Closure to “Discussion: Selective-Compliance-Based Lagrange Model and Multilevel Noncollocated Feedback Control of a Humanoid Robot” (Spyrakos-Papastavridis, E., Dai, J. S., Childs, P. R. N., and Tsagarakis, N. G., 2018, ASME J. Mech. Rob., 10(3), p. 031009)

Abstract

Abstract This closure exposes the technical inconsistencies, erroneous comments, and misconceptions contained in the Discussion Article (Medrano-Cerda, 2020, “Discussion: ‘Selective Compliance-Based Lagrange Model and Multilevel Noncollocated Feedback Control of a Humanoid Robot’,” ASME J. Mech. Rob., 10.1115/1.4049005 [1]). The majority of incorrect comments relating to stability are not based on mathematical rigor and equations, but on the reproduction of more generic statements made in some textbooks published in the early 1990s. The comments in the Discussion Article fail to demonstrate how any of these generic statements could be applied to the specific cases presented in the Paper (Spyrakos-Papastavridis et al., 2018, “Selective-Compliance-Based Lagrange Model and Multilevel Noncollocated Feedback Control of a Humanoid Robot,” ASME J. Mech. Rob., 10(3). 10.1115/1.4039394 [2]) criticized by the Discussion Article. Further, the only equation that appears in the Discussion Article is incorrect, as will be demonstrated in this closure. Apart from being expressed incorrectly, the text accompanying this equation reveals the fundamentally incorrect mathematical assumption that a diagonal matrix is not equal to its transpose. Moreover, a significant proportion of the comments in the Discussion Article relies upon misconceptions about flexible-joint robot control and humanoid robotics, in terms of their theory and practice, standing in contrast to results reported in these research fields over the last decades.