Inverse Kinematics for a Walking in-Pipe Robot Based on Linearization of Small Rotations

Abstract

Thepaper considers walking in-pipe robots, which represent a novel class of in-piperobots, with better agility but also a more complicated control compared withother, more prevalent in-pipe robot types. The focus of the paper is on theinverse kinematics (IK) of these robots. IK for walking in-pipe robots is adifficult problem due to a combination of factors, such as joint limits,multiple possible kinematic singularities, as well as a significant number ofjoints that these robots have. All this requires the use of an algorithm thatcould take into account multiple objectives and constraints when solving theproblem, and provide a solution in real time using on-board computers. Existingapproaches can achieve this with local linearization of both the objectivefunction and the constraints; alternatively they do it by taking the constraintsinto account. In this work, the IK is transformed into a quadratic program.Instead of linearizing the objective function, here the orientations of therobot’s links are approximated by convex combinations of rotation matrices.This allows relaxing the constraints associated with the special orthogonalgroup, placed on the matrices describing the links’ orientation. The papershows the form of the resulting quadratic program, discusses the practicalaspects of using this approach and lists its limitations.