Academics
Current Current position Research Areas of research Movies Movies I made in matlab Publications Paper publications Teaching Teaching Experience Notes Some expository notes Miscellaneous Other interests Links Some science related links RRI Researchers Returning to India Main Back to main page

Current Position

Currently I am a Postdoc at the Controls and Dynamical Systems group in Caltech with Jerry Marsden.

From June, 2006 to Dec, 2006, I was a postdoc at USC with Eva Kanso and a Visitor at Caltech with Jerry Marsden.

Before this, I spent lovely 5.5 years at Princeton doing my PhD. My thesis advisor was Naomi Leonard who was one of the recipients of 2004 MacArthur Fellowship. I defended my thesis in April 2006 and you can download a copy of my thesis in double-sided format here .

Research Interests

Broadly, my research interests lie in Geometric Mechanics and Nonlinear Control. Specifically, applying ideas from mechanics and designing energy-based stabilizing control laws for controlling an individual or group of mechanical systems. Such problems are important both from a control design perspective as well in applications.

Movies




This movie illustrates swing up of four pendula attached to the same cart. The forcing actuation is in the cart direction and the whole system is a very good example of highly underactuated system and how DMOC can be used to find nontrivial swing up solution.



This movie illustrates a "chaotic" surveillance of a circular region or radius 50 units using 8 underactuated hovercrafts, each with a sensor radius of 1.5 units. Collision avoidance is built into this scheme. Initially, a number of red points are distributed in the region. When a hovercraft passes over a red point, it turns green and indicates that the point has been surveyed. The plot on the right is the ration of green points to the total number of points versus time. For this particular case, it takes about 30 time units to cover 90% of the area.









The above two movies demonstrate the coordination and synchronization of two inverted pendulum systems. The controls are applied only in the cart direction. The goal is to synchronize their states as well as to make sure that the controls do not destabilize the individuals. Here, we think of the carts as lying in different tracks and hence do not worry about issues like collision avoidance. Depending upon the way dissipation controls are chosen, the systems goes asymptotically to a constant momentum solution or to a relative equilibrium. In the movie, this becomes apparent towards the end. (You might want to fast forward the movie as its a long one). In the constant momentum solution, you can see that after a while, the systems synchronize but the oscillations do not die away. But in the relative equilibrium case, you can see the systems synchronizing and the pendulum positions asymptotically going to the upright positions.









The above two movies demonstrates coordination and synchronization of vehicles with configuration space as SO(3) or SE(3). They are models for satellites in space following the Euler's equations of motion and underwater vehicles following Kirchoff's equations of motion respectively. In the former case, the goal is to make the three satellites point in a particular direction in inertial space and at the same time keep rotating about their otherwise unstable middle axis. In the latter case, in addition to pointing in a particular direction in inertial space, we also require the vehicles to translate along the same direction. In these movies, you will notice that the axis with the same colors align with each other after a while.



In this movie, you can think of the outer bodies as active parent fishes and the middle body as the passive baby. The controls are applied to the parents only. The baby only responds to the surrounding fluid. The movie demonstrates a situation where the parents are able to drag the baby along without losing it. The parents are moving to the right with constant velocities and at the same time oscillating out of phase (please see the movie for the precise sense). For the in phase oscillation case, they lose the baby, i.e., the middle body is thrown away and drifts to infinity. In this movie, I have scaled the y-motion of the baby so as to make the its periodic oscillations in the y-direction more visible. The moral of the story is that if parent do not act right, they risk losing their child :)



In this movie, a creature is trying to grab food in a potential flow. It could be for example a scallop or a jelly fish. People have known that vortices play a very important role for food grabbing in jelly fish for example. What the movie illustrates is that vortices play an essential role in food grabbing. As the movie demonstrates, the creature only lands up repelling the food particle away from itself if its a potential flow with no vortices.

Publications

Journal Papers

Peer reviewed conference papers

Miscellaneous papers/notes

Teaching Experience

Notes


Other interests

Free online math books and articles

Excellent science books and links I have come across