The underwater robotic vehicle presented here is inspired by an Ostraciiform form of swimming with three oscillatory fins to propel itself and control its orientation. A mathematical model is made to simulate the motion of the vehicle based on the fin oscillations to aid in the real-time vehicle control. The model predicts the forces produced by the oscillating rigid fins in the water. A new motion control approach for an underwater robot is proposed and investigated. In this paper, the oscillating fin arrangement is under-actuated and carries out four degrees of freedom (DOF) motion with three fins. The threes fins include: once caudal fin and two pectoral fins. The dynamic model developed for the robot has a highly nonlinear thrust vector map because of the thrust generation from these oscillation angles. Nonlinear control methods such as Backstepping control is applied to this robot model due to the continuous oscillatory motion of fins for achieving different DOF. Contrary to the feedback linearization technique which cancels potentially useful nonlinearities, this control scheme avoids the cancellation; resulting in a less complicated controller. Lyapunov stability theory was used to prove the system stability. RMS values of the error were used for tuning the controller gains constants. © 2019. The Authors. Published by Elsevier Ltd. All rights reserved.