Minimum Time and Minimum Energy Trajectories of an Industrial Robot


Minimum time and minimum energy point-to-point trajectories for an industrial robot of type Manutec r3 have been computed subject to a full nonlinear dynamical model of the robot dynamics taking into account forces and moments resulting from inertia, coriolis, centrifugal and gravitational effects. Furthermore, states on the control variables as well as on the state variables (as upper and lower bounds on the angular velocities and others) have been considered.

The developed optimization method DIRCOLhas demonstrated remarkable robustness and efficiency. The numerical results also show that the constraints on the angular velocities become active during large parts of the minimum time trajectory. But the resulting stress on the links can be significantly reduced by a minimum energy trajectory that is only about fifteen percent slower than the minimum time trajectory.

The optimization problem and the numerical solution approach have originally been presented in Chapter 8.4 of the doctoral dissertation. The animation has been implemented by Alexander Heim using the interactive graphics system SIGMA.


Intro.avi (12fps/1.961 KB)
Intro.avi (24fps/3.405 KB)
Intro.mpg (2.507 KB)

Zeitminimale Lösung:
Zeit.avi (12fps/2.201 KB)
Zeit.avi (24fps/3.504 KB)
Zeit.mpg (4.026 KB)

Energieminimale Lösung:
Energ.avi (12fps/2.427 KB)
Energ.avi (24fps/3.859 KB)
Energ.mpg (4.157 KB)

Vergleich der beiden Bahnen:
Vergl.avi (12fps/3.146 KB)
Vergl.avi (24fps,5.236 KB)
Vergl.mpg (5.057 KB)

Relevant Publications

Fachgebiet Simulation und Systemoptimierung, TU Darmstadt