Tracked mobile robots can overcome the limitations of wheeled and legged robots in environments, such as construction and mining, but there are still significant challenges to be addressed in terms of trajectory tracking. This study proposes a kinematic strategy to improve the trajectory-tracking performance of a PASTRo (Passively Articulated Suspension based Track-typed mobile robot), which comprises four tracks, two rockers, a differential gear, and a main body. Due to the difficulties in explicitly identifying track-terrain contact angles, suspension kinematics is used to identify track-terrain contact angles (TTCA) in arbitrarily rough terrains. Thus, the TTCA-based driving velocity projection method is proposed in this study to improve the maneuverability of PASTRo in arbitrarily rough terrains. The RecurDyn-Simulink co-simulator is used to examine the improvement of PASTRo compared to a tracked mobile robot non-suspension version. The results indicate that PASTRo has a 33.3% lower RMS(Root Mean Square) distance error, 56.3% lower RMS directional error, and 43.2% lower RMS offset error than the four-track skid-steer mobile robot (SSMR), even with planar SSMR kinematics. To improve the maneuverability of PASTRo without any information on the rough terrain, the TTCA is calculated from the suspension kinematics, and the TTCA obtained is used for both TTCA-based driving velocity projection methods. The results show that PASTRo, with the TTCA-based driving velocity projection method, has a 39.2% lower RMS distance error, 57.9% lower RMS directional error, and 51.9% lower RMS offset error than the four-track SSMR.