  Different from previous modelings of self-propelled particles, we develop a
method to propel the particles with a constant average velocity instead of a
constant force. This constant propulsion velocity (CPV) approach is validated
by its agreement with the conventional constant propulsion force (CPF) approach
in the flowing regime. However, the CPV approach shows its advantage of
accessing quasistatic flows of yield stress fluids with a vanishing propulsion
velocity, while the CPF approach is usually unable to because of finite system
size. Taking this advantage, we realize the cyclic self-propulsion and study
the evolution of the propulsion force with propelled particle displacement,
both in the quasistatic flow regime. By mapping shear stress and shear rate to
propulsion force and propulsion velocity, we find similar rheological behaviors
of self-propelled systems to sheared systems, including the yield force gap
between the CPF and CPV approaches, propulsion force overshoot,
reversible-irreversible transition under cyclic propulsion, and propulsion
bands in plastic flows. These similarities suggest the underlying connections
between self-propulsion and shear, although they act on systems in different
ways.
