This paper investigates the tracking control issue of a class of complicated space robots subject to actuator saturation and faults, unmodeled dynamics and external disturbances under asymmetric error constraints, and develops a Bias Radial Basis Function Neural Network (BIAS-RBFNN) based intelligent adaptive fault tolerant control scheme. First, considering that the unmodeled dynamics may be coupled with the states and inputs of the system, dynamic auxiliary signal and related mathematical tools are used to decouple and suppress the coupling uncertainties. Moreover, a mapping function based nonlinear error transformation technology is utilized to guarantee the transient performance of the system. Considering the shortcomings of traditional neural networks, the BIAS-RBFNNs have been constructed to improve the approximation and compensation performance. Finally, numerical simulations are carried out to illustrate the effectiveness and advantages of the proposed BIAS-RBFNN based intelligent adaptive fault tolerant control method.