This paper studies the problem of distributed robust actuator fault detection for multi-agent systems composed of multiple unicycle-type mobile agents with chained form dynamics. This objective is achieved through the design of cascades of predefined-time sliding mode observers to give an exact estimate of the global system state, whereby the settling time is a parameter defined in advance, which does not depend on the initial conditions of the system. The system structure allows us to reconstruct the disturbance inputs using the equivalent control concept to generate efficient residual signals. This method ensures global actuator fault detection, where each agent can detect its faults and those occurring elsewhere in the system using only local information.