Research

Current research interests

Path planning of autonomous vehicles, consensus problems in multi-agent systems, opinion dynamics.

Over the years, I have had the opportunity to explore several interesting problems in the areas of path planning of autonomous vehicles, cyclic pursuit strategies, missile guidance and opinion dynamics. I have tried to summarise the interesting aspects of these areas below:

Consensus in Path Planning Problems

As has been demonstrated in the vast literature of multi-agent systems, most of the problems involving 'multiple entities' can be viewed or transformed into consensus problems (for some or the other parameter). For example, the problem of a simultaneous arrival at a given point, for unicycle agents, can be viewed as a consensus problem in the time parameter (or the time-to-go parameter which is a variant of the former). The challenges then arise in achieving consensus under several constraints like weakly connected networks, switching networks, bounded control inputs, etc. Can we always achieve consensus under all these constraints?

Desired paths for Dubins Vehicles

A Dubins vehicle is a point mass entity which comes very close to representing real world systems like bicycles, cars, fixed-wing aircrafts, etc. L. E. Dubins showed us a way in 1957 to generate shortest paths between any points in the Euclidean plane using such a vehicle. His proposed path (aka Dubins path) was even proven to be optimal by H. H. Johnson in 1974. Interestingly, Dubins paths have no more than two points of jerk in the motion; this property allows for easy implementation of such paths using real world systems. Now, in real world problems, it might not always be feasible to traverse the shortest paths. For example, one might need to avoid collisions along the (shortest) path while going from one point to the other. So, designing trajectories of desired lengths can be very useful in practical applications. Given that Dubins paths have such nice properties, can we build upon such trajectories to generate paths of any desired lengths?

Cyclic Pursuit Problems

Cyclic pursuit is a simple strategy where every autonomous agent 'i' pursues only its neighbour, indexed as 'i+1'. Seemingly simple, but such local interactions between the agents can lead to complex global behaviours. Formations with linear agents in such a framework have been studied extensively in the literature. However, nonlinear formations still pose several fundamental issues like convergence to the desired formation. We are exploring the generation of such formations by exploiting the underlying symmetry in them.

Study of non-holonomic systems

Unlike linear systems, nonlinear systems can exhibit a variety of fascinating behaviours. We focus particularly on those which have non-holonomic kinematic constraints. The motivation lies in the fact that systems with non-holonomic constraints represent simplified models for complex vehicular systems like cars, missiles, even fixed-wing aircrafts! In one of the prior works, we explored and completely characterised the motions of a unicycle system in a particular framework. Several other scenarios in the direction remain unexplored and are of interest to me. The beautiful figure on the right is one of the intricate paths generated using a unicycle.

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