This module computes a multidimensional trajectory which describes the manipulator's position, velocity, and acceleration for each link. This module includes the human interface problem of describing the desired behavior of the manipulator. The complexity of this problem arises from the wide meaning of manipulator's behavior. In some applications we might need to specify only the goal position, whereas in some other applications, we might need to specify the velocity with which the end effector should move. Since trajectory generation occurs at run time on a digital computer, the trajectory points are calculated at a certain rate, called the path update rate. We return to this issue when we consider speed.
There are several strategies to calculate trajectory points which generate a smooth motion for the manipulator. It is important to guarantee this smoothness of the motion due to physical considerations such as the required torque that causes this motion, the friction at the joints, and the frequency of update required to minimize the sampling error.
One of the simplest methods is cubic polynomials, which assumes a cubic function for the angle of each link, by differentiating this equation the velocity and acceleration are computed (see [7]).