I. Introduction
Constraints (holonomic or nonholonomic) are usually used to describe the performance of the mechanical system in Lagrangian mechanics. From the control point of view, the central focus is to identify the control force or torque that renders the system to obey the constraints, which we shall call the constraint following. In the recent past, research efforts can be found in, for example, [1]–[8] and their bibliographies. In practice, if the constraint-following error, despite being small ultimately, is too large during the transient period, the performance may not be acceptable. This issue, which we shall call the bounded constraint-following error, is of practical significance.