Partitioning de Bruijn Graphs into Fixed-Length Cycles for Robot Identification and Tracking

We propose a new camera-based method of robot identification, tracking and orientation estimation. The system utilises coloured lights mounted in a circle around each robot to create unique colour sequences that are observed by a camera. The number of robots that can be uniquely identified is limited by the number of colours available, $q$, the number of lights on each robot, $k$, and the number of consecutive lights the camera can see, $\ell$. For a given set of parameters, we would like to maximise the number of robots that we can use. We model this as a combinatorial problem and show that it is equivalent to finding the maximum number of disjoint $k$-cycles in the de Bruijn graph $\text{dB}(q,\ell)$. We provide several existence results that give the maximum number of cycles in $\text{dB}(q,\ell)$ in various cases. For example, we give an optimal solution when $k=q^{\ell-1}$. Another construction yields many cycles in larger de Bruijn graphs using cycles from smaller de Bruijn graphs: if $\text{dB}(q,\ell)$ can be partitioned into $k$-cycles, then $\text{dB}(q,\ell)$ can be partitioned into $tk$-cycles for any divisor $t$ of $k$. The methods used are based on finite field algebra and the combinatorics of words.Comment: 16 pages, 4 figures. Accepted for publication in Discrete Applied Mathematic

Review of hardware cost estimation methods, models and tools applied to early phases of space mission planning

The primary purpose of this paper is to review currently existing cost estimation methods, models, tools and resources applicable to the space sector. While key space sector methods are outlined, a specific focus is placed on hardware cost estimation on a system level, particularly for early mission phases during which specifications and requirements are not yet crystallised, and information is limited. For the space industry, cost engineering within the systems engineering framework is an integral discipline. The cost of any space program now constitutes a stringent design criterion, which must be considered and carefully controlled during the entire program life cycle. A first step to any program budget is a representative cost estimate which usually hinges on a particular estimation approach, or methodology. Therefore appropriate selection of specific cost models, methods and tools is paramount, a difficult task given the highly variable nature, scope as well as scientific and technical requirements applicable to each program. Numerous methods, models and tools exist. However new ways are needed to address very early, pre-Phase 0 cost estimation during the initial program research and establishment phase when system specifications are limited, but the available research budget needs to be established and defined. Due to their specificity, for vehicles such as reusable launchers with a manned capability, a lack of historical data implies that using either the classic heuristic approach such as parametric cost estimation based on underlying CERs, or the analogy approach, is therefore, by definition, limited. This review identifies prominent cost estimation models applied to the space sector, and their underlying cost driving parameters and factors. Strengths, weaknesses, and suitability to specific mission types and classes are also highlighted. Current approaches which strategically amalgamate various cost estimation strategies both for formulation and validation of an estimate, and techniques and/or methods to attain representative and justifiable cost estimates are consequently discussed. Ultimately, the aim of the paper is to establish a baseline for development of a non-commercial, low cost, transparent cost estimation methodology to be applied during very early program research phases at a complete vehicle system level, for largely unprecedented manned launch vehicles in the future. This paper takes the first step to achieving this through the identification, analysis and understanding of established, existing techniques, models, tools and resources relevant within the space sector

Vision-Based Cooperative Pose Estimation for Localization in Multi-Robot Systems Equipped with RGB-D Cameras

We present a new vision based cooperative pose estimation scheme for systems of mobile robots equipped with RGB-D cameras. We first model a multi-robot system as an edge-weighted graph. Then, based on this model, and by using the real-time color and depth data, the robots with shared field-of-views estimate their relative poses in pairwise. The system does not need the existence of a single common view shared by all robots, and it works in 3D scenes without any specific calibration pattern or landmark. The proposed scheme distributes working loads evenly in the system, hence it is scalable and the computing power of the participating robots is efficiently used. The performance and robustness were analyzed both on synthetic and experimental data in different environments over a range of system configurations with varying number of robots and poses