Robot trajectory tracking is intrinsically limited by the interplay of kinematic and dynamic constraints

while current theories have primarily investigated these limitations separately from one another. In this work

we analyze the role of the coupling between kinematic and dynamic constraints in the determination of theoretical performance limits of trajectory tracking using principles of analytical mechanics

control theory

and nonlinear dynamics. Specifically

we develop a theoretical framework for quantifying the coupling of constraints and its implications for trajectory tracking. Our results show that both kinematic and dynamic constraints affect trajectory tracking by their mutual interactions: the dynamic feasibility of a trajectory depends not only on its geometry but also on its time parameterization

whereas dynamic capabilities of the robot define the feasible set of kinematically feasible trajectories. In addition

we introduce the notion of the "feasibility region of trajectory tracking" as the set of feasible reference trajectories with respect to the robot's kinematic and dynamic capabilities. We derive necessary and sufficient conditions for tracking feasibility and characterize the tracking error bounds that depend on the mismatch between desired and feasible accelerations. This study contributes a theoretical basis for trajectory planning

control design

and performance assessment

providing actionable insights for robot design and operation.