Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from nois… (see more)y sensors. To render the state estimation problem tractable, many systems assume that the motion and measurement noise, as well as the state distribution, are unimodal and Gaussian. However, there are numerous scenarios and systems that do not comply with these assumptions. Existing nonparametric filters that are used to model multimodal distributions have drawbacks that limit their ability to represent a diverse set of distributions. This paper introduces a novel approach to nonparametric Bayesian filtering on motion groups, designed to handle multimodal distributions using harmonic exponential distributions. This approach leverages two key insights of harmonic exponential distributions: a) the product of two distributions can be expressed as the element-wise addition of their log-likelihood Fourier coefficients, and b) the convolution of two distributions can be efficiently computed as the tensor product of their Fourier coefficients. These observations enable the development of an efficient and asymptotically exact solution to the Bayes filter up to the band limit of a Fourier transform. We demonstrate our filter's performance compared with established nonparametric filtering methods across simulated and real-world localization tasks.

2025-01-07

IEEE Robotics and Automation Letters (published)

doi.org

arxiv.org

Reducing Two-Way Ranging Variance by Signal-Timing Optimization

Mohammed Ayman Shalaby

Charles Champagne Cossette

James Richard Forbes

Jerome Le Ny

Time-of-flight-based ranging among transceivers with different clocks requires protocols that accommodate varying rates of the clocks. Doubl… (see more)e-sided two-way ranging (DS-TWR) is 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, which is then compared to the Cramer-Rao Lower Bound (CRLB). This is then used to formulate an optimization problem over the response delays in order to maximize the information gained from range measurements. The derived analytical variance model and optimized protocol are validated experimentally with 2 ranging UWB transceivers, where 29 million range measurements are collected.

2024-05-31

IEEE Transactions on Aerospace and Electronic Systems (published)

doi.org

arxiv.org

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

Syed Shabbir Ahmed

Mohammed Ayman Shalaby

Jerome Le Ny

James Richard Forbes

This paper introduces a set of customizable and novel cost functions that enable the user to easily specify desirable robot formations, such… (see more) 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.

2023-12-31

IEEE/RSJ International Conference on Intelligent Robots and Systems (published)

doi.org

arxiv.org

The Invariant Rauch-Tung-Striebel Smoother

Niels van der Laan

Mitchell Cohen

Jonathan Arsenault

James Richard Forbes

This paper presents an invariant Rauch-Tung- Striebel (IRTS) smoother applicable to systems with states that are an element of a matrix Lie … (see more)group. In particular, the extended Rauch-Tung-Striebel (RTS) smoother is adapted to work within a matrix Lie group framework. The main advantage of the invariant RTS (IRTS) smoother is that the linearization of the process and measurement models is independent of the state estimate resulting in state-estimate-independent Jacobians when certain technical requirements are met. A sample problem is considered that involves estimation of the three dimensional pose of a rigid body on SE(3), along with sensor biases. The multiplicative RTS (MRTS) smoother is also reviewed and is used as a direct comparison to the proposed IRTS smoother using experimental data. Both smoothing methods are also compared to invariant and multiplicative versions of the Gauss-Newton approach to solving the batch state estimation problem.

2020-09-30

IEEE Robotics and Automation Letters (published)

doi.org

arxiv.org

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