Crack Sealing Control of Concrete Pipe by Robust Sliding Mode Control with Different Reaching Law

In this work, the branch (three links) of the tree robot has been controlled for crack sealing. This tree robot dealt with the tree robot for repair and maintenance purposes. This tree robot manoeuvres inside the vertical pipe, horizontal pipes and surfaces. A CAD model of the pipe has been modelled in SolidWorks, and a mimic of the existing crack has been simulated inside the pipes. Furthermore, the crack repair has been assured for the branch of the tree robot. However, due to the presence of uncertainty and disturbances, the end-effector of the tree robot doesn’t follow the desired crack trajectory. The control of crack trajectory in the presence of parametric perturbation and external disturbance is a challenging task. Sliding mode control is a well-known method to address such types of problems. Therefore, the sliding mode control (SMC) is proposed with different reaching laws for this work. The four-reaching laws of SMC, constant rate reaching law (CRL), constant plus proportional rate reaching law (CPPRL), power rate reaching law (PRRL) and general reaching law (GRL) have been designed and compared. After performing the simulation and numerous iterations, it has been found that the CPPRL reaching law gives a more promising result in comparison with other mentioned laws. However, the constant rate reaching has to be less chattering than other reaching laws. Furthermore, the work exploits the Lyapunov candidate function to ensure the asymptotic stability of the crack trajectory.