Smooth joint trajectory planning for a point-to-point task

In most cases, the joint trajectory for a point-to-point (PTP) task is generated from a given joint velocity profile. However, the given joint velocity profile may not generate a smooth joint trajectory and/or it may have undesirable frequency components for controlling a manipulator. The authors propose a PTP joint trajectory planning scheme in the joint space which generates a smooth joint trajectory profile for the given joint velocity profile. In order to exclude the undesirable frequency components, they approximate the given joint velocity profile in terms of the Nth partial sum of Fourier series by using the Fourier transform of the given joint velocity profile. The coefficients of the Fourier series are computed from the inverse kinematic solutions at each end-point of the given PTP tasks so that a smooth joint trajectory can be generated. The proposed method is applied to a PUMA 560 manipulator for the cases of the minimum energy and the minimum time. Also, the joint velocity profiles are analysed by the Fourier transform