Geometric Work of Manipulators and Path Planning Based on Minimum Energy Consumption

The energy efficiency of the robots of today’s generation is in general very poor due to the existence of “geometric work.” The geometric work is geometry dependent and can be eliminate by adopting a special geometry which decouples the gravitational motion from the horizontal motions. Instead of adopting a special geometry, this paper studies the geometric work of a regular open-chained manipulator and applies it to the path planning for minimum energy consumption. For a given manipulator geometry and end-effector position, the zones of velocity with zero geometric work are determined analytically. A map which describes these zones of zero geometric work at various positions in workspace is then constructed for path planning with zero geometric work. The path planning for minimum energy consumption is generated by the dynamic programming method and the results are compared with the map of zero geometric work. It is found that the end-effector tends to move within the zones of zero geometric work as much as possible. If the end-effector has to cross the boundary of a zone at some point, it again moves within the zones after crossing the boundary. The presented method can also be used to arrange the pick and place positions for minimum travel energy consumption. That is, the two positions should be selected so that a continuous path which connects them with zero geometric work and with monotonously ascending or descending features is available.