This paper proposes a closed-form modulation strategy for inductor current minimization of cascaded buck+boost converters (CBBCs). The minimum rms current trajectory (MCT) is analytically derived achieving low conduction and switching losses, and high efficiency. The proposed method does not rely on look-up tables that are widely used in existing optimization methods, significantly reducing the digital implementation effort. Moreover, instead of traditional instantaneous current detection, the average inductor current control is introduced to ensure the converter operates along MCT, eliminating the requirement for dc-to-MHz wide-bandwidth current sensing. High efficiency and easy implementation are achieved with the proposed method. The theoretical analysis is verified via computer simulation.