Asynchronous Network Formation in Unknown Unbounded Environments

In this paper, we study the Online Network Formation Problem (ONFP) for a mobile multi-robot system. Consider a group of robots with a bounded communication range operating in a large open area. One of the robots has a piece of information which has to be propagated to all other robots. What strategy should the robots pursue to disseminate the information to the rest of the robots as quickly as possible? The initial locations of the robots are unknown to each other, therefore the problem must be solved in an online fashion. For this problem, we present an algorithm whose competitive ratio is $O(H \cdot \max\{M,\sqrt{M H}\})$ for arbitrary robot deployments, where $M$ is the largest edge length in the Euclidean minimum spanning tree on the initial robot configuration and $H$ is the height of the tree. We also study the case when the robot initial positions are chosen uniformly at random and improve the ratio to $O(M)$. Finally, we present simulation results to validate the performance in larger scales and demonstrate our algorithm using three robots in a field experiment

Reinforcement Learning and Planning for Preference Balancing Tasks

Robots are often highly non-linear dynamical systems with many degrees of freedom, making solving motion problems computationally challenging. One solution has been reinforcement learning (RL), which learns through experimentation to automatically perform the near-optimal motions that complete a task. However, high-dimensional problems and task formulation often prove challenging for RL. We address these problems with PrEference Appraisal Reinforcement Learning (PEARL), which solves Preference Balancing Tasks (PBTs). PBTs define a problem as a set of preferences that the system must balance to achieve a goal. The method is appropriate for acceleration-controlled systems with continuous state-space and either discrete or continuous action spaces with unknown system dynamics. We show that PEARL learns a sub-optimal policy on a subset of states and actions, and transfers the policy to the expanded domain to produce a more refined plan on a class of robotic problems. We establish convergence to task goal conditions, and even when preconditions are not verifiable, show that this is a valuable method to use before other more expensive approaches. Evaluation is done on several robotic problems, such as Aerial Cargo Delivery, Multi-Agent Pursuit, Rendezvous, and Inverted Flying Pendulum both in simulation and experimentally. Additionally, PEARL is leveraged outside of robotics as an array sorting agent. The results demonstrate high accuracy and fast learning times on a large set of practical applications

WSR: A WiFi Sensor for Collaborative Robotics

In this paper we derive a new capability for robots to measure relative direction, or Angle-of-Arrival (AOA), to other robots operating in non-line-of-sight and unmapped environments with occlusions, without requiring external infrastructure. We do so by capturing all of the paths that a WiFi signal traverses as it travels from a transmitting to a receiving robot, which we term an AOA profile. The key intuition is to "emulate antenna arrays in the air" as the robots move in 3D space, a method akin to Synthetic Aperture Radar (SAR). The main contributions include development of i) a framework to accommodate arbitrary 3D trajectories, as well as continuous mobility all robots, while computing AOA profiles and ii) an accompanying analysis that provides a lower bound on variance of AOA estimation as a function of robot trajectory geometry based on the Cramer Rao Bound. This is a critical distinction with previous work on SAR that restricts robot mobility to prescribed motion patterns, does not generalize to 3D space, and/or requires transmitting robots to be static during data acquisition periods. Our method results in more accurate AOA profiles and thus better AOA estimation, and formally characterizes this observation as the informativeness of the trajectory; a computable quantity for which we derive a closed form. All theoretical developments are substantiated by extensive simulation and hardware experiments. We also show that our formulation can be used with an off-the-shelf trajectory estimation sensor. Finally, we demonstrate the performance of our system on a multi-robot dynamic rendezvous task.Comment: 28 pages, 25 figures, *co-primary author

Contributions To Pursuit-Evasion Game Theory.

This dissertation studies adversarial conflicts among a group of agents moving in the plane, possibly among obstacles, where some agents are pursuers and others are evaders. The goal of the pursuers is to capture the evaders, where capture requires a pursuer to be either co-located with an evader, or in close proximity. The goal of the evaders is to avoid capture. These scenarios, where different groups compete to accomplish conflicting goals, are referred to as pursuit-evasion games, and the agents are called players. Games featuring one pursuer and one evader are analyzed using dominance, where a point in the plane is said to be dominated by a player if that player is able to reach the point before the opposing players, regardless of the opposing players' actions. Two generalizations of the Apollonius circle are provided. One solves games with environments containing obstacles, and the other provides an alternative solution method for the Homicidal Chauffeur game. Optimal pursuit and evasion strategies based on dominance are provided. One benefit of dominance analysis is that it extends to games with many players. Two foundational games are studied; one features multiple pursuers against a single evader, and the other features a single pursuer against multiple evaders. Both are solved using dominance through a reduction to single pursuer, single evader games. Another game featuring competing teams of pursuers is introduced, where an evader cooperates with friendly pursuers to rendezvous before being captured by adversaries. Next, the assumption of complete and perfect information is relaxed, and uncertainties in player speeds, player positions, obstacle locations, and cost functions are studied. The sensitivity of the dominance boundary to perturbations in parameters is provided, and probabilistic dominance is introduced. The effect of information is studied by comparing solutions of games with perfect information to games with uncertainty. Finally, a pursuit law is developed that requires minimal information and highlights a limitation of dominance regions. These contributions extend pursuit-evasion game theory to a number of games that have not previously been solved, and in some cases, the solutions presented are more amenable to implementation than previous methods.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120650/1/dwoyler_1.pd

Safe Spacecraft Rendezvous and Proximity Operations via Reachability Analysis

The rapid expansion of the utilization of space by nations and industry has presented new challenges and opportunities to operate efficiently and responsibly. Reachability analysis is the process of computing the set of states that can be reached given all admissible controls and can be a valuable component in an autonomous mission planning system if conducted efficiently. In the current research, reachability analysis is used with several relative motion models to show that all ranges of orbits can be computed in milliseconds, and that it is a feasible approach for on-board autonomous mission planning. Reachability analysis is then combined with an Artificial Potential Function (APF) derived guidance control law to conduct safe spacecraft rendezvous between a deputy in a Natural Motion Circumnavigation (NMC) relative orbit around a chief while avoiding obstacles. While the APF employed in this research requires improvements for trajectory computation, this research demonstrates the feasibility of combining reachability analysis with an APF for safe, on-board, autonomous mission planning