@article{article_494343, title={Inverse Kinematics for a Walking in-Pipe Robot Based on Linearization of Small Rotations}, journal={The Eurasia Proceedings of Science Technology Engineering and Mathematics}, pages={50–55}, year={2018}, author={Savın, Sergei and Vorochaev, Alexander and Vorochaeva, Ludmila}, keywords={In-pipe walking robot,Inverse kinematics,Orthogonal matrices,Constraint relaxation}, abstract={ The paper considers walking in-pipe robots, which represent a novel class of in-pipe robots, with better agility but also a more complicated control compared with other, more prevalent in-pipe robot types. The focus of the paper is on the inverse kinematics (IK) of these robots. IK for walking in-pipe robots is a difficult problem due to a combination of factors, such as joint limits, multiple possible kinematic singularities, as well as a significant number of joints that these robots have. All this requires the use of an algorithm that could take into account multiple objectives and constraints when solving the problem, and provide a solution in real time using on-board computers. Existing approaches can achieve this with local linearization of both the objective function and the constraints; alternatively they do it by taking the constraints into account. In this work, the IK is transformed into a quadratic program. Instead of linearizing the objective function, here the orientations of the robot’s links are approximated by convex combinations of rotation matrices. This allows relaxing the constraints associated with the special orthogonal group, placed on the matrices describing the links’ orientation. The paper shows the form of the resulting quadratic program, discusses the practical aspects of using this approach and lists its limitations. }, number={4}, publisher={ISRES Publishing}