Implementation of stability analysis approach for in-pipe inspection robot movement through pipeline fittings

The paper presents the implementation of the system stability testing approach based on the direct Lyapunov method. For this purpose, a pipeline inspection robot consisting of a driving and a driven part was used as an example. A kinematic model of the robot is shown, which describes its movement through the pipe fittings, the elbow, and the T-piece. In addition, a dynamic model based on the Lagrange function is given. The data set of this model is linearised and given in the so-called state space form, which is suitable for the application of the direct Lyapunov method. The approach is illustrated in a flow chart and is iterative in nature. The simulation was carried out with the computer program ©MATLAB.