In this paper is presented a method for generating continuous and differentiable trajectory from an input path described by a polyline while maintaining accelerations and velocities constraints. The method in based on replacing the path corners with parabolic blends of constant acceleration. The complete spatial control of the resulted trajectory is obtained with a velocity reduction procedure which ensures that the trajectory doesn't deviate from the input path further than a settable value. The total time is minimized by replacing the non-maximized constant velocity sections with boost sequences containing maximized symmetrical accelerating and decelerating time frames while also keeping the velocity constraints. The method was successfully tested in practice and the results were very good even on complex input paths.
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