Three-wheeled omnidirectional mobile robots (TOMRs) are widely used to accomplish precise transportation tasks in narrow environments owing to their stability, flexible operation, and heavy loads. However, these robots are susceptible to slippage. For wheeled robots, almost all faults and slippage will directly affect the power consumption. Thus, using the energy consumption model data and encoder data in the healthy condition as a reference to diagnose robot slippage and other system faults is the main issue considered in this paper. We constructed an energy model for the TOMR and analyzed the factors that affect the power consumption in detail, such as the position of the gravity center. The study primarily focuses on the characteristic relationship between power consumption and speed when the robot experiences slippage or common faults, including control system faults. Finally, we present the use of a table-based artificial neural network (ANN) to indicate the type of fault by comparing the modeled data with the measured data. The experiments proved that the method is accurate and effective for diagnosing faults in TOMRs.