The synthesis of smooth trajectories for pick-and-place operations

A spline-based method of programming smooth trajectories for pick-and-place operations is introduced. Unlike continuous-path operations, which impose a unique Cartesian trajectory, an infinite number of smooth trajectories can be described between any given pick and its corresponding place configuration. The method begins with the mapping of the pick and the place configuration in Cartesian space into joint-coordinate space, using a general-purpose inverse kinematics package that handles singularities and redundancies. Next, a trajectory, composed of a C²-continuous, periodic cubic spline segment, is defined between the pick and the place configurations in the joint-coordinate space. It is demonstrated that C²-continuity will prevail in Cartesian space as well. The software implementing this method includes a graphics package as well as an interface to an offline programming system to realize the synthesis of the actual robot motion. Details of the procedure are illustrated with a numerical example applied to a commercial industrial robot