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This paper discusses the design and implementation of the Modular Pipe Climber inside ASTM D1785 -15e1 standard pipes [1]. The robot has three tracks which operate independently and are mounted on three modules which are oriented at 120° to each other. The tracks provide for greater surface traction compared to wheels [2]. The tracks are pushed onto the inner wall of the pipe by passive springs which help in maintaining the contact with the pipe during vertical climb and while turning in bends. The modules have the provision to compress asymmetrically, which helps the robot to take turns in bends in all directions. The motor torque required by the robot and the desired spring stiffness are calculated at quasistatic and static equilibriums when the pipe climber is in a vertical climb. The springs were further simulated and analyzed in ADAMS MSC. The prototype built based on these obtained values was experimented on, in complex pipe networks. Differential speed is employed when turning in bends to improve the efficiency and reduce the stresses experienced by the robot.

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Abstract. Clustering and classification hierarchies are organizational structures of a set of objects. Multiple hierarchies may be derived over the same set of objects, which makes distance computation between hierarchies an important task for summarization and similarity search of hierarchical patterns. In this paper, we model the classification and clustering hierarchies as rooted, leaf-labeled, unordered trees. We propose a novel distance metric Split-Order distance to evaluate the organizational structure difference between two hierarchies over the same set of leaf objects. The Split-Order distance reflects the order in which subsets of the tree leaves are differentiated from each other and can be used to explain the relationships between the leaf objects. We also propose an efficient algorithm for computing Split-Order distance between two trees in O(n 2 d 4 ) time, where n is the number of leaves, and d is the maximum number of children of any node. Our experiments on both real and synthetic data demonstrate the efficiency and effectiveness of our algorithm.