An Extended Kalman Filter for Magnetic Field SLAM Using Gaussian Process Regression.

We present a computationally efficient algorithm for using variations in the ambient magnetic field to compensate for position drift in integrated odometry measurements (dead-reckoning estimates) through simultaneous localization and mapping (SLAM). When the magnetic field map is represented with a reduced-rank Gaussian process (GP) using Laplace basis functions defined in a cubical domain, analytic expressions of the gradient of the learned magnetic field become available. An existing approach for magnetic field SLAM with reduced-rank GP regression uses a Rao-Blackwellized particle filter (RBPF). For each incoming measurement, training of the magnetic field map using an RBPF has a computational complexity per time step of O(NpNm2), where Np is the number of particles, and Nm is the number of basis functions used to approximate the Gaussian process. Contrary to the existing particle filter-based approach, we propose applying an extended Kalman filter based on the gradients of our learned magnetic field map for simultaneous localization and mapping. Our proposed algorithm only requires training a single map. It, therefore, has a computational complexity at each time step of O(Nm2). We demonstrate the workings of the extended Kalman filter for magnetic field SLAM on an open-source data set from a foot-mounted sensor and magnetic field measurements collected onboard a model ship in an indoor pool. We observe that the drift compensating abilities of our algorithm are comparable to what has previously been demonstrated for magnetic field SLAM with an RBPF.

Pin-on-Disc Modelling with Mesh Deformation Using Discrete Element Method.

The pin-on-disc test is a standard sliding wear test used to analyse sliding properties, including wear contour and wear volume. In this study, long-term laboratory test performance is compared with a short-term numerical model. A discrete element method (DEM) approach combined with an Archard wear model and a deformable geometry technique is used. The effect of mesh size on wear results is evaluated, and a scaling factor is defined to relate the number of revolutions between the experiment and the numerical model. The simulation results indicate that the mesh size of the disc has a significant effect on the wear contour. The wear depth and wear width follow a normal distribution after experiencing a run-in phase, while the wear volume has a quadratic relation with the number of revolutions. For the studied material combination, the calibration of the wear coefficient shows that the wear volume of the pin-on-disc test accurately matches the simulation results for a minimum of eight revolutions with a wear coefficient lower than 2 × 10-11 Pa-1.