A procedure is presented for planning optimal trajectories for application to industrial robots. First, trajectories are optimised by considering the nominal dynamics of a robot with rigid links and joints and with constraints on joint torque and speed. The minimum-time optimisation criterion is complemented by a miminal dynamic energy criterion that leads to smoother actuator inputs that do not excite joint vibrations. Weighting factors for these cost functions are then determined by trial simulations. By these means the effect of controller characteristics and elasticity, friction and backlash in the joints may be taken into account. A minimum-time movement for the real-world robot is obtained which displays the dynamical behaviour predicted in the planning procedure. Results from measurements and simulations for a PUMA 562 robot illustrate the approach. Further improvements may be achieved by a custom controller with the feedforward torques as shown in a comparison of trajectories executed with a VAL2 controller and a custom controller.
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Wapenhans, H., Hölzl, J., Steinle, J. et al. Optimal trajectory planning with application to industrial robots. Int J Adv Manuf Technol 9, 49–55 (1994). https://doi.org/10.1007/BF01792867
- Industrial robots
- Joint elasticity
- Optimal trajectories
- Path planning