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Summary: In this article, the problem of finite‐time attitude‐tracking control for rigid spacecraft is addressed. Uncertainties caused by external disturbances, unknown inertial matrix, actuator failures, and saturation constraints are tackled simultaneously. First, a smooth function that is more qualified to approximate the standard saturation characteristics is presented to deal with the actuator saturation constraints. Second, a fast nonsingular terminal sliding mode (FNTSM) manifold is constructed as a foundation of controllers design. By incorporating the fuzzy logic system into FNTSM technique, a less demanding solution of coping with model uncertainties is provided because the requirement of a prior knowledge of unknown inertial parameters and external disturbances in many existing achievements is removed. To reduce the number of parameters to be estimated, the norm approximation approach is exploited. Subsequently, an antichattering attitude controller is presented such that all the tracking errors converge into arbitrary small domains around the origin in finite time. The result is further extended to obtain a fault‐tolerant controller against completely failed actuators. Finally, numerical simulation is conducted to verify the effectiveness of the proposed control scheme and comparison with relevant literature demonstrates its high performance. Furthermore, an experiment for the large satellite Hubble Space Telescope is carried out to validate the practical feasibility. [ABSTRACT FROM AUTHOR]