A unified approach to general constraint motion control is presented. Robotic systems interacting with the task environment having complex dynamics are described as a set of state equations and algebraic constraints; the former represents the dynamics of the individual robots and task processes, and the latter describes the constraints and boundary conditions created by the interactions among the robots and the task processes. The resultant mathematical model of the constrained system is high-index differential-algebraic equations (DAE). This paper provides a powerful solver for this class of high-index DAE by using sliding mode control and singular perturbation theories. The singularly perturbed sliding manifolds method guarantees computational stability and accuracy. A numerical example illustrates the modeling and realization procedure and its computational performance.