Fig. 1

Flowchart of multi-objective DE

Fig. 2

Non-dominated solutions of each algorithm on three-objective DTLZ5 problem

Fig. 3

Non-dominated solutions of each algorithm on three-objective DTLZ7 problem

Fig. 4

Non-dominated solutions of each algorithm on three-objective WFG4 problem

Fig. 5

Non-dominated solutions of each algorithm on three-objective WFG5 problem

Table 1

IGD performance metric comparison of each algorithm

Table2

HV performance metric comparison of each algorithm

Table 3

D-H parameters of KUKA KR3 R540 robotic arm

Fig. 6

D-H link coordinate system of robotic arm

Fig. 7

Simulation o f robotic arm

Table 4

Interpolated path points

Fig. 8

Path curves obtained by fusing 3-5-3 degree polynomials with B-spline curve interpolation

Fig. 9

Path curves optimized by MOPSO algorithm

Fig. 10

Path curves optimized by MODE algorithm

Fig. 11

Path curves optimized by GMODE algorithm

Fig. 12

Time, impact, and energy convergence for each joint of robotic arm under different algorithms

Fig. 13

Time, energy, and jerk curves for each joint under different algorithms with adaptive weighting

Table 5

Weight proportion verification

Fig. 14

Multi-objective optimization convergence curves under two weighting schemes

Table 6

D-H parameters of RS007L

Fig. 15

Motion process of robotic arm

Table 7

Joint angle scorre sponding to path point sof robotic arm

Fig. 16

Comparison of curves before and after changing objective weights

Table 8

Joint angle scorre sponding to path points

Fig. 17

Numerical distribution of computational efficiency

Table 9

Computational strategy verification