Intrinsic PID controller for a segway type mobile robot

The control of underactuated constrained systems have proven to be a challenging task. This paper extends an intrinsic geometric PID controller developed for fully actuated mechanical systems to a class of under actuated non-holonomic systems. As an illustration the results are applied to a self balancing Segway type mobile robot. The Segway is constrained to move under no slip conditions and has only two control inputs. We show that the geometric PID controller proposed in this paper ensures almost global locally exponential stability of the upright motion of the Segway even in the presence of large parameter uncertainties.