  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.
