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Robot motion is commonly specified as a Cartesian trajectory of its end-effector. For executing the end-effector trajectory on-line, a look-ahead of a few points on the trajectory is used to generate the joint trajectories. This paper describes the construction of on-line cubic spline joint trajectories, for a limited-point look-ahead on a specified end-effector trajectory, not necessarily Cartesian. An analytical derivation for the ideal number of look-ahead points on the end-effector trajectoryfor cubic spline interpolation is given. Experimental and simulation results of the on-line spline interpolation schemes show improved end-effector path tracking and smooth motion for a wide range of sampling rates on the effector trajectory.
Chand et al. (Sat,) studied this question.