This article presents a multivariable event-triggered generalized super-twisting sliding-mode algorithm for a nonholonomic mobile-robot safe navigation in unknown indoor environment. For robot safe navigation, vision-based variable gain composite guidance law is proposed to generate desired angular velocity. The guidance strategy uses the centroid of the depth map of the obstacles obtained from RGB-depth sensor. The propose controller follows the path generated by the guidance law. Stability analysis of the controller is done to show the fast convergence as compared to the existing controllers. To show the robustness of the controller in comparison to the existing super-twisting algorithm, a sensitivity analysis is carried out. Furthermore, for minimizing the controller effort, an event-triggered condition for the proposed controller is obtained using Lyapunov stability theory. Comparative simulation study is carried out to show the fast convergence and robustness of the proposed controller. Experiments are done for robot safe navigation in presence of disturbance.