Energy optimization of trajectories for high level scheduling

Minimization of energy consumption is today an issue of utmost importance in manufacturing industry. A previously presented technique for scheduling of robot cells, which exploits variable execution time for the individual robot operations, has shown promising results in energy minimization. In order to slow down a manipulator's movement the method utilizes a linear time scaling of the time optimal trajectory. This paper attempts to improve the scheduling method by generating energy optimal data using dynamic time scaling. Dynamic programming can be applied to an existing trajectory and generate a new energy optimal trajectory that follows the same path but with another execution time. With the new method, it is possible to solve the optimization problem for a range of execution times in one run. A simple two-joint planar example is presented in which energy optimal dynamic time scaling is compared to linear time scaling. The results show a small decrease in energy usage for minor scaling, but a significant reduction for longer execution times.