International audience

In robotic networks relying on noisy range measurements between agents for cooperative localization, the achievable positioning accuracy strongly depends on the network geometry. This motivates the problem of planning robot trajectories in such multirobot systems in a way that maintains high localization accuracy. We present potential-based planning methods, where localizability potentials are introduced to characterize the quality of the network geometry for cooperative position estimation. These potentials are based on Cramér Rao lower bounds (CRLB) and provide a theoretical lower bound on the error covariance achievable by any unbiased position estimator. In the process, we establish connections between CRLBs and the theory of graph rigidity, which has been previously used to plan the motion of robotic networks. We develop decentralized deployment algorithms appropriate for large networks, and we use equality-constrained CRLBs to extend the concept of localizability to scenarios where additional information about the relative positions of the ranging sensors is known. We illustrate the resulting robot deployment methodology through simulated examples and an experiment.

Accurate and real-time position estimates are cru-cial for mobile robots. This work focuses on ranging-based positioning systems, which rely on distance measurements between known points, called anchors, and a tag to localize. The topology of the network formed by the anchors strongly influences the tag's localizability, i.e., its ability to be accurately localized. Here, the tag and some anchors are supposed to be carried by robots, which allows enhancing the positioning accuracy by planning the anchors' motions. We leverage Bayesian Cramer-Rao Lower Bounds (CRLBs) on the estimates' covariance in order to quantify the tag's localizability. This class of CRLBs can capture prior information on the tag's position and take it into account when deploying the anchors. We propose a method to decrease a potential function based on the Bayesian CRLB in order to maintain the localizability of the tag while having some prior knowledge about its position distribution. Then, we present a new experiment highlighting the link between the localizability potential and the precision expected in practice. Finally, two real-time anchor motion planners are demonstrated with ranging measurements in the presence or absence of prior information about the tag's position.

Position estimation in Multi-Robot Systems (MRS) relies on relative angle or distance measurements between the robots, which generally deteriorate as distances increase. Moreover, the localization accuracy is strongly influenced both by the quality of the raw measurements but also by the overall geometry of the network. In this paper, we design a cost function that accounts for these two issues and can be used to develop motion planning algorithms that optimize the localizability in MRS, i.e., the ability of individual robots to localize themselves accurately. This cost function is based on computing new Cramér Rao Lower Bounds characterizing the achievable positioning performance with range and angle measurements that deteriorate with increasing distances. We describe a gradient-based motion-planning algorithm for MRS deployment that can be implemented in a distributed manner, as well as a non-myopic strategy to escape local minima. Finally, we test the proposed methodology experimentally for range measurements obtained using ultra-wide band transceivers and illustrate the improvements resulting from leveraging the more accurate measurement model in the robot placement algorithms.

Ranging systems can provide inexpensive, accurate, energy- and computationally-efficient navigation solutions for mobile robots. This work focuses on location and pose estimation in ranging networks composed of anchors with known positions as well as mobile robots modeled as rigid bodies, each carrying multiple tags to localize. Noisy distance measurements can be obtained between a subset of the nodes (anchors and tags), and the robots can move in order to improve the accuracy of the localization process, which depends on the geometry of the network. We propose a method to find trajectories for the robots leading to configurations that locally optimize this localization accuracy. These trajectories minimize a cost function based on the constrained Cramér-Rao Lower Bound (CRLB), where the constraints capture the information about the known distances between tags carried by the same robot. A primal-dual optimization scheme aims to enforce these distance constraints between tags in the motion planner as well. An important feature of the approach is that the gradient terms necessary to plan the motion can be computed essentially in closed form, thereby simplifying the implementation. We compare the proposed method to a naive two-stage algorithm that optimizes the positions and orientations of the robots independently. Simulation results illustrate the benefits of using the constrained optimization approach.

The ability to accurately measure signal time-of-flight between ultra-wideband (UWB) wireless communication transceivers, even in multipath environments, makes this technology ideally suited to develop ranging-based positioning systems, especially for indoor applications where GPS signals are not available. In recent years, low-cost commercial UWB transceivers have become more easily available and increasingly used to develop custom robot positioning systems. In this paper, we focus in particular on positioning techniques requiring the synchronization of base stations such as Time of Arrival (TOA) and Time Difference of Arrival (TDOA). We present a protocol based on Kalman filtering for simultaneous synchronization of multiple UWB base stations and positioning of an arbitrary number of passive UWB receivers. We illustrate experimentally using our protocol and an EKF-based navigation system design the level of accuracy achievable with small low-power UWB modules for mobile robot positioning. We discuss in details measurement errors and system tuning issues applicable to popular commercial UWB transceivers.