In this thesis, an approach for robot motion control with collision avoidance and human-following is investigated. Using velocity potential fields approach in a modified, quasi-harmonic, solution, the navigation controller is developed. A quasi-harmonic function based controller uses harmonic solutions for collision avoidance and smoothly changes toward a non-harmonic solution which tends toward a zero velocity command only when approaching the goal. After the motion controller was created, human-following strategy was designed to let a non-holonomic robot have the ability to follow a human in an unknown environment with obstacles. The approach is based on velocity potential fields that permit to generate velocity vector commands that drive the robot at a safe distance with regard to the human while avoiding obstacles. The quasi-harmonic approach is investigated analytically using symbolic math solutions of MAPLETM as well as in simulations using MATLABTM. Motion simulations of both holonomic and non-holonomic robot motion illustrate how the proposed approach operates. Experiments are also made with LEGO MINDSTROMS NXT robot to test the algorithm in environment with simple and complex obstacles.