A new approach to synthesizing free motions of robotic manipulators based on a concept of unit motions

A concept of unit motions and a new scheme for synthesizing free motions of robotic manipulators are proposed. Unit motions are defined as smooth primitive motions in the hand coordinate system by employing normalized uniform B-spline functions. Complex motions are then generated as a superposition of time-shifted and weighted unit motions. Corresponding to unit motions, a concept of unit control inputs is also introduced and an entire control input is then obtained in exactly the same way as complex motions are generated from unit motions. Moreover, in order to build further complex motions from simpler ones in a systematic way, operations on motions are defined including spatial, temporal and structural ones. Based on unit motions and unit control inputs, we then develop a formal method for motion planning and control for robotic manipulators. Motions are represented formally as the time series of weight vectors, or equivalently as the so-called control polygons, and the operations on motions are then regarded as operations on control polygons. Simulation examples are included to demonstrate how to generate motions from unit motions and operations, and properties of the resulting motions are also described