The PIDcontroller is a time-tested and versatile controller in control theory. It hasonly three parameters - the proportional, integral and derivative gains and itguarantees robustness to constant disturbances in the system. For second orderlinear systems, the design of PID controller is straightforward and simple. Allmechanical systems are intrinsically second order linear systems as accordingto Newton’s laws, the force vector is directly proportional to the accelerationvector which is the second derivative of position. However, since mostmechanical systems evolve on non-linear spaces (smooth manifolds), there is noglobal coordinate system that is free of singularities. Also, when theequations of motions are written down in such local coordinates, they becomehighly non-linear and hence difficult to analyze. Therefore, the need forthinking geometrically regarding systems without any algebra of coordinatesbecomes imperative. In this talk, a geometric analog of the PID controller ispresented for mechanical systems whose configuration spaces are Lie Groups andare subject to non-holonomic constraints on velocity. Applications abound asall mechanical systems are constrained interconnections of rigid bodies and theconfiguration space of a rigid body is a Lie group called the Special EuclideanGroupin three dimensions.