Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

Voronoi diagrams—a survey of a fundamental geometric data structure

Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)

During the last decade, sampling-based path planning algorithms, such as probabilistic roadmaps (PRM) and rapidly exploring random trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g. as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g. showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e. such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

Sampling-based algorithms for optimal motion planning

This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.

Algorithms in Combinatorial Geometry

This paper provides a unified discussion of the Delaunay triangulation. Its geometric properties are reviewed and several applications are discussed. Two algorithms are presented for constructing the triangulation over a planar set ofN points. The first algorithm uses a divide-and-conquer approach. It runs inO(N logN) time, which is asymptotically optimal. The second algorithm is iterative and requiresO(N
2) time in the worst case. However, its average case performance is comparable to that of the first algorithm.

/pdf/two-algorithms-for-constructing-a-delaunay-triangulation-27hvskxlr4.pdf

Two algorithms for constructing a Delaunay triangulation

Travel time is a fundamental measure in transportation. Accurate travel-time prediction also is crucial to the development of intelligent transportation systems and advanced traveler information systems. We apply support vector regression (SVR) for travel-time prediction and compare its results to other baseline travel-time prediction methods using real highway traffic data. Since support vector machines have greater generalization ability and guarantee global minima for given training data, it is believed that SVR will perform well for time series analysis. Compared to other baseline predictors, our results show that the SVR predictor can significantly reduce both relative mean errors and root-mean-squared errors of predicted travel times. We demonstrate the feasibility of applying SVR in travel-time prediction and prove that SVR is applicable and performs well for traffic data analysis.

/pdf/travel-time-prediction-with-support-vector-regression-3nxajn3hpe.pdf

Travel-time prediction with support vector regression

Security remains a major roadblock to universal acceptance of the Web for many kinds of transactions, especially since the recent sharp increase in remotely exploitable vulnerabilities have been attributed to Web application bugs. Many verification tools are discovering previously unknown vulnerabilities in legacy C programs, raising hopes that the same success can be achieved with Web applications. In this paper, we describe a sound and holistic approach to ensuring Web application security. Viewing Web application vulnerabilities as a secure information flow problem, we created a lattice-based static analysis algorithm derived from type systems and typestate, and addressed its soundness. During the analysis, sections of code considered vulnerable are instrumented with runtime guards, thus securing Web applications in the absence of user intervention. With sufficient annotations, runtime overhead can be reduced to zero. We also created a tool named.WebSSARI (Web application Security by Static Analysis and Runtime Inspection) to test our algorithm, and used it to verify 230 open-source Web application projects on SourceForge.net, which were selected to represent projects of different maturity, popularity, and scale. 69 contained vulnerabilities. After notifying the developers, 38 acknowledged our findings and stated their plans to provide patches. Our statistics also show that static analysis reduced potential runtime overhead by 98.4%.

/pdf/securing-web-application-code-by-static-analysis-and-runtime-3407usw3c4.pdf

Securing web application code by static analysis and runtime protection

The medial axis transformation is a means first proposed by Blum to describe a shape. In this paper we present a 0(n log n) algorithm for computing the medial axis of a planar shape represented by an n-edge simple polygon. The algorithm is an improvement over most previously known results interms of both efficiency and exactness and has been implemented in Fortran. Some computer-plotted output of the program are also shown in the paper.

Medial Axis Transformation of a Planar Shape

We study the computational complexity of the art gallery problem originally posed by Klee, and its variations. Specifically, the problem of determining the minimum number of vertex guards that can see an n -wall simply connected art gallery is shown to be NP-hard. The proof can be modified to show that the problems of determining the minimum number of edge guards and the minimum number of point guards in a simply connected polygonal region are also NP-hard. As a byproduct, the problem of decomposing a simple polygon into a minimum number of star-shaped polygons such that their union is the original polygon is also shown to be NP-hard.

Der-Tsai Lee

Papers

Two algorithms for constructing a Delaunay triangulation

Travel-time prediction with support vector regression

Securing web application code by static analysis and runtime protection

Medial Axis Transformation of a Planar Shape

Computational complexity of art gallery problems