Optimal Robot Formations: Balancing Range-Based Observability and User-Defined Configurations

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.

Gaussian-Sum Filter for Range-based 3D Relative Pose Estimation in the Presence of Ambiguities

Multi-robot systems must have the ability to accurately estimate relative states between robots in order to perform collaborative tasks, possibly with no external aiding. Three-dimensional relative pose estimation using range measurements oftentimes suffers from a finite number of non-unique solutions, or ambiguities. This paper: 1) identifies and accurately estimates all possible ambiguities in 2D; 2) treats them as components of a Gaussian mixture model; and 3) presents a computationally-efficient estimator, in the form of a Gaussian-sum filter (GSF), to realize range-based relative pose estimation in an infrastructure-free, 3D, setup. This estimator is evaluated in simulation and experiment and is shown to avoid divergence to local minima induced by the ambiguous poses. Furthermore, the proposed GSF outperforms an extended Kalman filter, demonstrates similar performance to the computationally-demanding particle filter, and is shown to be consistent.

IMU Preintegration for Multi-Robot Systems in the Presence of Bias and Communication Constraints

This document is in supplement to the paper titled "Multi-Robot Relative Pose Estimation and IMU Preintegration Using Passive UWB Transceivers", available at [1]. The purpose of this document is to show how IMU biases can be incorporated into the framework presented in [1], while maintaining the differential Sylvester equation form of the process model.

STAR-loc: Dataset for STereo And Range-based localization

This document contains a detailed description of the STAR-loc dataset. For a quick starting guide please refer to the associated Github repository (https://github.com/utiasASRL/starloc). The dataset consists of stereo camera data (rectified/raw images and inertial measurement unit measurements) and ultra-wideband (UWB) data (range measurements) collected on a sensor rig in a Vicon motion capture arena. The UWB anchors and visual landmarks (Apriltags) are of known position, so the dataset can be used for both localization and Simultaneous Localization and Mapping (SLAM).

Multi-Robot Relative Pose Estimation and IMU Preintegration Using Passive UWB Transceivers

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 UWB-based 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 56% improvement in localization accuracy.

Reducing Two-Way Ranging Variance by Signal-Timing Optimization

Time-of-flight-based range measurements among transceivers with different clocks requires ranging protocols that accommodate for the varying rates of the clocks. Double-sided two-way ranging (DS-TWR) has recently been widely adopted as a standard protocol due to its accuracy; however, the precision of DS-TWR has not been clearly addressed. In this paper, an analytical model of the variance of DS-TWR is derived as a function of the user-programmed response delays. Consequently, this allows formulating an optimization problem over the response delays in order to maximize the information gained from range measurements by addressing the effect of varying the response delays on the precision and frequency of the measurements. The derived analytical variance model and proposed optimization formulation are validated experimentally with 2 ranging UWB transceivers, where 29 million range measurements are collected.

Calibration and Uncertainty Characterization for Ultra-Wideband Two-Way-Ranging Measurements

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/decarsg/uwb_calibration.

Relative Position Estimation in Multi-Agent Systems Using Attitude-Coupled Range Measurements

The ability to accurately estimate the position of robotic agents relative to one another, in possibly GPS-denied environments, is crucial to execute collaborative tasks. Inter-agent range measurements are available at a low cost, due to technologies such as ultra-wideband radio. However, the task of three-dimensional relative position estimation using range measurements in multi-agent systems suffers from unobservabilities. This letter presents a sufficient condition for the observability of the relative positions, and satisfies the condition using a simple framework with only range measurements, an accelerometer, a rate gyro, and a magnetometer. The framework has been tested in simulation and in experiments, where 40-50 cm positioning accuracy is achieved using inexpensive off-the-shelf hardware.

Optimal Multi-robot Formations for Relative Pose Estimation Using Range Measurements

In multi-robot missions, relative position and attitude information between agents 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-agent 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-agent 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.