## 5 Conclusions, Discussion, and Future Work  
We have proposed a novel method for reducing energy consumption in repeated robotic arm tasks. The energy saving in comparison to a default trajectory generated by a controller (standard trapezoid movement) in our test cases ranges from 10% to almost 40%. The necessary values were directly acquired from the robotic arm, without the need of a complex power consumption model. The method relies on the PSO algorithm. In combination with a Bezier curve generator, the proposed method generates smooth and energy efficient trajectories for point-to-point movements. The proposed method is applicable to robotic arms with the same kinematic structure (6 DOF). It is possible to generalize this method to a manipulator with arbitrary kinematic structure. Another benefit of this method is the possibility to quickly find the optimal trajectory under a different objective metric by using a proper fitness function, e.g., minimum acceleration, jerk, torque, etc. Because the method does not use higher polynomial trajectory generation, the computation has fewer limitations (like zero derivations, restrictions for start or end points) and it may be able to search a wider solution space. The potential weakness of this approach is in the necessity of performing several hundreds of real-world trials to find the optimal trajectory. However, there was a relatively fast convergence to the optimal trajectory in most experiments (see Figure 4). With a precise dynamic model, it would be possible to find the optimal trajectory without the need for any real-world movement execution. In order to achieve this, we have also tried simulations of movements in the simulation system CoppeliaSim (Figure 5a). However, the energy prediction from the CoppeliaSim tool does not perfectly correspond to real-world measurements. In our future work, we will try to find a way to lower the error of predicted energy consumption and remove the dependency on real robotic arm trials. Figure 10: Comparision of movej (dotted line) and PSO optimized (solid line) joints and tool centre point (TCP) trajectories; elbow is represented by blue color, wrist joints with red and green and TCP trajectory is depicted with black line. The proposed method does not implement any collision detection or avoidance mechanism and it requires the proper setting of velocity boundaries on the robotic arm. Moreover, we did not use any payload or end-effector. The size of the payload would change the energy consumption. We intend to investigate the influence of payload (or the ratio of payload) concerning the robotic arm mass distribution in the future. Experience that was gathered during this work suggested some interesting topics for future work. The most challenging is the possibility to train a model for power consumption with a feed-forward or recurrent neural network. If successful, this would remove the need for time-consuming real-world trials while still enabling an accurate solution and the possibility to quickly find optimized trajectories with different endpoints. The robotic arm manufacturer could deliver such a neural network or one could be produced by the robotic community to further ease the energy usage and make more efficient robot motion. Another topic would be the use of reinforcement learning. The shaped reward function with energy consumption term could be led to a practical adoption of energy saving methods for robotic movements. Conceptualization, R.P. and Z.B. ; methodology, R.P. ; software, R.P. ; validation, A.V., J.S. and T.K. ; formal analysis, A.V. ; resources, A.V. ; data curation, J.S. ; writing--original draft preparation, R.P. and A.V. ; writing-review and editing, T.K. and P.N. ; visualization, A.V. ; supervision, Z.B. ; project administration, V.S. ; funding acquisition, P.N. All authors have read and agreed to the published version of the manuscript.