Calculation of the inverse kinematics solution of the 7-DOF redundant robot manipulator by the firefly algorithm and statistical analysis of the results in terms of speed and accuracy

Figures & data

Figure 1. The structure of SUNGUR 370.

Table 1. D-H parameters for robot manipulator.

i	ai(m)	αi (°)	di(m)	Θi (°)(Range)
1	0	−90	l1 = 0.5	−180 < Θ1 < 180
2	l2 = 0.2	90	0	−90 < Θ2 < 30
3	l3 = 0.25	−90	0	−90 < Θ3 < 120
4	l4 = 0.3	90	0	−90 < Θ4 < 90
5	l5 = 0.2	−90	0	−90 < Θ5 < 90
6	l6 = 0.2	0	0	−90 < Θ6 < 90
7	l7 = 0.1	0	d7 = 0.05	−30 < Q7 < 90

Figure 2. Representing the position error.

Figure 3. Determined position of the end effector for this study.

Figure 4. Flowchart of firefly algorithm.

Table 2. Particle number, computation time and position error simulation results.

Firefly number	Solution time (s)	Position error (cm)
30	0,1825	8,77e−03
40	0,5678	5,90e−04
50	0,8788	1.23e−05
60	1,8641	8.38e−07
70	5,8822	5.14e−08
80	6,0668	4.17e−09
90	8,8297	5.59e−11

Table 3. The angle of the joints obtained by the number of particles.

Manual	45	0	45	0	45	0	0
	Estimated final angle of joints
Firefly number	θ1	θ2	θ3	θ4	θ5	θ6	θ7
30	105,218	5,890	−28,611	−37,947	60,792	39,698	25,477
40	38,135	29,674	78,172	−6,108	−3,328	−49,456	59,064
50	138,874	−5,254	−48,312	−19,639	7,576	66,989	26,008
60	161,233	1,565	−49,229	7,320	−47,714	−38,932	55,175
70	95,716	26,773	−6,055	−33,4	26,509	−59,975	79,581
80	156,924	29,087	−82,614	−38,518	25,683	17,636	43,932
90	63,975	−15,475	46,035	−1,071	0,336	40,476	67,894

Table 4. Positions of the end effector in work space.

	Px (cm)	Py (cm)	Pz (cm)
Target position	−24,7487	100,9619	50	–	–
Firefly number	Estimated positions			Position error (cm)	Computation time (s)
30	−24,2647	100,2518	49,8330	8,77e−03	0,1825
40	−24,7363	100,9702	49,9915	5,90e−04	0,5678
50	−24,7466	100,9619	49,9949	1,23e−05	0,8788
60	−24,7444	100,9641	50,0021	8,38e−07	1,8641
70	−24,7624	100,9565	50,0079	5,14e−08	5,8821
80	−24,7447	100,9637	49,9965	4,17e−09	6,0668
90	−24,7412	100,9625	50,0042	5,59e−11	8,8297

Figure 5. Solving contribution of swarm numbers.

Figure 6. The graphic of computation time and position error.

Figure 7. Final position of the 7-DOF manipulator according to the number of firefly.

Table 5. Comparative results of other techniques.

	Actual Position	PSO	ABC	Firefly
PX (cm)	−24.7487	−24,6665	−24.7149	−24.7402
PY (cm)	100.9619	100,3896	101.8105	100.9723
PZ (cm)	50	49,6557	50.0104	49.9989
Error	–	6,72e−03	5.45e−04	6.53e−05
Computation time (s)	–	0.4498	0,4441	0,9204
Parameters		Particle number: 300	Population: 100	Firefly number: 50
		c1: 1.7	Limit: 350	Gamma (γ): 0.9
		c2: 1.7	Onlooker:100	Alpha (α): 0.3
		Initial: Randomly	Initial: Randomly	Beta (β): 0.9
				Initial: Randomly

Figure 8. The graphic of computation time [50].

Figure 9. The graphic of position error (cm) and iteration [50].

Dereli S, Köker R. A meta-heuristic proposal for inverse kinematics solution of 7-DOF serial robotic manipulator: quantum behaved particle swarm algorithm. Artifi Intell Rev. 2019; 1–16. doi:10.1007/s10462-019-09683-x

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