Jason M. O'Kane

Computing Pareto Optimal Coordinations on Roadmaps

We consider the coordination of multiple robots in a common environment, each robot having its own (distinct) roadmap. Our primary contribution is a classification of and exact algorithm for computing vector-valued (or Pareto) optima for collision-free coordination. We indicate the utility of new geometric techniques from CAT(0) geometry and give an argument that curvature bounds are the key distinguishing feature between systems for which the classification is finite and for those in which it is not.

Localization With Limited Sensing

Localization is a fundamental problem for many kinds of mobile robots. Sensor systems of varying ability have been proposed and successfully used to solve the problem. This paper probes the lower limits of this range by describing three extremely simple robot models and addresses the active localization problem for each. The robot, whose configuration is composed of its position and orientation, moves in a fully-known, simply connected polygonal environment. We pose the localization task as a planning problem in the robots information space, which encapsulates the uncertainty in the robots configuration. We consider robots equipped with: 1) angular and linear odometers; 2) a compass and contact sensor and; 3) an angular odometer and contact sensor. We present localization algorithms for models 1 and 2 and show that no algorithm exists for model 3. An implementation with simulation examples is presented.

Almost-Sensorless Localization

We present a localization method for robots equipped with only a compass, a contact sensor and a map of the environment. In this framework, a localization strategy can be described as a sequence of directions in which the robot moves maximally. We show that a localizing sequence exists for any simply connected polygonal environment by presenting an algorithm for computing such a sequence. We have implemented the algorithm and we present several computed examples. We also show that the sensing model is minimal by showing that replacement of the compass by an angular odometer precludes the possibility of performing localization.

Global localization using odometry

This paper presents a global localization technique for a robot with only linear and angular odometers. The robot, whose configuration is composed of its position and orientation, moves in a fully-known environment by alternating rotations and forward translations. We pose the problem as a discrete-time planning problem in the robots information space, which encapsulates the uncertainty in the robots configuration. Our contribution is to show that in any simply-connected, bounded polygonal environment, localization by odometry alone is possible, but only up to the symmetries in the environment

Exact Pareto-optimal coordination of two translating polygonal robots on an acyclic roadmap

We present an algorithm that computes the complete set of Pareto-optimal coordination strategies for two translating polygonal robots in the plane. A collision-free acyclic roadmap of piecewise-linear paths is given on which the two robots move. The robots have a maximum speed and are capable of instantly switching between any two arbitrary speeds. Each robot would like to minimize its travel time independently. The Pareto-optimal solutions are the ones for which there exist no solutions that are better for both robots. The algorithm computes exact solutions in time O(mn/sup 2/ log n), in which m is the number of paths in the roadmap, n is the number of coordination space vertices. An implementation is presented.

Adaptive robot design with hand and face tracking for use in autism therapy

This research explores interactive games using hand and face tracking with a robot as a tool for autism therapy. The robot is equipped with a head and two arms, each with two degrees of freedom, and a camera. We trained a classifier to detect human hands and subsequently, used this classifier along with a standard face tracker to create two interactive games. In the first game the robot waits for the child to initiate an interaction by raising one or both hands. In the second game, the robot initiates interactions. These games are designed to increase attention, promote turn-taking skills and encourage child-led verbal and non-verbal communication through simple imitative play. This research makes two specific contributions: (1) We present a low-cost robot design which measures and adapts to a childs actions during interactive games and, (2) we train and test a hand detector, based on Haar-like features, which is usable in various kinds of human-robot interactions.

Information spaces for mobile robots

Planning with sensing uncertainty is central to robotics. Sensor limitations often prevent accurate state estimation of the robot. Two general approaches can be taken for solving robotics tasks given sensing uncertainty. The first approach is to estimate the state and to solve the given task using the estimate as the real state. However, estimation of the state may sometimes be harder than solving the original task. The other approach is to avoid estimation of the state, which can be achieved by defining the information space, the space of all histories of actions and sensing observations of a robot system. Considering information spaces brings better understanding of problems involving uncertainty, and also allows finding better solutions to such problems. In this paper we give a brief description of the information space framework, followed by its use in some robotic tasks.

On comparing the power of mobile robots

Minimalist models have been studied for a broad array of tasks in robotics. In this paper, we consider the taskcompleting power of robots in terms of the sensors and actuators with which the robot is equipped. Our goal is to understand the relative power of different sets of sensors and actuators and to determine which of these sets enable the robot to complete its task. We define robots as collections of robotic primitives and provide a formal method for comparing the sensing and actuation power of robots constructed from these primitives. This comparison, which is based on the how the robots progress through their information spaces, induces a partial order over the set of robot systems. We prove some basic properties of this partial order and then apply it to a limited-sensing version of the global localization problem.

Planning for provably reliable navigation using an unreliable, nearly sensorless robot

This paper addresses a navigation problem for a certain type of simple mobile robot modeled as a point moving in the plane. The only requirement on the robot is that it must be able to translate in a desired direction, with bounded angular error (measured in a global reference frame), until it reaches the nearest obstacle in its motion direction. One straightforward realization of this capability might use a noisy compass and a contact sensor. We present a planning algorithm that enables such a robot to navigate reliably through its environment. The algorithm constructs a directed graph in which each node is labeled with a subset of the environment boundary. Each edge of the graph is labeled with a sequence of actions that can move the robot from any location in one such set to some location in the other set. We use a variety of local planners to generate the edges, including a “corner-finding” technique that allows the robot to travel to and localize itself at a convex vertex of the environment boundary. The algorithm forms complete plans by searching the resulting graph. We have implemented this algorithm and present results from both simulation and a proof-of-concept physical realization.

Shortest paths for visibility-based pursuit-evasion

We present an algorithm that computes a minimal-cost pursuer trajectory for a single pursuer to solve the visibility-based pursuit-evasion problem in a simply-connected two-dimensional environment. This algorithm improves upon the known algorithm of Guibas, Latombe, LaValle, Lin, and Motwani, which is complete but not optimal. Our algorithm uses a Tour of Segments (ToS) subroutine to construct a pursuer path that minimizes the distance traveled by the pursuer while guaranteeing that all evaders in the environment will be captured. We have implemented our algorithm in simulation and provide results.