This paper introduces a set of customizable and novel cost functions that enable the user to easily specify desirable robot formations, such as a "high-coverage" infrastructure-inspection formation, while maintaining high relative pose estimation accuracy. The overall cost function balances the need for the robots to be close together for good ranging-based relative localization accuracy and the need for the robots to achieve specific tasks, such as minimizing the time taken to inspect a given area. The formations found by minimizing the aggregated cost function are evaluated in a coverage path planning task in simulation and experiment, where the robots localize themselves and unknown landmarks using a simultaneous localization and mapping algorithm based on the extended Kalman filter. Compared to an optimal formation that maximizes ranging-based relative localization accuracy, these formations significantly reduce the time to cover a given area with minimal impact on relative pose estimation accuracy.

Ultra-wideband (UWB) systems are becoming increasingly popular as a means of inter-robot ranging and communication. A major constraint associated with UWB is that only one pair of UWB transceivers can range at a time to avoid interference, hence hindering the scalability of UWBbased localization. In this paper, a ranging protocol is proposed that allows all robots to passively listen on neighbouring communicating robots without any hierarchical restrictions on the role of the robots. This is utilized to allow each robot to obtain more range measurements and to broadcast preintegrated inertial measurement unit (IMU) measurements for relative extended pose state estimation directly on$SE_{2}(3)$. Consequently, a simultaneous clock-synchronization and relative-pose estimator (CSRPE) is formulated using an on-manifold extended Kalman filter (EKF) and is evaluated in simulation using Monte-Carlo runs for up to 7 robots. The ranging protocol is implemented in C on custom-made UWB boards fitted to 3 quadcopters, and the proposed filter is evaluated over multiple experimental trials, yielding up to 48% improvement in localization accuracy.

Ultra-Wideband (UWB) systems are becoming increasingly popular for indoor localization, where range measurements are obtained by measuring the time-of-flight of radio signals. However, the range measurements typically suffer from a systematic error or bias that must be corrected for high-accuracy localization. In this paper, a ranging protocol is proposed alongside a robust and scalable antenna-delay calibration procedure to accurately and efficiently calibrate antenna delays for many UWB tags. Additionally, the bias and uncertainty of the measurements are modelled as a function of the received-signal power. The full calibration procedure is presented using experimental training data of 3 aerial robots fitted with 2 UWB tags each, and then evaluated on 2 test experiments. A localization problem is then formulated on the experimental test data, and the calibrated measurements and their modelled uncertainty are fed into an extended Kalman filter (EKF). The proposed calibration is shown to yield an average of 46% improvement in localization accuracy. Lastly, the paper is accompanied by an open-source UWB-calibration Python library, which can be found at https://github.com/decargroup/uwb_calibration.

The ability to rapidly test a variety of algorithms for an arbitrary state estimation task is valuable in the prototyping phase of navigation systems. Lie group theory is now mainstream in the robotics community, and hence estimation prototyping tools should allow state definitions that belong to manifolds. A new package, called navlie, provides a framework that allows a user to model a large class of problems by implementing a set of classes complying with a generic interface. Once accomplished, navlie provides a variety of on-manifold estimation algorithms that can run directly on these classes. The package also provides a built-in library of common models, as well as many useful utilities. The open-source project can be found at https://github.com/decargroup/navlie

In multi-robot missions, relative position and attitude information between robots is valuable for a variety of tasks such as mapping, planning, and formation control. In this paper, the problem of estimating relative poses from a set of inter-robot range measurements is investigated. Specifically, it is shown that the estimation accuracy is highly dependent on the true relative poses themselves, which prompts the desire to find multi-robot formations that provide the best estimation performance. By direct maximization of Fischer information, it is shown in simulation and experiment that large improvements in estimation accuracy can be obtained by optimizing the formation geometry of a team of robots.

A coordinate system is proposed that replaces the usual three-dimensional Cartesian x, y, z position coordinates, for use in robotic localization applications. Range, azimuth, and elevation measurement models become greatly simplified, and, unlike spherical coordinates, the proposed coordinates do not suffer from the same kinematic singularities and angle wraparound. When compared to Cartesian coordinates, the proposed coordinate system results in a significantly enhanced ability to represent the true distribution of robot positions, ultimately leading to large improvements in state estimation consistency.