Purpose This paper aims on the trajectory tracking of the developed six wheel-legged robot with heavy load conditions under uncertain physical interaction. The accuracy of trajectory tracking and stable operation with heavy load are the main challenges of parallel mechanism for wheel-legged robots, especially in complex road conditions. To guarantee the tracking performance in an uncertain environment, the disturbances, including the internal friction, external environment interaction, should be considered in the practical robot system. Design/methodology/approach In this paper, a fuzzy approximation-based model predictive tracking scheme (FMPC) for reliable tracking control is developed to the six wheel-legged robot, in which the fuzzy logic approximation is applied to estimate the uncertain physical interaction and external dynamics of the robot system. Meanwhile, the advanced parallel mechanism of the electric six wheel-legged robot (BIT-NAZA) is presented. Findings Co-simulation and comparative experimental results using the BIT-NAZA robot derived from the developed hybrid control scheme indicate that the methodology can achieve satisfactory tracking performance in terms of accuracy and stability. Originality/value This research can provide theoretical and engineering guidance for lateral stability of intelligent robots under unknown disturbances and uncertain nonlinearities and facilitate the control performance of the mobile robots in a practical system.