an approach to the dynamic modeling and sliding mode control of the constrained robot is proposed in this article. on the basis of the udwadia-kalaba approach, the explicit equation of the constrained robot system is obtained first. this equation is applicable to systems with either holonomic or non-holonomic constraints, as well as with either ideal or non-ideal constraint forces. second, fully considering the uncertainty of the non-ideal force, that is, the dynamic friction in the constrained robot system, the sliding mode control algorithm is put forward to trajectory tracking of the end-effector on a vertical constrained surface to obtain actual values of the unknown constraint force. moreover, model order reduction method is innovatively used in the udwadia-kalaba approach and sliding mode controller to reduce variables and simplify the complexity of the calculation. based on the demonstration of this novel method, a detailed robot system example is finally presented.