Vector-field-guided constraint-following control for path following of uncertain mechanical systems

Achieving dynamics-level control is a critical yet challenging problem for accurate, high-speed geometric path-following of uncertain robotic systems. This paper proposes a vector-field-guided constraint-following control framework for geometric path following of uncertain mechanical systems. The key idea is to encode vector-field guidance as a velocity constraint, enabling a unified force/torque control design for a class of fully actuated and underactuated systems with desired paths that may be self-intersecting. A global, explicit error estimate connects constraint-following accuracy to path-following performance with convergence guarantees. An adaptive robust extension further addresses heterogeneous time-varying uncertainties with unknown bounds and ensures ultimately bounded path-following error. Applications to an underactuated aircraft system and a fully actuated manipulator system demonstrate the effectiveness and advantages of the framework.