The wheeled robots trajectory tracking control methods rarely constrain the torque and speed at the same time. In actual application, the torque and speed of the robot cannot exceed the saturation limit of the actuator. This paper develops a model-based trajectory tracking parameter optimization controller with both velocity and torque constraints, using a gradient descent parameter iterative learning strategy to minimize the settling time index of the system. Trajectory tracking time optimization methods usually require a given analytical expression of the system time, while this time optimization method only requires that the settling time is solvable. The MATLAB simulation experiments show that the proposed parameter optimization controller for trajectory tracking can perform velocity and torque constraints while having a relatively good overall rapidity time index. If the resolution of the robot sensor can meet the design requirements, the optimization method can strictly control the system torque maximum to a reasonably small expected value. When the resolution of the robot sensor is limited, this optimization method can restrict the system torque maximum within a reasonable saturation constraint range.