Thesis Defense: Geometrical Analysis of Spatio-temporal Planning Problems

Abhishek Tiwari

Abstract: In this talk I will represent and analyze spatially and temporally constrained multi-agent planning problems using tools from geometry and advanced calculus. The two problems that I will consider are multi-agent rendezvous and dynamic sensor coverage. Together these problems encompass cooperation, constraint representation, and task scheduling aspects of multi-agent planning problems.

I have represented the constraint of the rendezvous problem on the phase space and shown that the fulfilment of rendezvous constraints is equivalent to certain conical regions being invariant. Alternatively for the dynamic coverage problem the constraints can be adequately represented on the uncertainty space and sensor motion laws can be obtained by partitioning the uncertainty space and making decisions based on which partition the uncertainty lies in. I have examined convergence behavior of sensor motion under such laws.