Assessment of reaching laws for linear and nonlinear sliding surfaces: Improving performance of pipe crack sealing manipulator

Abstract

This study investigates the control of a tree-type pipe crack sealing manipulator (PCSM) with five specialized branches, designed to seal cracks inside the concrete pipes. This PCSM has the ability to navigate in vertical and horizontal pipes for crack repair tasks. A CAD model of the pipe with target crack and PCSM has been modelled in SolidWorks, and conclusive data of the crack has been further exported in Simulink for precise control. Observation and simulation studies in SolidWorks reveal that only the fifth branch of the PCSM successfully and effectively executes crack repair over substantial lengths. Furthermore, the repair of the crack has been assured for the branch of the PCSM. However, the accurate trajectory tracking in pipe crack sealing tasks is challenging due to model uncertainties and disturbances in confined environments. Sliding mode control (SMC) with various reaching laws for linear and nonlinear sliding surfaces has been examined to counter these challenges. The research investigated the efficacy of nine SMC reaching laws. These reaching laws are based on recent advancements in SMC. The novelty of this work uniquely compares nine reaching laws on both linear and nonlinear surfaces, where only CPRL (constant plus proportional rate reaching law) has previously been explored in nonlinear cases. Simulation-based evaluation using a SolidWorks-modeled PCSM and trajectory control in Simulink, incorporating mass uncertainty (+5 %) and joint disturbances equal to 40 % of the mean torque, demonstrates that nonlinear sliding surfaces consistently outperform linear ones in terms of tracking accuracy and disturbance rejection. Among the nine tested reaching laws on nonlinear surfaces, FTSMRL (novel fast terminal sliding mode reaching law), TSMRL (terminal sliding mode reaching law), and NSMRL (new sliding mode reaching law) demonstrated significantly lower tracking errors compared to the others, with the rms error of these three laws are comparable. The control efforts of FTSMRL and TSMRL were moderately high and chattering is very high compared to NSMRL. Therefore, NSMRL is proposed as the most suitable reaching law in this study due to its balanced performance, minimal chattering and control effort, as well reliable tracking accuracy. Furthermore, the study also calculated the reaching times for each law and confirmed their asymptotic stability using the Lyapunov stability criterion, demonstrating the efficacy of SMC in enhancing PCSM control.