The problem of stabilizing a robot-wheel at a target point on a straight line subject to the control and phase constraints is considered. The phase and control constraints are met by applying an advanced two-parameter feedback law in the form of nested saturation functions. The selection of the parameters is discussed that optimizes the performance of the con- troller. An optimal controller is defined to be that that ensures the great- est convergence rate near the target point, while preserving a node-like phase portrait of the nonlinear system. The paper continues the work re- ported at the Optima 2020 conference [1], where the problem was solved by seeking a straight separatrix dividing the plane into two invariant sub- sets. It aims at improving the results obtained in [1] by allowing the separatrix to be an arbitrary smooth curve. We show that the optimal convergence rate in this case is greater than that obtained in [1] by a factor of 2e?.