In this paper, we study the free-locomotion of a miniature bio-mimetic underwater vehicle inspired by carangiform swimming fish. The vehicle is propelled by a vibrating Ionic Polymer Metal Composite (IPMC) attached to a compliant passive fin. The IPMC vibration is remotely controlled through the vehicle's onboard electronics that consists of a small-sized battery pack, an H-Bridge circuit, and a wireless module. The planar motion of the vehicle body is described using rigid-body dynamics. Hydrodynamic effects, such as added mass and damping, are included in the model to enable a thorough description of the vehicle's surge, sway, and yaw motions. The time-varying actions exerted by the vibrating IPMC on the vehicle body, including thrust, lift, and moment, are estimated by combining force and vibration measurements with reduced order modeling based on modal analysis. The model predictions are validated through experimental results on the planar motion of the fish-like robotic swimmer.