Brief Announcement: Energy Constrained Depth First Search

Depth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this is asymptotically optimal over all exploration strategies. This paper considers a variant of such search strategies where the length of each route is bounded by a positive integer B (e.g. due to limited energy resources of the searcher). The objective is to cover all the edges of a tree T using the minimum number of routes, each starting and ending at the root and each being of length at most B. To this end, we analyze the following natural greedy tree traversal process that is based on decomposing a depth first search traversal into a sequence of limited length routes. Given any arbitrary depth first search traversal R of the tree T, we cover R with routes R_1,...,R_l, each of length at most B such that: R_i starts at the root, reaches directly the farthest point of R visited by R_{i-1}, then R_i continues along the path R as far as possible, and finally R_i returns to the root. We call the above algorithm piecemeal-DFS and we prove that it achieves the asymptotically minimal number of routes l, regardless of the choice of R. Our analysis also shows that the total length of the traversal (and thus the traversal time) of piecemeal-DFS is asymptotically minimum over all energy-constrained exploration strategies. The fact that R can be chosen arbitrarily means that the exploration strategy can be constructed in an online fashion when the input tree T is not known in advance. Each route R_i can be constructed without any knowledge of the yet unvisited part of T. Surprisingly, our results show that depth first search is efficient for energy constrained exploration of trees, even though it is known that the same does not hold for energy constrained exploration of arbitrary graphs

A Constant-Factor Approximation Algorithm for Online Coverage Path Planning with Energy Constraint

In this paper, we study the problem of coverage planning by a mobile robot with a limited energy budget. The objective of the robot is to cover every point in the environment while minimizing the traveled path length. The environment is initially unknown to the robot. Therefore, it needs to avoid the obstacles in the environment on-the-fly during the exploration. As the robot has a specific energy budget, it might not be able to cover the complete environment in one traversal. Instead, it will need to visit a static charging station periodically in order to recharge its energy. To solve the stated problem, we propose a budgeted depth-first search (DFS)-based exploration strategy that helps the robot to cover any unknown planar environment while bounding the maximum path length to a constant-factor of the shortest-possible path length. Our $O(1)$-approximation guarantee advances the state-of-the-art of log-approximation for this problem. Simulation results show that our proposed algorithm outperforms the current state-of-the-art algorithm both in terms of the traveled path length and run time in all the tested environments with concave and convex obstacles

Electrical switching in a diakoptics based tram traction simulation tool and its implementation in a SCADA environment

Safe electrical switching is a pre-requisite for secure and reliable operation and maintenance in any electrical utility and traction network. Electrical system safety regulatory bodies and corporate electrical regulations provide protocols including ‘no inadvertent system switching’ and are very strict regarding system safety policies and practices. An electrical High Voltage system ensures coded, legal and safe operational practices to achieve the required system safety, meeting, for instance, ‘on-time-every-time’ operational requirements. Every electrical entity needs to report their safe work practices in proper system safety documentation and effective coded demonstrations, and ensure safety through training-refresher programs to be accredited by technical commission and regulators. Electrical industries usually track real-time system parameters by remote monitoring, higher-level visual foot patrols, local-drone-online camera monitoring and preventative maintenance plans over the lifetime of the network system-switchgear maintenance regime. They undertake required maintenance and corrective progressive work with a systematically safe approach and in a documented manner. Safe electrical system isolation-restoration programs and effective workgroup safety is guaranteed by job specific risk assessment and job safety procedures. This thesis proposes an automated isolation-restoration switching method to be applied in the traction industry with special emphasis on system safety switching practices. It elaborates on how diakoptics, a mathematical method of tearing, stands out as one of the best methods to simulate and analyze a large-scale tram traction network. Examples based on traction systems in Adelaide, South Australia are used in this thesis as case studies on safe and effective isolation-restoration switching practices. The diakoptics algorithm splits a complex traction network into smaller pieces which are solved separately, and gets the optimized simulation of the whole electrical network in real time. Solutions of electrical subsections are combined to produce the correct representation of the entire network’s de-energized or energized switchgear state at a given time. The diakoptics - based ‘model tram traction simulator’ has been developed to cope with the system safety network switchgear orientation and system operational switching requirements. The model focuses on achieving electrical section-wise bottom to up topological power isolation, operational power restoration and entire network instantaneous electrical isolation-restoration in planned, unplanned and absolute emergency situations. A competent electrical operator, by working with the mimic of the traction simulator overhead and substation switchgear, can make an informed decision to progress. The on-duty electrical control officer updates the simulator to a system operational status. As the simulator switchgear connection-orientation mimics the real-time system switchgear operational state, the crew virtually makes a real-time patrol of the work location and the isolation limits, being able to plan safe maintenance work or prepare for a system upgrade. The system switching demonstrations, formally approved switching templates, related catenary system and detailed substation switchgear mimics which the maintainer requires are also included in the simulation tool. An automated isolation-restoration switching program to undertake any planned, unplanned and emergency maintenance work has been extensively tested and verified. The simulator has been upgraded to accommodate any future extensions and bypasses of the network. ‘One click’ immediate remote de-energization of the entire traction system has been included in the tool. Asset management, system safety management options, and system remote switching have been addressed. The tool is also capable of accommodating for future legislative changes to remote locking & tagging requirements.Thesis (Ph.D.) -- University of Adelaide, Electrical and Electronic Engineering, 202

Brief announcement: Energy constrained depth first search

Depth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this is asymptotically optimal over all exploration strategies. This paper considers a variant of such search strategies where the length of each route is bounded by a positive integer B (e.g. due to limited energy resources of the searcher). The objective is to cover all the edges of a tree T using the minimum number of routes, each starting and ending at the root and each being of length at most B. To this end, we analyze the following natural greedy tree traversal process that is based on decomposing a depth first search traversal into a sequence of limited length routes. Given any arbitrary depth first search traversal R of the tree T, we cover R with routes R_1,...,R_l, each of length at most B such that: R_i starts at the root, reaches directly the farthest point of R visited by R_{i-1}, then R_i continues along the path R as far as possible, and finally R_i returns to the root. We call the above algorithm piecemeal-DFS and we prove that it achieves the asymptotically minimal number of routes l, regardless of the choice of R. Our analysis also shows that the total length of the traversal (and thus the traversal time) of piecemeal-DFS is asymptotically minimum over all energy-constrained exploration strategies. The fact that R can be chosen arbitrarily means that the exploration strategy can be constructed in an online fashion when the input tree T is not known in advance. Each route R_i can be constructed without any knowledge of the yet unvisited part of T. Surprisingly, our results show that depth first search is efficient for energy constrained exploration of trees, even though it is known that the same does not hold for energy constrained exploration of arbitrary graphs