  Microswimmers typically move near walls, which can strongly influence their
motion. However, direct experimental measurements of swimmer-wall separation
remain elusive to date. Here, we determine this separation for model catalytic
microswimmers from the height dependence of the passive component of their
mean-squared displacement. We find that swimmers exhibit "ypsotaxis", a
tendency to assume a fixed height above the wall for a range of salt
concentrations, swimmer surface charges, and swimmer sizes. Our findings
indicate that ypsotaxis is activity-induced, posing restrictions on future
modeling of their still debated propulsion mechanism.
