Håkan Jonsson

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.

Finding the shortest watchman route in a simple polygon

Abstract. We present the first polynomial time algorithm that finds the shortest route in a simple polygon such that all points of the polygon are visible from the route. This route is called the shortest watchman route, and we do not assume any restrictions on the route or on the simple polygon. Our algorithm runs in worst case O(n6) time, but it is adaptive, making it run faster on polygons with a simple structure.

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.

Finding the Shortest Watchman Route in a Simple Polygon

We present the first polynomial-time algorithm that finds the shortest route in a simple polygon such that all points of the polygon is visible from some point on the route. This route is sometimes called the shortest watchman route, and it does not allow any restrictions on the route or on the simple polygon. Our algorithm runs in O(n3) time.

Computing a Shortest Watchman Path in a Simple Polygon in Polynomial-Time

In this paper we present the first polynomial-time algorithm for finding the shortest polygonal chain in a simple polygon such that each point of the polygon is visible from some point on the chain. This chain is called the shortest watchman path, or equivalently, the shortest weakly visible curve of the polygon. In proving this result we also give polynomial time algorithms for finding the shortest aquarium-keepers path that visits all edges of the polygon, and for finding the shortest postman path that visits all vertices of a polygon.

The Traveling Salesman Problem for lines in the plane

Abstract We present an algorithm that computes the shortest route that intersects n lines in the plane in time polynomial in n; the time complexity is dominated by the time it takes to compute a shortest watchman route in a simple polygon of size n. We also present a simple O(n) time algorithm for computing a route that intersects the lines but which is guaranteed to have a length at most 2 times longer than the shortest route.

An approximative solution to the Zookeeper's Problem

Consider a simple polygon P containing disjoint convex polygons each of which shares an edge with P. The Zookeepers Problem then asks for the shortest route in P that visits all convex polygons without entering their interiors. Existing algorithms that solve this problem run in time super-linear in the size of P and the convex polygons. They also suffer from numerical problems.In this paper, we shed more light on the problem and present a simple linear time algorithm for computing an approximate solution. The algorithm mainly computes shortest paths and intersections between lines using basic data structures. It does not suffer from numerical problems. We prove that the computed approximation route is at most 6 times longer than the shortest route in the exact solution.

Using flipped classroom, peer discussion, and just-in-time teaching to increase learning in a programming course

In this paper we report on an experiment conducted in an attempt to improve further the learning environment in a basic campus course on Object-Oriented Programming and Design given to first-year engineering students studying Computer Science and Engineering. This course has for years had the same traditional set-up that is common also in other engineering schools around the world including lectures, mandatory programming assignments, and a final written exam. What we did was to substitute the lectures for in-class sessions based on a variant of the teaching method known as “flipping the classroom” combined with certain elements of Peer Discussion and Just-in-time teaching. To make all this work, we introduced a web-based MOOC tool into the course. To be able to investigate the quantitative effects of our experiment, we had an experiment class consisting of 70 students taking the course in this new way and a control class of 57 students taking the course in the traditional way. On the final written exam, which was identical for the two classes and marked the same way, 81% of the students in the experiment class passed compared to 60% in the control class. Moreover, the share of students passing with good grades was 58% in the experiment class compared to 32% in the control class. So, not only did the share of students passing the course increase by a third, but also the share of students passing with good grades almost doubled.

Structuring and Presenting Lifelogs Based on Location Data

Lifelogging techniques help individuals to log their life and retrieve important events, memories and experiences. Structuring lifelogs is a major challenge in lifelogging systems since the system should present the logs in a concise and meaningful way to the user. In this paper the authors present an approach for structuring lifelogs as places and activities based on location data. The structured lifelogs are achieved using a combination of density-based clustering algorithms and convex hull construction to identify the places of interest. The periods of time where the user lingers at the same place are then identified as possible activities. In addition to structuring lifelogs the authors present an application in which images are associated to the structuring results and presented to the user for reviewing. The system is evaluated through a user study consisting of 12 users, who used the system for 1 day and then answered a survey. The proposed approach in this paper allows automatic inference of information about significant places and activities, which generates structured image-annotated logs of everyday life.

Voronoi-Based ISD and Site Density Characteristics for Mobile Networks

Inter-Site Distance (ISD) is a common measure for characterizing the site density in a mobile network. However, obtaining a good estimation of the ISD for a real world network is not trivial since the physical layout is usually quite more complex than a perfect theoretical hexagonal grid, due to a number of unavoidable factors such as site availability and traffic density. Voronoi diagrams have been suggested for approximating cells from network layouts, providing a method for partitioning the covered area into cells defined by the proximity to the given set of sites. This yields a framework for site coverage approximation based on the actual site distribution, rather than an underlying theoretical model. We present a novel measure, based on Voronoi diagrams, for characterizing the site density of a cellular network and provide a comparison to the more traditional ISD measure. This measure improves capacity assessments and modeling of real networks.