The problem of stabilizing a robot-wheel at a target point on a straight line subject to control and phase constraints is considered. The phase and control constraints are met by applying an advanced feedback law in the form of nested saturation functions. The selection of the feedback coefficients is discussed that optimizes the performance of the controller. An optimal controller is defined to be that that ensures the greatest convergence rate near the target point, while preserving a node-like phase portrait of the nonlinear system. The paper continues the work reported at the Optima 2020 conference [1], where an estimate of the greatest rate was obtained. The goal of this paper is to improve the results obtained in that work by considering a curvilinear asymptote and to get the exact value of the greatest rate.