Date of Award

2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mechanical Engineering & Applied Mechanics

First Advisor

Vijay Kumar

Abstract

An exciting application of robots is using multi-robot systems to accomplish complex tasks. Harnessing the productive capacity of multi-robot systems requires enabling robots to safely and efficiently navigate their environment both individually and in formation as a team. These teams, however, may have robots with constraints on their motion and each robot may be different in terms of speed and maneuverability.

This thesis addresses the development of motion planning algorithms for robot teams that account for motion constraints and heterogeneity in maximum speeds. The problem studied is, given a team of robots and a set of unlabeled goal locations, assign each robot to a goal location and generate collision-free trajectories to these goal locations. This problem was also studied in the context of maneuvering and changing formations.

The first contribution is a motion planning algorithm for teams of robots with minimum turning radius constraints. This algorithm provides completeness and collision avoidance guarantees while being computationally tractable -- both key features for coordinating large teams of robots. The second contribution builds on the first by developing a motion planning algorithm for a team of fixed-wing aircraft in formation flight. The algorithm allows a team of aircraft to maintain a specified formation as well as the ability to change formation during flight and on demand, while also providing collision avoidance guarantees. The third contribution extends the results to teams of robots with heterogeneous speeds. By accounting for the speed capabilities of each robot, this algorithm also enables rapid formation transitions that are faster than the transitions that would occur using traditional solutions that apply to robots with homogeneous speed capabilities. Specifically, an algorithm was proposed that designs collision-free transitions by solving a linear bottleneck assignment problem (LBAP). The theory and resulting guarantees in this dissertation are empirically verified through a combination of computer simulations and experiments using multi-robot teams in the laboratory and in large field experiments with industry partners.

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