Concurrent Dynamic Programming for Grid-Based Optimisation Problems Stephen Cossell A DISSERTATION SUBMITTED IN FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. May 2015 School of Mechanical and Manufacturing Engineering Faculty of Engineering The University of New South Wales Sydney, NSW 2052, Australia PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet Surname or Family name: Cossell First name: Stephen Abbreviation for degree as given in the University calendar: PhD School: Mechanical and Manufacturing Engineering Faculty: Engineering Title: Concurrent dynamic programming for grid-based optimisation problems. Abstract 350 words maximum: (PLEASE TYPE) A particular class of optimisation problems can be solved using a technique known as dynamic programming. This technique applies to problems that have many possible solutions, each consisting of a number of individual decision points. In theory, a globally optimal solution relative to a given metric can be obtained by recursively choosing the most optimal option at each decision point. In practice, however, applications of dynamic programming are computationally expensive for the scale of real-world domains. This thesis examines the existing array of robot motion planning algorithms and applications, a core application of dynamic programming for ground and aerial vehicles. In particular, the thesis highlights that the sequential nature of traditional algorithms does not scale in practice as modern central processing units begin to reach physical limits in terms of computational throughput. This thesis then outlines current parallel processing unit architectures that have emerged in the last decade with particular focus on graphical processing units. The main contribution of this thesis is a new class of concurrent dynamic programming algorithms that are applicable to multi-core processor architectures. The core mechanic of the algorithms is proven to generate an equally optimal global solution to existing sequential algorithms, with a computational complexity of O(n), assuming enough cores are available relative to the problem size. Various implementation flavours are developed and benchmarked over a variety of two-dimensional configuration spaces, with the most efficient being able to plan on the scale of the main campus of the University of New South Wales (a 1000m×500m area) with 1m×1m resolution in sub-second time. Higher dimensional configuration spaces are also investigated with a proof-of-concept experiment presented to assess the feasibility and performance as the dimensionality increases | a factor notorious in traditional approaches that increases the computational complexity exponentially. The work presented here gains an increased concurrent benefit as the dimensionality of the problem increases and hence is able to perform an order of magnitude more efficiently in the presented three-dimensional experiments. Designing concurrent algorithms can be more difficult, but the implementation benefits will continue to increase as the level of parallelism found in modern hardware approaches that found in nature. Declaration relating to disposition of project thesis/dissertation I hereby grant to the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all property rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstracts International (this is applicable to doctoral theses only). 21st September 2015 Signature Witness Date The University recognises that there may be exceptional circumstances requiring restrictions on copying or conditions on use. Requests for restriction for a period of up to 2 years must be made in writing. Requests for a longer period of restriction may be considered in exceptional circumstances and require the approval of the Dean of Graduate Research. FOR OFFICE USE ONLY Date of completion of requirements for Award: 1 Concurrent Dynamic Programming for Grid-Based Optimisation Problems Stephen Cossell Abstract A particular class of optimisation problems can be solved using a technique known as dynamic programming. This technique applies to problems that have many possible solutions, each consisting of a number of individual decision points. In theory, a globally optimal solution relative to a given metric can be obtained by recursively choosing the most optimal option at each decision point. In practice, however, applications of dynamic programming are computationally expensive for the scale of real-world domains. This thesis examines the existing array of robot motion planning algorithms and applications, a core application of dynamic programming for ground and aerial vehicles. In particular, the thesis highlights that the sequential nature of traditional algorithms does not scale in practice as modern central processing units begin to reach physical limits in terms of computational throughput. This thesis then outlines current parallel processing unit architectures that have emerged in the last decade with particular focus on graphical processing units. The main contribution of this thesis is a new class of concurrent dynamic pro- gramming algorithms that are applicable to multi-core processor architectures. The core mechanic of the algorithms is proven to generate an equally optimal global so- lution to existing sequential algorithms, with a computational complexity of O(n), assuming enough cores are available relative to the problem size. Various implemen- tation flavours are developed and benchmarked over a variety of two-dimensional configuration spaces, with the most efficient being able to plan on the scale of the main campus of the University of New South Wales (a 1000m×500m area) with 1m×1m resolution in sub-second time. Higher dimensional configuration spaces are also investigated with a proof-of- i concept experiment presented to assess the feasibility and performance as the di- mensionality increases | a factor notorious in traditional approaches that increases the computational complexity exponentially. The work presented here gains an in- creased concurrent benefit as the dimensionality of the problem increases and hence is able to perform an order of magnitude more efficiently in the presented three- dimensional experiments. Designing concurrent algorithms can be more difficult, but the implementation benefits will continue to increase as the level of parallelism found in modern hardware approaches that found in nature. ii Originality Statement I hereby declare that this submission is my own work and to the best of my knowl- edge it contains no materials previously published or written by another person, or substantial proportions of material with have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowl- edged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged. Stephen Cossell Signed: Date: 21st September 2015 iii Copyright Statement I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or part in the University libraries in all forms of media, now and here after known, subject to the provisions of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstract International (this is applicable to doctoral theses only). I have either used no substantial portions of copyright material in my theses of I have obtained permission to use copyright material; where permission has not been granted I have applied/will apply for a partial restriction of the digital copy of my thesis or dissertation. Signed: Date: 21st September 2015 Authenticity Statement I certify that the Library deposit digital copy is a direct equivalent of the final officially approved version of my thesis. No emendation of content has occurred and if there are minor variations in formatting, they are the result of the conversion to digital format. Signed: Date: 21st September 2015 iv Publications Relevant Peer Reviewed Journal Publications • S. Cossell and J. Guivant, \Concurrent dynamic programming for grid-based problems and its application for real-time path planning," Robotics and Au- tonomous Systems, Vol. 62, No. 6, pp. 737-751, June 2014. (DOI: 10.1016/j.robot.2014.03.002) • S. Cossell and J. Guivant, \Parallel evaluation of a spatial travesability cost function on GPU for efficient path planning," Journal of Intelligent Learning Systems and Applications, Vol. 3, No. 4, pp. 191-200, November 2011. (DOI: 10.4236/jilsa.2011.34022) Relevant Peer Reviewed Conferences • S. Cossell and J. Guivant,