On-manifold Decentralized State Estimation using Pseudomeasurements and Preintegration

This paper addresses the problem of decentralized, collaborative state estimation in robotic teams. In particular, this paper considers problems where individual robots estimate similar physical quantities, such as each other's position relative to themselves. The use of \emph{pseudomeasurements} is introduced as a means of modelling such relationships between robots' state estimates, and is shown to be a tractable way to approach the decentralized state estimation problem. Moreover, this formulation easily leads to a general-purpose observability test that simultaneously accounts for measurements that robots collect from their own sensors, as well as the communication structure within the team. Finally, input preintegration is proposed as a communication-efficient way of sharing odometry information between robots, and the entire theory is appropriate for both vector-space and Lie-group state definitions. The proposed framework is evaluated on three different simulated problems, and one experiment involving three quadcopters.Comment: 15 pages, 13 figures, submitted to IEE

Cascaded Filtering Using the Sigma Point Transformation (Extended Version)

It is often convenient to separate a state estimation task into smaller "local" tasks, where each local estimator estimates a subset of the overall system state. However, neglecting cross-covariance terms between state estimates can result in overconfident estimates, which can ultimately degrade the accuracy of the estimator. Common cascaded filtering techniques focus on the problem of modelling cross-covariances when the local estimators share a common state vector. This letter introduces a novel cascaded and decentralized filtering approach that approximates the cross-covariances when the local estimators consider distinct state vectors. The proposed estimator is validated in simulations and in experiments on a three-dimensional attitude and position estimation problem. The proposed approach is compared to a naive cascaded filtering approach that neglects cross-covariance terms, a sigma point-based Covariance Intersection filter, and a full-state filter. In both simulations and experiments, the proposed filter outperforms the naive and the Covariance Intersection filters, while performing comparatively to the full-state filter.Comment: This is an extended version of the original letter to be published in the IEEE Robotics and Automation Letter

Magnetic Navigation using Attitude-Invariant Magnetic Field Information for Loop Closure Detection

Indoor magnetic fields are a combination of Earth's magnetic field and disruptions induced by ferromagnetic objects, such as steel structural components in buildings. As a result of these disruptions, pervasive in indoor spaces, magnetic field data is often omitted from navigation algorithms in indoor environments. This paper leverages the spatially-varying disruptions to Earth's magnetic field to extract positional information for use in indoor navigation algorithms. The algorithm uses a rate gyro and an array of four magnetometers to estimate the robot's pose. Additionally, the magnetometer array is used to compute attitude-invariant measurements associated with the magnetic field and its gradient. These measurements are used to detect loop closure points. Experimental results indicate that the proposed approach can estimate the pose of a ground robot in an indoor environment within meter 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.Comment: 5 pages, 4 figures, submitted to 2023 International Conference on Acoustics, Speech and Signal Processing (ICASSP

Lagrangian Derivation of Variable-Mass Equations of Motion using an Arbitrary Attitude Parameterization

Lagrange’s equation is a popular method of deriving equations of motion due to the ability to choose a variety of generalized coordinates and implement constraints. When using a Lagrangian formulation, part of the generalized coordinates may describe the attitude. This paper presents a means of deriving the dynamics of variable-mass systems using Lagrange’s equation while using an arbitrary constrained attitude parameterization. The equivalence to well-known forms of the equations of motion is shown

navlie: A Python Package for State Estimation on Lie Groups

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.Comment: 6 pages, 8 figures, presented at the 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS