  In this paper, we propose to use a nonlinear adaptive PID controller to
regulate the joint variables of a mobile manipulator. The motion of the mobile
base forces undue disturbances on the joint controllers of the manipulator. In
designing a conventional PID controller, one should make a trade-off between
the performance and agility of the closed-loop system and its stability
margins. The proposed nonlinear adaptive PID controller provides a mechanism to
relax the need for such a compromise by adapting the gains according to the
magnitude of the error without expert tuning. Therefore, we can achieve agile
performance for the system while seeing damped overshoot in the output and
track the reference as close as possible, even in the presence of external
disturbances and uncertainties in the modeling of the system. We have employed
a Bayesian optimization approach to choose the parameters of a nonlinear
adaptive PID controller to achieve the best performance in tracking the
reference input and rejecting disturbances. The results demonstrate that a
well-designed nonlinear adaptive PID controller can effectively regulate a
mobile manipulator's joint variables while carrying an unspecified heavy load
and an abrupt base movement occurs.
