Tracking Level Curves

Dr. Fumin Zhang, Post-doctoral Research Associate,
MAE Department, Princeton University

In this talk I will first discuss how to use a team of mobile robots
to estimate level curves of a scalar field. In collaboration with N.
E. Leonard, we show that in many 2D cases, performance of the
estimator depends on the shape of the team. Therefore, it is
reasonable to study formation control laws. We introduce a class of
such laws which utilize the so called "shape space".

We then utilize the obtained information about the level curves to
design motion of the robot team so that a nearly "global"
understanding of the scalar field can be inferred from the motion
trajectories. As the simplest example, one such motion may be to move
along a level curve.? We prove that by using a team of four robots we
can trace a regular level curve with desired field value. It is then
possible to generate an overall contour map using many such teams.
Although simple, this level curve tracking motion is an essential
building block for underwater adaptive sampling.

I will then discuss the connection between the level curve tracking
motion and obstacle avoidance or navigation algorithms for swarms.
In collaboration with P. S. Krishnaprasad, E.W. Justh and S. Haq, we
design a control law and prove that in the plane with obstacles
having smooth closed boundaries, three goals are achieved. First,
collisions between robots are prevented. Second, collisions with the
obstacles are avoided and third, the whole team moves along a
boundary curve with desired clearance.