Corné E. van Daalen

E. Visser, C. E. van Daalen, J. C. Schoeman

Bayesian optimization (BO) is a popular method for optimizing expensive black-box functions. BO has several well-documented shortcomings, including computational slowdown with longer optimization runs, poor suitability for non-stationary or ill-conditioned objective functions, and poor convergence characteristics. Several algorithms have been proposed that incorporate local strategies, such as trust regions, into BO to mitigate these limitations; however, none address all of them satisfactorily. To address these shortcomings, we propose the LABCAT algorithm, which extends trust-region-based BO by adding a rotation aligning the trust region with the weighted principal components and an adaptive rescaling strategy based on the length-scales of a local Gaussian process surrogate model with automatic relevance determination. Through extensive numerical experiments using a set of synthetic test functions and the well-known COCO benchmarking software, we show that the LABCAT algorithm outperforms several state-of-the-art BO and other black-box optimization algorithms.

Bongani B. Maseko, Corné E. van Daalen, Johann Treurnicht

Path planners based on basic rapidly-exploring random trees (RRTs) are quick and efficient, and thus favourable for real-time robot path planning, but are almost-surely suboptimal. In contrast, the optimal RRT (RRT*) converges to the optimal solution, but may be expensive in practice. Recent work has focused on accelerating the RRT*'s convergence rate. The most successful strategies are informed sampling, path optimisation, and a combination thereof. However, informed sampling and its combination with path optimisation have not been applied to the basic RRT. Moreover, while a number of path optimisers can be used to accelerate the convergence rate, a comparison of their effectiveness is lacking. This paper investigates the use of informed sampling and path optimisation to accelerate planners based on both the basic RRT and the RRT*, resulting in a family of algorithms known as optimised informed RRTs. We apply different path optimisers and compare their effectiveness. The goal is to ascertain if applying informed sampling and path optimisation can help the quick, though almost-surely suboptimal, path planners based on the basic RRT attain comparable or better performance than RRT*-based planners. Analyses show that RRT-based optimised informed RRTs do attain better performance than their RRT*-based counterparts, both when planning time is limited and when there is more planning time.

J. C. Schoeman, C. E. van Daalen, J. A. du Preez

In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian parametrisations where the positive-definite constraint of the covariance matrix has been relaxed. For this purpose, we derive various statistical operations and results (such as marginalisation, multiplication and affine transformations of random variables) that extend the capabilities of Gaussian factors to these degenerate settings. By using this principled factor definition, degeneracies can be accommodated accurately and automatically at little additional computational cost. As illustration, we apply our methodology to a representative example involving recursive state estimation of cooperative mobile robots.

Clint D. Lombard, Corné E. van Daalen

For mobile robots to operate autonomously in general environments, perception is required in the form of a dense metric map. For this purpose, we present the stochastic triangular mesh (STM) mapping technique: a 2.5-D representation of the surface of the environment using a continuous mesh of triangular surface elements, where each surface element models the mean plane and roughness of the underlying surface. In contrast to existing mapping techniques, a STM map models the structure of the environment by ensuring a continuous model, while also being able to be incrementally updated with linear computational cost in the number of measurements. We reduce the effect of uncertainty in the robot pose (position and orientation) by using landmark-relative submaps. The uncertainty in the measurements and robot pose are accounted for by the use of Bayesian inference techniques during the map update. We demonstrate that a STM map can be used with sensors that generate point measurements, such as light detection and ranging (LiDAR) sensors and stereo cameras. We show that a STM map is a more accurate model than the only comparable online surface mapping technique$\unicode{x2014}$a standard elevation map$\unicode{x2014}$and we also provide qualitative results on practical datasets.