We present an evolutionary trajectory planning method for mobile robots following a novel evolution strategy (NES) algorithm. The 2-D trajectory planning problem of a mobile robot among polygonal obstacles is formulated as a constrained time-optimum control problem considering motion. Unlike traditional evolutionary representation, special representation of individuals and crossover are used for the evolutionary search. Swapping crossover, insertion, and deletion mutations are used as background operators for maximum evolutionary algorithm flexibility. Polygonal obstacles in the world coordinate frame are modeled as circles from visibility and sensor modeling concepts. An appropriate cost (fitness) function is constructed as the only link between the evolutionary algorithm and environment. Our proposed evolution is effective for collision-free optimum trajectory planning in robot simulation within a heavily constrained (obstacle) environment.