Aiming at the problem that the tracking error of mobile robot is large and the input torque is large, the Riccati differential controller is designed and the control effect is verified by simulation. A wheeled mobile cooperative robot was created, the dynamic equation of robot motion was derived, and a state-dependent Riccati differential controller was designed by referring to Riccati differential equation. Under the nonholonomic constraints, the parameterization of robot state correlation coefficient and control structure were deduced, and the Riccati differential controller was achieved of the stability of the moving manipulator. MATLAB software was used to simulate the motion output error and input torque of the mobile robot. The results show that the method overcomes the instability problem of the robot’s nonholonomic constraint system, with the maximum output error reduced by 424% and the response time of input torque shortened by 50%. The Riccati differential controller can improve the tracking accuracy and the motion stability of the robot. The research research results provide a theoretical basis for the in-depth study of robot control methods.