Abstract: A situation in which a robot’s joint actuator torque amplitude and amplitude rate outputs are constrained is an actual problem which could be faced in space applications. This paper discusses a dynamics control problem for coordinated movement of an unknown parameter space robot system, under joint actuator torque amplitude and amplitude rate saturation constraints. According to linear momentum conversation and the Lagrange approach, a dynamic equation for a free-floating space robot system is developed. Based on it, a control scheme using an adaptive fuzzy neural network is proposed, which contraposes the joint actuator output torque’s amplitude and the saturation constraints of its rate to control the desired trajectory of the joint hinge to follow the expected movement track of the space robot system. Said control scheme is combined with an adaptive fuzzy neural network controller and an anti-saturation parameter adaptive law. Firstly, the finite difference approximation is used to transform an amplitude rate saturation constraint condition into an amplitude saturation constraint condition, which is compared with a torque limiting condition which been set in advance in this paper, ensuring a limited range of torque trends in every sampling moment, thus guaranteeing that the output torque of the actuator is within the dynamic limited range by designing an anti-saturation parameter adaptive law. Based on the stability theory of Lyapunov, it proves said controller may ensure that the control system is asymptotically stable. Simulation comparison experiments testify to the effectiveness of this control scheme.