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In order to achieve high precision control of the constrained space robot, a reduced order adaptive neural network sliding mode control algorithm based on U-K (Udwadia-Kalaba) equation is proposed. Firstly, On the basis of the U-K equation and considering the ideal and non-ideal constrained forces at the terminal of the constrained space robot, the detailed dynamic equations are derived. Secondly, considering the uncertainty of the non-ideal constrained force (mainly the tangential force on the terminal of the constrained space robot) and the chattering phenomenon when using sliding mode control alone, the adaptive neural network sliding mode control algorithm is proposed to realize the high-precision tracking of each joint angle, angle speed and the non-ideal constrained force. Thirdly, for the constrained model of the system, the dynamic equation and the sliding mode controller are reduced to decrease the variables and simplify the calculation process. Finally, in order to verify the correctness and rationality of the proposed algorithm, the 2-DOF constrained space robot is taken as the simulated object. The simulation results show that the tracking errors of joint angles, angle speed and the non-ideal constrained force are less than 10-4 order of magnitude.