DH-TABLE
FIGURE 8 Articulated PUMA type manipulator schematic and DH parameters。
TABLE IX Articulated manipulator task specifications and constraints
TABLE X Articulated circular cross-section (SI units)
DI D2 d1
function
d2 Torque evaluations
TABLE XI Articulated square cross-section (SI Units)
TABLE XII Articulated rectangular cross-section (SI units)
function LI L2 BI B2 DI D2 b1 b2 d1 d2 Torque evaluations
function function function
Torque evaluations Torque evaluations Torque evaluations
p aoo 3oo zdo
'’ 10 15 20 25 30 35 40 46 50
FIGURE 9 Articulated manipulator objective function history。
meeting the constraints when compared for all three approaches。 The objective function history for the articulated manipulator for each cross-section is shown in Fig。 9。 It is observed that the DE technique converges faster than the other two in a monotonic fashion and requires about 20 generations。
4。3。 Additional Discussion of Results
The results presented show the objective function value (torque value) and number of function evaluations for each evolutionary approach for each cross-section analyzed。
374 P。S。 SHIAKOLAS et at。
It is observed that the torque value, the objective function used during the optimization process, for each cross-section is consistent between the three approaches。 The smallest is obtained from DE followed by GAE (GA with elitism) with the largest value given by the simple GA。 This indicates that the traditional GA techniques do not minimize the objective function or design variables even with a larger number of generations。
Another interesting observation is that the number of function evaluations follows a similar trend with the DE reaching a steady state or convergence type of behavior in only 20 generations。 Even though the traditional GA techniques were allowed to run for more generations thus increasing the number of function evaluations, their objective functions were not even close to those obtained by DE。
The large difference in the number of function evaluations required to minimize the objective function is directly related to time savings。 These time savings are amplified considering that the DE operates on real-valued design variables and does not require binary conversion as the GA。来*自-优=尔,论:文+网www.youerw.com 机器人优化设计英文文献和中文翻译(9):http://www.youerw.com/fanyi/lunwen_82103.html