The subject of this paper is the local minima problem (LMP) inherent in potential field methods (PFMs). Firstly, the underlying theoretical basis of LMP is formulated and its theoretical difficulty of control design is analyzed. It is shown that there does not exist a static state feedback control to solve LMP. Then a time-varying continuous control law is proposed to tackle this problem. In particular, challenges of finding continuous control solutions of LMP are discussed and explicit design strategies are then proposed. Moreover, systematic rigorous Lyapunov proof is given to show both global goal convergence provided that the goal is globally reachable and obstacle avoidance of the proposed controls. Simulation results are provided to illustrate the validity and effectiveness.