Page - 223 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

to the standardmanipulationof the robotcontrol. In theupperpartofFigure4 the jointanglesof thesignalenergyoptimalmanipulationincomparison to the standard manipulation of the robot are plotted over time. Obviously, the smooth characteristic of theoptimalsolution,whichcorresponds to thedashed linecanbeseen. However, thestandardma- nipulation,whichcorresponds to thesolid line, showsthecommonlyusedstandardmotioncalculated by the robot controller. In the lowerpart ofFigure4 the torquesare depictedover the time. Here, the smoothcharacteristicof theoptimizedsolutioncan beseen clearly. 0 0.2 0.4 0.6 0.8 1 0 −20 −40 −60 −80 −100 0 0.2 0.4 0.6 0.8 1 0 −3 −6 −9 −12 −15 0 0.2 0.4 0.6 0.8 1 0 20 40 10 30 50 0 0.2 0.4 0.6 0.8 1 −3 −2 −1 0 1 2 3 0 0.2 0.4 0.6 0.8 1 0.4 0.5 0.6 0 0.2 0.4 0.6 0.8 1 0 −0.2 0.2 0.4 −0.3 −0.1 0.1 0.3 Figure4. Trajectoryof thestatesand torques in theaxis 6. Conclusions andoutlook To reach a desired endpoint within a predefined time, the definition of a Scrap-function is required only. Inaddition,various requests to thesystembehaviorcan beconsidered in the integralpart of the cost functional, such as the signal energy ofan industrial robot. This paper should reveal that the trajectory with minimal signal energy does not lead automatically to the mechanical energy optimalmanipulationof the robot. Nevertheless, in practice such quadratic input termsareoftenusedbecause this leads to lessstressof thecomponents. Insimplytermsyoucan say that the electrical parts are protected against overheating and the operation life span is increased additionally if the torques remain small and smoothover themanipulations. For the results in Section 5.2. we neglected the three degrees of freedom of the wrist and fixed them to keep the equations of motion and the necessary matrices simple. However, if we consider this joint angles in the system equations it is possible to reach a predefined endpoint in different ways. This means thatmore than onefinal configurationof the robot existswhich meet theend point in the coordinatesof the toolcenterpoint. 223