This paper presents an integrated optimal control framework for velocity and steering control of an autonomous pursuit vehicle, where the control objectives satisfy the requirements of collision avoidance and moving target tracking. A distinctive feature of the proposed velocity and steering control is the application of logarithmic penalty functions to both. The control barrier imposed by logarithmic function provides a unique tool in computing a balanced trajectory with optimal tracking error, control effort and safety margin. Trajectories compliant with the safety regulations for autonomous driving have been planned based on estimated intention of the target and the obstacles. Effects of the controller weights have been extensively simulated to assess the performance of the proposed strategy in a variety of dynamic situations. The controller has been validated on a real-life robot by using a shrinking horizon control policy for iterative optimisation.