Social robotics and human-robot partnership are becoming very relevant topics in the next decades defining many challenges for speech technology. In addition, the COVID pandemic imposed an awareness of technology challenges to fight massive health problems. In this paper, the first system to estimate respiratory distress in a human-robot interaction (HRI) environment is presented. The training procedure of the dyspnea estimation models by simulating the HRI acoustic environment with real room impulse responses (estimated with a PR2 robot) and additive noise is described. The training and testing data were processed using two beamforming techniques: delay-and-sum and MVDR. The results suggest that it should be possible to reduce significantly the degradation in precision of estimates of respiratory distress in a real HRI scenario. The improvements in accuracy and AUC with MVDR when compared to baseline processing without beamforming are 7% and 4%, respectively.