In order for robots to be operated in a variety of environmental conditions, a smooth motion trajectory to goal point is needed in accordance with actuators specifications of the robot. In this paper, a conventional cubic polynomial method for symmetric curve (S-curve) trajectory planning is extended to the smooth (infinitely differentiable and continuous) symmetric and asymmetric curve (AS-curve) trajectory planning derived from a smooth jerk function. In other words, the proposed methods are able to generate the trajectory as S/AS-curve form as well as to satisfy several physical limits such as jerk limit, acceleration limit, and velocity limit. The effectiveness of the proposed methods is shown through comparative studies with existing method.
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