  This paper analyses the impact of collisions in a system of $N$ identical
hard-core particles driven according to a velocity jump process. The physical
space is essentially a channel in $\mathbb{R}$ with a probability of occupants
being able to pass each other. The system mimics what nature does, where
individuals pass one another in a narrow channel while making incidental
contact with those moving in the opposite direction. The passing probability
may depend on the particles' size and the channel's width. Starting from the
particle level model, we systematically derive a nonlinear transport equation
based on an asymptotic expansion. Under low-occupied fractions, numerical
solutions of both the kinetic model and the stochastic particle system are
compared well during biased and unbiased random velocity changes. Analysis of
the subpopulation motility within a large population exhibits the consequences
of volume exclusions and channel confinements on the travelling speeds.
