumar
Abstract The problems related to the navigation of an object connected with the trolley in the presence of obstacles would be investigated. The sensor uncertainties would be estimated using the 3-D crane system and the camera arrangement. Work requires addressing the amount of uncertainty that the system would be able to tolerate. Another objective is to design a controller for precise positioning of the trolley in the presence of sensor and actuator uncertainties.

Vision based localization for autonomous and semi-autonomous navigation of a quadcopter
Project duration Jan 2016 - July 2017
Principal Investigator Leena Vachhani
Abstract Location estimation with respect to the global/local frame of reference is the foremost objective of any autonomous or semi-autonomous task. The challenge in localizing using visual data is in extracting relevant information. The proposal would aim to solve the localization problem by reaching to a nearest location from the set of known locations by efficient information extraction technique. Focus would be to establish results under erroneous measurement and inaccurate command execution.

Doppler Velocity Log (DVL) based Autonomous Underwater Vehicle (AUV) localization and navigation for detecting underwater acoustic sources
Source Naval Research Board
Project duration Nov 2014 - June 2016
Principal Investigator Leena Vachhani
Co-Principal Investigator Hemendra Arya (Aerospace) and V. Kartik (Mechanical)
Abstract This project intends to develop a localization and navigation system for an autonomous underwater vehicle (AUV) equipped with a Doppler Velocity log (DVL) and an acoustic reception module. Objective includes the location estimate of the sound-emitting object that has applications in global localization (when the global position of the sound-emitting object is known) and surveillance (when the position of the sound-emitting object is unknown).
The developed system is planned to be integrated with the Matsya AUV being developed at IIT Bombay.

Differential geometric techniques applied to problems in control
Sponsor National Board for Higher Mathematics
Project duration 2012 - 2016
Principal Investigator R. N. Banavar
Objective The objective of this project (study) is to examine certain facets of the differential geometric framework for the stabilization of engineering systems which are described by a combination of ordinary differential equations (ODEs) and partial differential equations (PDEs) (applications: chemical process control, flexible mechanical structures coupled to rigid bodies, fluid in a container - aerospace vehicles.)

Spacecraft orientation manoeuvres under control and state constraints
Sponsor Indian Space Research Organization (ISRO)
Project duration 2014 - 2016
Principal Investigator R. N. Banavar and D. Chatterjee
Objective Attitude stabilization of a rigid body is a classical problem of significant importance, and has been widely studied in aerospace and mechanical engineering applications. Even though the state-space for this problem is a nonlinear manifold, classically, this problem has been analyzed using local coordinate representations such as Euler angles or, global but redundant representations like quaternions, resulting in differential equations on a Euclidean space.

It is only in the recent past that the problem has been analyzed in a 'coordinate-free' framework, where one works with the dynamics directly on the nonlinear state space, that evolves on a smooth manifold. The motivation for doing this, rather than use a coordinate dependent approach, has been documented well in the literature. One of the main advantages of the coordinate-free approach is that it allows a global analysis of the designed feedback control law.

Further, the issue of incorporating both control magnitude and state constraints at the control synthesis stage, for this class of problems, is yet to be investigated.

Towards a convex-analytic view of information structures
Source IRCC, IIT Bombay
Project duration 2013 - 2016
Principal Investigator Ankur Kulkarni
Amount 20 lakhs
Objective The aim of this project is to develop an approach to stochastic control problems with nonclassical information structures based on the shape of the set of joint distributions they induce.
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