||We present constants of motion for the finite-dimensional Lohe type aggregation models with frustration, and apply them to the analysis of collective behaviors. The Lohe type models have been proposed as possible non-abelian and higher-dimensional generalizations of the Kuramoto model, which is a prototype phase model for synchronization. In this paper, we study the emergent collective dynamics of these models under the effect of (interaction) frustration, which generalizes phase-shift frustrations in the Kuramoto model. To this end, we provide constants of motion, i.e., conserved quantities along the flow generated by the models under consideration. From the perspective of the low-dimensional dynamics, we derive several results on the emergent asymptotic patterns of the Kuramoto and Lohe sphere models. (C) 2020 Elsevier B.V. All rights reserved.