A plan for using Penning ion traps to solve fundamental physical problems is presented. Placed in the secondary beam from the high-flux PIK reactor they can be used for direct high-precision measurements of the mass of exotic nuclides participating in different nuclear and astrophysical processes, some of which can be difficult to achieve in other currently existing facilities. Traps used in an autonomous regime outside a beam will make it possible to perform measurements with long-lived and stable nuclei for atomic, nuclei, and neutron physics as well as other areas of science.