This article presents a distributed control strategy for herding groups of evaders towards a predefined goal region using a team of robotic herders. In herding problems, evaders tend to move away from each other to increase their coverage regions. This makes it challenging to develop control solutions since the wandering evaders need to be collected while driving the herd. To address this, we propose the distributed outmost push strategy, where each robotic herder pushes the evader that is farthest from the goal region. The intuition behind this strategy is that robotic herders should focus on evaders that are further from the goal region as they are more likely to be missed during the herding process. The outmost evaders are selected from the local field of view, and the robotic herders make decisions in a decentralized manner. We also analyze the convergence of the designed dynamics and the minimum sensing range required for herders. The proposal's effectiveness and generality are validated through numerical simulations and real robotic experiments.