Tomas Berglund

Planning Smooth and Obstacle-Avoiding B-Spline Paths for Autonomous Mining Vehicles

We study the problem of automatic generation of smooth and obstacle-avoiding planar paths for efficient guidance of autonomous mining vehicles. Fast traversal of a path is of special interest. We consider fourwheel four-gear articulated vehicles and assume that we have an a priori knowledge of the mine wall environment in the form of polygonal chains. Computing quartic uniform B-spline curves, minimizing curvature variation, staying at least at a proposed safety margin distance from the mine walls, we plan high speed paths. We present a study where our implementations are successfully applied on eight path-planning cases arising from real-world mining data provided by the Swedish mining company Luossavaara-Kiirunavaara AB (LKAB). The results from the study indicate that our proposed methods for computing obstacle-avoiding minimum curvature variation B-splines yield paths that are substantially better than the ones used by LKAB today. Our simulations show that, with an average 32.13%, the new paths are faster to travel along than the paths currently in use. Preliminary results from the production at LKAB show an overall 5%-10% decrease in the total time for an entire mining cycle. Such a cycle includes both traveling, ore loading, and unloading.

An obstacle-avoiding minimum variation B-spline problem

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the minimum variation B-spline problem, which is a linearly constrained optimization problem over curves, defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.

Circle Sector Expansions for On-Line Exploration

A novel and effective method denoted circle sector expansion (CSE) is presented that can be used to generate reduced Voronoi diagrams. It is intuitive and can be used to efficiently compute possible paths for a vehicle. The idea is to model free space instead of the features in the environment. It is easy to implement and can be used while a vehicle moves and collects new data of its surrounding. The method is directly applicable and has properties for fast computations of safety margins while at the same time having low complexity. We have successfully implemented the algorithm and its methods and performed real-life tests using an autonomous wheelchair equipped with a range scanning laser, a rate gyro, and wheel-encoders. Tests showed good results for supporting the use of CSE. The results are applicable for example to improve assistive technology for wheelchair users.

Estimation of curl in paper using a combination of shape measurement and least-squares modelling

Abstract Curl is a quality problem that makes paper less suitable for printing. A paper sheet that has structural variations in its thickness such as gradients of fibre orientation, density and filler content, will curl and hence assume a cylindrical shape when its humidity content is changed. We propose a method to measure curl that can be used for automated analysis of the paper quality. The shape of the curled paper is measured using a stereoscopic camera system, which is capable of viewing a random pattern that is projected onto the specimen. The shape of the object is found by calculating the perspective difference in the camera set-up using digital image correlation. The quality parameters that are searched for are the magnitude of curl, which is defined as the inverse of the radius of curvature and the orientation of the curled paper. These parameters are estimated by performing a least-squares fit of a cylindrical shape to the three-dimensional measurement data. The least-squares model is non-linear and an iterative technique based on the Gauss–Newton algorithm is used.

Signature Graphs for Effective Localization

We present a novel method for the localization of an autonomous vehicle in two dimensions. Instead of focussing on properties of obstacles, we emphasize the description of free-space. We introduce the concept of signature graphs which is a compact data structure describing available free-space of an environment. It therefore also represents a map of the environment. A signature is an edge in the graph and is defined by seven parameters. An edge indicates that it is possible for the vehicle to move between two graph nodes. The signature graph is flexible and can easily be updated as new information about the environment is collected. We have with an autonomous wheelchair implemented our methods and tests them with successful results