Recent advances in mobile robotic technologies have enabled significant progress to be made in the development of Stair-Climbing Mobility Systems (SCMSs) for people with mobility impairments and limitations. These devices are mainly characterized by their ability to negotiate those architectural barriers associated with climbing stairs (curbs, ramps, etc.). The development of advanced trajectory generators with which to surpass such architectural barriers is one of the most important aspects of SCMSs that has not yet been appropriately exploited. These advanced trajectory generators have a considerable influence on the time invested in the stair climbing process and on passenger comfort and, consequently, provide people with physical disabilities with greater independence and a higher quality of life. In this paper, we propose a new nonlinear trajectory generator for an SCMS. This generator balances the stair-climbing time and the user`s comfort and includes the most important constraints inherent to the system behavior: the geometry of the architectural barrier, the reconfigurable nature of the SCMS (discontinuous states), SCMS state-transition diagrams, comfort restrictions and physical limitations as regards the actuators, speed and acceleration. The SCMS was tested on a real two-step staircase using different time-comfort combinations and different climbing strategies to verify the effectiveness and the robustness of the proposed approach.