Redundant robots can be used for additional optimization purposes with redundant degrees of freedom. Aiming at the problem of robot motion control under space constraints, the geometric invariance and sliding modal algorithm were used to realize the effective control of redundant robots, and the simulation results were verified. By establishing the mathematical model of the redundant robot system, the typical control scheme of the redundant robot trajectory tracking was given, and the redundant robot control target was optimized. The geometric invariance and sliding mode algorithm was deduced by which the robot joint position vector couldbe ensured in the constrained space, and the redundant robot joint could smoothly reach the constraint boundary.The planar 3R redundant robot system was simulated by the mathematical software MATLAB. At the same time, the simulation results were compare and analyze with the calculation results without using the algorithm. The simulation results show that when the redundant robot joint is subjected to external constraints, all the joints can be kept in the constrained space by geometric invariance and sliding modal algorithm. At the same time, the joint can smoothly approach the constraint boundary, and the joint error can converge quickly in 3.2 s.