This paper describes a distributed, linear-time algorithm for localizing sensor network nodes in the presence of range measurement noise and demonstrates the algorithm on a physical network. We introduce the probabilistic notion of robust quadrilaterals as a way to avoid flip ambiguities that otherwise corrupt localization computations. We formulate the localization problem as a two-dimensional graph realization problem: given a planar graph with approximately known edge lengths, recover the Euclidean position of each vertex up to a global rotation and translation. This formulation is applicable to the localization of sensor networks in which each node can estimate the distance to each of its neighbors, but no absolute position reference such as GPS or fixed anchor nodes is available.We implemented the algorithm on a physical sensor network and empirically assessed its accuracy and performance. Also, in simulation, we demonstrate that the algorithm scales to large networks and handles real-world deployment geometries. Finally, we show how the algorithm supports localization of mobile nodes.

A robot exploring an environment can estimate its own motion and the relative positions of features in the environment. Simultaneous Localization and Mapping (SLAM) algorithms attempt to fuse these estimates to produce a map and a robot trajectory. The constraints are generally non-linear, thus SLAM can be viewed as a non-linear optimization problem. The optimization can be difficult, due to poor initial estimates arising from odometry data, and due to the size of the state space.We present a fast non-linear optimization algorithm that rapidly recovers the robot trajectory, even when given a poor initial estimate. Our approach uses a variant of Stochastic Gradient Descent on an alternative state-space representation that has good stability and computational properties. We compare our algorithm to several others, using both real and synthetic data sets.

The Rapidly-exploring Random Tree (RRT) algorithm, based on incremental sampling, efficiently computes motion plans. Although the RRT algorithm quickly produces candidate feasible solutions, it tends to converge to a solution that is far from optimal. Practical applications favor "anytime" algorithms that quickly identify an initial feasible plan, then, given more computation time available during plan execution, improve the plan toward an optimal solution. This paper describes an anytime algorithm based on the RRT * which (like the RRT) finds an initial feasible solution quickly, but (unlike the RRT) almost surely converges to an optimal solution. We present two key extensions to the RRT * , committed trajectories and branch-and-bound tree adaptation, that together enable the algorithm to make more efficient use of computation time online, resulting in an anytime algorithm for real-time implementation. We evaluate the method using a series of Monte Carlo runs in a high-fidelity simulation environment, and compare the operation of the RRT and RRT * methods. We also demonstrate experimental results for an outdoor wheeled robotic vehicle.

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In this paper we describe Atlas, a hybrid metrical/topological approach to simultaneous localization and mapping (SLAM) that achieves efficient mapping of large-scale environments. The representation is a graph of coordinate frames, with each vertex in the graph representing a local frame and each edge representing the transformation between adjacent frames. In each frame, we build a map that captures the local environment and the current robot pose along with the uncertainties of each. Each map's uncertainties are modeled with respect to its own frame. Probabilities of entities with respect to arbitrary frames are generated by following a path formed by the edges between adjacent frames, computed using either the Dijkstra shortest path algorithm or breath-first search. Loop closing is achieved via an efficient map-matching algorithm coupled with a cycle verification step. We demonstrate the performance of the technique for post-processing large data sets, including an indoor structured environment (2.2 km path length) with multiple nested loops using laser or ultrasonic ranging sensors.