SE PhD Prospectus Defense of Mahroo Bahreinian

TITLE: LINEAR PROGRAMMING FOR ROBUST LOCALIZATION AND NAVIGATION

ABSTRACT: Linear programming is an established, well-understood technique optimization problem; the goal of this thesis is to show that we can still use linear programming to advance the state of the art in two important blocks of modern robotic systems, namely perception and control.

In the context of perception, we study the effects of outliers in the solution of localization problems. At its essence, this problem reduces to finding the coordinates of a set of nodes in a common reference frame starting from relative pairwise measurements and is at the core of many applications such as Structure from Motion (SfM), sensor networks, and Simultaneous Localization And Mapping (SLAM). In practical situations, the accuracy of the relative measurements is marred by noise and outliers (large magnitude errors). In particular, outliers might introduce significant errors in the final result, hence, we have the problem of quantifying how much we should trust the solution returned by some given localization solver. In this work, we focus on the question of whether an L1-norm robust optimization formulation can recover a solution that is identical to the ground truth, under the scenario of translation-only measurements corrupted exclusively by outliers and no noise.

In the context of control, we study the problem of robust path planning. Path planning deals with the problem of finding a path from an initial state toward a goal state while considering collision avoidance. We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of robust min-max Linear Programming problems on the elements of a cell decomposition of the environment. The optimization problems are formulated using linear Control Lyapunov Function (CLF) and Control Barrier Function (CBF) constraints, to provide stability and safety guarantees, respectively. We show through simulations that the resulting controllers are robust to significant deformations of the environment.

For the future, we plan to find the controller synthesis using the bearing only measurements, implement our approach with a sample-based path planning method, and add uncertainty to the model of the system. In addition, we aim to implement our method to constrained nonlinear systems.

COMMITTEE: ADVISOR Roberto Tron, SE, ME; John Baillieul, SE, ME; Sean Andersson, SE, ME; Calin Belta, SE, ME