<p>Curved cylinders composed of photo-responsive materials exhibit self-sustained rolling under constant illumination, both on horizontal and inclined surfaces, distinguishing them from their straight counterparts. The complex deformation mechanisms inherent to soft materials, coupled with the nonlinearities arising from multi-physics interactions and contact mechanics, pose significant challenges to simulating such autonomous locomotion and their interactions with the environment using finite element methods. Here we conduct a comprehensive parametric analysis to investigate the influence of imposed eigenstrain on the illumination surface, light penetration depth, illumination angle, aspect ratio, friction coefficient, and tilt angle on rolling behavior. We predict continuous in-plane vibration as a byproduct of rolling on both horizontal and inclined surfaces, and the observed periods of vibration can be approximated by the formula for the 1st mode of vibration in beam theory for free slender cylinders. The in-plane vibration plays the role of transitioning cylinders from rolling with slipping to pure-rolling, whereas sliding friction modulates curvature tailored for pure roll, and also propels translation. Intriguing rolling and slipping scenarios can be identified by a phase diagram, highlighting the roles of photo-induced curvature and sliding friction. Our findings contribute to a deeper understanding of the fabrication and control of photo-responsive soft actuators and provide a framework for optimizing their design and enhancing performance.</p> Graphical Abstract <p></p>