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The control method based on the time-state control form has been proposed to stabilize the chained system, which is a canonical-form nonlinear system. In this study, the control method is used for controlling a mobile robot in auto-parking situations. The proposed controller includes a parameter that is allowed to switch at arbitrary times without loss of the stability of the system. The robot employing the proposed controller reaches the target position by switching its traveling direction to avoid collisions with obstacles. However, the shape of the robot gives a problem. We resolve this by using the switchable parameter included in the proposed controller, and show the availability of switching the parameter. Furthermore, the appropriate switching of the traveling direction and the parameter enables the robot to reach the target faster. Thus, we search the appropriate values of the parameter and the switching points of the traveling direction using the genetic algorithm. In the auto-parking experiments that incorporate the search results, the robot can reach the target position faster.