An LQR-assisted Control Algorithm for an Under-actuated In-pipe Robot in Water Distribution Systems

TL;DR

This paper presents a control algorithm combining LQR and PID for an under-actuated in-pipe robot, enhancing its stabilization and mobility in water distribution systems through simulation validation.

Contribution

It introduces a novel control scheme integrating LQR and PID for an under-actuated pipe robot, validated via MATLAB simulations for improved stability and agility.

Findings

Controller stabilizes robot inside pipes with initial angles between -25° and +25°.

Robot maintains desired velocities of 10cm/s, 30cm/s, and 50cm/s.

Simulation confirms effective stabilization and mobilization in various conditions.

Abstract

To address the operational challenges of in-pipe robots in large pipes of water distribution systems (WDS), in this research, a control algorithm is proposed for our previously designed robot [4]. Our size adaptable robot has an under-actuated modular design that can be used for both leak detection and quality monitoring. First, nonlinear dynamical governing equations of the robot are derived with the definition of two perpendicular planes, and two sets of states are defined for the robot for stabilization and mobilization. For stabilization, we calculated the auxiliary system matrices and designed a stabilizer controller based on the linear quadratic regulator (LQR) controller, and combined it with a proportional-integral-derivative (PID) based controller for mobilization. The controller scheme is validated with simulation in MATLAB in various operation conditions in three iterations. The simulation results show that the controller can stabilize the robot inside the pipe by converging the stabilizing states to zero and keeping them in zero with initial values between -25 degree and +25 degree and tracking velocities of 10cm/s, 30cm/s, and 50cm/s which makes the robot agile and dexterous for operation in pipelines.