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In this paper, we present two near-optimal methods to determine the real-time collision-free path for a mobile vehicle moving in a dynamically changing environment. The proposed designs are based on the polynomial parameterization of feasible trajectories by explicitly taking into account boundary conditions, kinematic constraints, and collision-avoidance criteria. The problems of finding optimal solutions to the parameterized feasible trajectories are then formulated with respect to a near-minimal control-energy performance index and a near-shortest distance performance index, respectively. The obtained optimal solutions are analytical and suitable for practical applications which may require real-time trajectory planning and replanning. Computer simulations are provided to validate the effectiveness of the proposed near-optimal trajectory-planning methods.