This article describes an emotional adaption approach to proactively trigger increased helpfulness towards a robot in task-related human-robot interaction (HRI). Based on social-psychological predictions of human behavior, the approach aims at inducing empathy, paired with a feeling of similarity in human users towards the robot. This is achieved by two differently expressed emotional control variables: by an explicit statement of similarity before task-related interaction, and implicitly expressed by adapting the emotional state of the robot to the mood of the human user, such that the current values of the human mood in the dimensions of pleasure, arousal, and dominance (PAD) are matched. The thereby shifted emotional state of the robot serves as a basis for the generation of task-driven emotional facial-and verbal expressions, employed to induce and sustain high empathy towards the robot throughout the interaction. The approach is evaluated in a user study utilizing an expressive robot head. The effectiveness of the approach is confirmed by significant experimental results. An analysis of the individual components of the approach reveals significant effects of explicit emotional adaption on helpfulness, as well as on the HRI-key concepts anthropomorphism and animacy.