Tracked inspection robots possess prominent advantages in dealing with severe environment rescue, safety inspection, and other important tasks, and have been used widely. However, tracked robots are affected by skidding and slipping, so it is difficult to achieve accurate control. For example, the control parameters of a tracked robot are the same during driving, but the pressure, shear force and steering resistance of the robot on the road surface are different, which affects the steering characteristics of the robot on complex terrain. Based on analysis of the structural parameters and steering radius of the robot, the traction force and resistance torque models of the tracked robot were established, and the plane dynamics of the robot’s steering were analyzed and solved. The corresponding relationships between the road parameters, relative steering radius, and lateral relative offset of the robot on three typical roads were obtained. Mathematical models of the robot’s track speed and relative steering radius with and without skid and slip were established. Through simulation analysis of Matlab software, the corresponding relationship between the relative steering radius of the robot and the velocity difference of the two tracks were obtained. Taking angular obstacles as an example, three obstacle-avoidance steering control strategies, once turning in situ center, twice turning in situ center, and large-radius steering were developed. The tracked robot and obstacle multi-body dynamic simulation models were constructed using ADAMS simulation software. The simulation results show that all three methods can complete the steering tasks according to the requirements; however, under the influence of skid and slip, the trajectory of the robot deviates from the ideal trajectory, which has a great impact on large-radius steering, even though the large-radius obstacle-avoidance steering control strategy has the advantages of a smooth trajectory, fast steering speed, and high efficiency. The obstacle-avoidance steering experiments were completed by the robot prototype, which verifies the rationality of robot steering theory, which could provide the corresponding theoretical basis for autonomous obstacle-avoidance navigation control of a tracked robot.