Gibson's (1979 The Ecological Approach to Visual Perception) ecological approach to visual perception is based on several key notions (i.e., affordance, optic flow, and invariants). Early research focused on identifying invariants (π-numbers) to describe affordances using geometric body-scaled measures. Kadar and Koszeghy (2010 International Journal of Sport Psychology 41(3) 80–81) generalized π-numbers to invariant functions (π-functions) to allow dynamically scaled description of driving through gates of variable width. The present study further investigated the dynamic invariants of human locomotion in walking towards and passing through gates. Six participants were instructed to walk through gates of four different sizes with either comfortable or fast walking speed while holding a tray by two hands. Consistent with the results of Kadar and Koszeghy (2010) dynamically-scaled π-functions were identified. The speed control of the approach phase was further assessed in relation to the use of the optical τ parameter derived from optic flow specifying estimated time to contact with the virtual plane defined by the frontal surfaces of the aperture. Aperture size and walking speed have influenced the control of speed at the approach phase: the derivative of τ in the neighborhood of the aperture increased with increasing width of the aperture. Analysis of the approach phase suggests a need for searching an even higher-level invariant structure of the dynamics of this passing through task.