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.
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