Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization

doi:10.1007/s11465-021-0630-x

Frontiers of Mechanical Engineering

2021, Vol. 16

Issue (3): 435-450 https://doi.org/10.1007/s11465-021-0630-x

本期目录

Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization

Boyu MA, Zongwu XIE, Zainan JIANG(

), Hong LIU

School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China; State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China

全文: PDF(1311 KB) HTML

Abstract：

Seven-degree-of-freedom redundant manipulators with link offset have many advantages, including obvious geometric significance and suitability for configu-ration control. Their configuration is similar to that of the experimental module manipulator (EMM) in the Chinese Space Station Remote Manipulator System. However, finding the analytical solution of an EMM on the basis of arm angle parameterization is difficult. This study proposes a high-precision, semi-analytical inverse method for EMMs. Firstly, the analytical inverse kinematic solution is established based on joint angle parameterization. Secondly, the analytical inverse kinematic solution for a non-offset spherical–roll–spherical (SRS) redundant manipulator is derived based on arm angle parameterization. The approximate solution of the EMM is calculated in accordance with the relationship between the joint angles of the EMM and the SRS manipulator. Thirdly, the error is corrected using a numerical method through the analytical inverse solution based on joint angle parameterization. After selecting the stride and termination condition, the precise inverse solution is computed for the EMM based on arm angle parameterization. Lastly, case solutions confirm that this method has high precision, and the arm angle parameterization method is superior to the joint angle parameterization method in terms of parameter selection.

Key words： 7-DOF redundant manipulator inverse kinematics semi-analytical arm angle link offset

收稿日期: 2020-10-10 出版日期: 2021-09-24

Corresponding Author(s): Zainan JIANG

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2021, 16(3): 435-450.
Boyu MA, Zongwu XIE, Zainan JIANG, Hong LIU. Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization. Front. Mech. Eng., 2021, 16(3): 435-450.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-021-0630-x
https://academic.hep.com.cn/fme/CN/Y2021/V16/I3/435

Fig.1

Link $i$	$a i − 1 (DH)$ /m	$α i − 1 (DH)$ /( $°$ )	$d i (DH)$ /m	$θ i (DH)$ /( $°$ )
1	0	90	$a 0$	0
2	0	90	$a 1$	0
3	0	–90	$a 2$	-90
4	$a 3$	0	$a 4$	0
5	$a 5$	0	$a 6$	90
6	0	90	$a 7$	0
7	0	–90	$a 8$	0
8	0	90	0	90

Tab.1

Fig.2

Fig.3

Joint angle	EMM	SRS manipulator	Relationship
$θ 1$ , $θ 2$	$(a 0 + p x − a 8 n x) c 2 + [(a 8 n y − p y) c 1 + (p z − a 8 n z) s 1] s 2 + (a 2 + a 4 + a 6) = 0$	$(a 0 + p x − a 8 n x) c 2 ′ + [(a 8 n y − p y) c 1 ′ + (p z − a 8 n z) s 1 ′] s 2 ′ + (a 2 + a 4 + a 6) = 0$	$θ 1 = θ ′ 1$ , $θ 2 = θ ′ 2$
$θ 6$	$c 6 = − (n z s 1 − n y c 1) s 2 − n x c 2$	$c 6 ′ = − (n z s 1 ′ − n y c 1 ′) s 2 ′ − n x c 2 ′$	$θ 6 = θ ′ 6$
$θ 7$	${c 7 = (s z s 1 − s y c 1) s 2 + s x c 2 s 6, s 7 = − (a z s 1 − a y c 1) s 2 + a x c 2 s 6$	${c 7 ′ = (s z s 1 ′ − s y c 1 ′) s 2 ′ + s x c 2 ′ s 6 ′, s 7 ′ = − (a z s 1 ′ − a y c 1 ′) s 2 ′ + a x c 2 ′ s 6 ′$	$θ 7 = θ ′ 7$
$θ 4$	$c 4 = A 2 + B 2 − a 32 − a 52 2 a 3 a 5$	$c 4 ′ = A ′ 2 + B ′ 2 − a 32 − a 52 2 a 3 a 5$	The EMM $a 1 ≠ 0$ and $a 7 ≠ 0,$ and the SRS manipulator $a 1 = a 7 = 0$ . Therefore, $A ≠ A ′$ , $B ≠ B ′$ , $θ 4 ≠ θ ′ 4,$ $θ 3 ≠ θ ′ 3,$ and $θ 5 ≠ θ ′ 5 .$ $θ 345$ has no relationship with $a 1$ and $a 7$ ; hence, $θ 345 = θ 3 ′ 4 ′ 5 ′ .$
$θ 3$	${s 3 = A (a 3 + a 5 c 4) − B a 5 s 4 a 32 + a 52 + 2 a 3 a 5 c 4, c 3 = B (a 3 + a 5 c 4) + A a 5 s 4 a 32 + a 52 + 2 a 3 a 5 c 4$	${s 3 ′ = A ′ (a 3 + a 5 c 4 ′) − B ′ a 5 s 4 ′ a 32 + a 52 + 2 a 3 a 5 c 4 ′, c 3 ′ = B ′ (a 3 + a 5 c 4 ′) + A ′ a 5 s 4 ′ a 32 + a 52 + 2 a 3 a 5 c 4 ′$
$θ 5$	$θ 5 = (θ 3 + θ 4 + θ 5) − (θ 3 + θ 4) ? ? ? ? ? ? ? ? ? ? ? ? ? ? = arctan ? 2 (s 345, c 345) − (θ 3 + θ 4)$	$θ 5 ′ = (θ 3 ′ + θ 4 ′ + θ 5 ′) − (θ 3 ′ + θ 4 ′) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = a r c t a n 2 (s 3 ′ 4 ′ 5 ′, c 3 ′ 4 ′ 5 ′) − (θ 3 ′ + θ 4 ′)$
$θ 3 + θ 4 + θ 5$	${s 345 = − n z c 1 + n y s 1 s 6, c 345 = − [(s z c 1 + s y s 1) s 7 + (a z c 1 + a y s 1) c 7]$	${s 3 ′ 4 ′ 5 ′ = − n z c 1 ′ + n y s 1 ′ s 6 ′, c 3 ′ 4 ′ 5 ′ = − [(s z c 1 ′ + s y s 1 ′) s 7 ′ + (a z c 1 ′ + a y s 1 ′) c 7 ′]$

Tab.2

Inverse solution	$θ 1$ /(° )	$θ 2$ /(° )	$θ 3$ /(° )	$θ 4$ /(° )	$θ 5$ /(° )	$θ 6$ /(° )	$θ 7$ /(° )	Actual arm angle $ψ ˜$ /(° )
1	–75.0144	77.9015	–35.0088	–67.7947	–106.9448	108.4550	78.4236	129.7819
2	–75.0144	77.9015	–32.9623	–93.9476	97.1616	–108.4550	–101.5764	130.1939
3	104.9856	–77.9015	145.4975	–44.7304	–130.5154	108.4550	78.4236	142.4985
4	104.9856	–77.9015	157.5737	–83.3832	76.0612	–108.4550	–101.5764	142.5272
5	65.0858	129.3636	–170.4417	76.7806	–83.3659	87.0906	–58.9323	126.6470
6	65.0858	129.3636	–160.6816	39.4032	124.2514	–87.0906	121.0677	125.3823
7	–114.9142	–129.3636	12.8840	96.8902	–106.8012	87.0906	–58.9323	140.8476
8	–114.9142	–129.3636	10.8205	75.3257	96.8267	–87.0906	121.0677	140.3597

Tab.3

Fig.4

Inverse solution	$θ 1$ /(° )	$θ 2$ /(° )	$θ 3$ /(° )	$θ 4$ /(° )	$θ 5$ /(° )	$θ 6$ /(° )	$θ 7$ /(° )	Actual arm angle $ψ ˜$ /(° )
1	–79.6594	80.0057	–31.7645	–68.5655	–107.4127	112.4957	81.6077	134.9996
2	–79.2564	79.8118	–29.8156	–94.8141	96.7095	–112.1390	–98.6737	135.0003
3	111.1286	–75.5521	143.0353	–46.8091	–128.5043	103.3635	74.3511	135.0000
4	111.4466	–75.4437	154.0291	–84.2827	77.8483	–103.1072	–105.8565	134.9999
5	57.8508	124.0487	–170.7387	75.5782	–86.7634	81.7248	–53.1516	135.0002
6	56.9938	123.3800	–162.8315	40.3714	119.9489	–81.0841	127.5950	134.9995
7	–109.5662	–132.8739	14.2388	97.0154	–104.6965	90.9200	–62.6529	134.9997
8	–109.8352	–132.7062	12.9465	74.4857	98.9454	–90.7312	117.5244	135.0001

Tab.4

Fig.5

Fig.6

Inverse solution	$θ 1$ /(° )	$θ 2$ /(° )	$θ 3$ /(° )	$θ 4$ /(° )	$θ 5$ /(° )	$θ 6$ /(° )	$θ 7$ /(° )	Actual arm angle $ψ ˜$ /(° )
1	–74.5529	41.1411	59.0447	–147.0799	39.7875	96.3458	–25.6682	135.8676
2	–74.5529	41.1411	33.3418	–123.9961	–137.5933	–96.3458	154.3318	122.7169
3	105.4471	–41.1411	–127.4815	–121.8101	21.0440	96.3458	–25.6682	146.4159
4	105.4471	–41.1411	–151.1755	–97.6415	–159.4307	–96.3458	154.3318	136.0138
5	25.7588	113.7663	103.5857	97.3836	139.3401	121.8922	98.1554	138.8542
6	25.7588	113.7663	85.7979	125.7015	–51.1899	–121.8922	–81.8446	131.6935
7	–154.2412	–113.7663	–99.9945	121.7516	138.5523	121.8922	98.1554	139.3173
8	–154.2412	–113.7663	–124.9401	145.1176	–39.8680	–121.8922	–81.8446	125.0305

Tab.5

Inverse solution	$θ 1$ /(° )	$θ 2$ /(° )	$θ 3$ /(° )	$θ 4$ /(° )	$θ 5$ /(° )	$θ 6$ /(° )	$θ 7$ /(° )	Actual arm angle $ψ ˜$ /(° )
1	–74.2549	40.5634	58.1106	–147.0877	40.4691	96.8771	–25.9693	135.0011
2	-77.9949	51.0466	43.4482	–125.4135	–143.7159	–87.7922	159.8987	134.9980
3	113.0101	–31.4347	–137.9357	–123.3949	26.0090	105.8662	–30.5921	135.0012
4	105.9051	–40.2642	–151.8906	–97.6617	–159.0967	–97.1529	153.8738	135.0007
5	23.3078	116.7033	100.6682	97.9066	140.0811	118.3647	96.9436	135.0007
6	27.5818	111.2742	88.3354	125.4589	–52.2753	–124.7980	–80.9160	134.9985
7	–156.4982	–116.4861	–103.1285	121.4000	140.5163	118.6301	97.0378	135.0014
8	–150.2092	–107.8211	–117.2833	146.4267	–46.1905	–128.7216	–79.7563	135.0004

Tab.6

Fig.7

Fig.8

Combination of joint angles	Type of interval	Interval of actual arm angle $ψ ˜$ /(° )
$θ 2 +$ , $θ 4 −$ , $θ 6 +$	Non-solution	$(16.1116, ? ? 26.2073) ∪ (168.8087, ? 172.7647)$
$θ 2 −$ , $θ 4 −$ , $θ 6 +$	Repetition-solution	$[16.1116, ? 26.2073] ∪ [168.8087, ? 172.7647]$
$θ 2 +$ , $θ 4 −$ , $θ 6 −$	Non-solution	$(31.4828, ? 36.0285) ∪ (151.4337, ? 162.3077)$
$θ 2 −$ , $θ 4 −$ , $θ 6 −$	Repetition-solution	$[31.4828, ? 36.0285] ∪ [151.4337, ? 162.3077]$
$θ 2 −$ , $θ 4 +$ , $θ 6 +$	Non-solution	$(− 166.8049, ? − 160.3144) ∪ (− 29.4358, ? − 17.4838)$
$θ 2 +$ , $θ 4 +$ , $θ 6 +$	Repetition-solution	$[− 166.8049, ? − 160.3144] ∪ [− 29.4358, ? − 17.4838]$
$θ 2 −$ , $θ 4 +$ , $θ 6 −$	Non-solution	$(− 167.1600, ? − 156.2214) ∪ (− 31.5175, ? − 25.6658)$
$θ 2 +$ , $θ 4 +$ , $θ 6 −$	Repetition-solution	$[− 167.1600, ? − 156.2214] ∪ [− 31.5175, ? − 25.6658]$

Tab.7

$a i$ $(i = 0, ? ? 1, ? ..., ? 8)$	Link length of the EMM
$a s i j$ $(i, ? j = 1, ? 2, ? 3)$	Element of the ith row and jth column of matrix $R 3 0$
$a w i j$ $(i, ? j = 1, ? 2, ? 3)$	Element of the ith row and jth column of matrix $EE R 4$
$d$	Vector which is the projection of vector $e$ on vector $w$
$e$	Vector from shoulder point S to elbow point E
$e 0$	Vector expressed by $e$ in base coordinate system $Σ 0$
$e 0 0$	Vector expressed by $e 0$ when arm angle $ψ = 0$
$I 3$	$3 × 3$ identity matrix
$k$	Vector which is on the plane that contains vectors $V$ and $w$ and perpendicular to $w$
$k^$	Unit vector of $k$
$l$	Multiplication cross vector of $V$ and $w$ , defined as $l = V × w$
$p$	Vector which is perpendicular to $w$ and passes through point E, defined as $p = e − d$
$p^$	Unit vector of $p$
$P E E 0$	Position vector of end coordinate system $Σ EE$ in base coordinate system $Σ 0$
$R i j$ $(i, ? j = 0, ? 1, ? ..., ? 7, ? EE)$	Rotation matrix of coordinate system $Σ i$ relative to coordinate system $Σ j$ (EE corresponds to end coordinate system $Σ EE$ )
$R 4 ψ = 0 0$	Rotation matrix of coordinate system $Σ 4$ relative to base coordinate system $Σ 0$ when $ψ = 0$
$R ψ 0$	Rotation matrix which represents the rotation of arm angle $ψ$ about vector $w$
$T i j$ $(i, ? j = 0, ? 1, ? ..., ? 7, ? EE)$	Homogeneous transformation matrix of coordinate system $Σ i$ relative to coordinate system $Σ j$
$[u l ×]$	Skew-symmetric matrix of vector $l$
$[u w ×]$	Skew-symmetric matrix of vector $w$
$V$	Unit vector parallel to the rotation axis of joint 1
$V 0$	Vector expressed by $V$ in base coordinate system $Σ 0$ , defined as $V 0 = [− 1 00] T$
$w$	Vector from shoulder point S to wrist point W
$w^$	Unit vector of $w$
$w 0$	Vector expressed by $w$ in base coordinate system $Σ 0$
$w 0 0$	Vector expressed by $w 0$ when arm angle $ψ = 0$
$x 3 4$ , $y 3 4$ , and $z 3 4$	Unit vectors of three coordinate axes of coordinate system $Σ 3$ relative to coordinate system $Σ 4$
$x 40 0$ , $y 40 0$ , and $z 40 0$	Unit vectors of three coordinate axes of coordinate system $Σ 4$ relative to base coordinate system $Σ 0$ when arm angle $ψ = 0$ , and $x 30 0$ has the same meaning
$α$	Angle from $w 0 0$ rotation to $e 0 0$
$β$	Angle between $S E ⊥$ and $E ⊥ W ⊥$
$ψ$	Nominal arm angle of the EMM
$ψ ˜$	Actual arm angle of the EMM
$θ i$ $(i = 1, ? 2, ? ..., ? 7)$	Joint angle of the EMM
$θ ′ i$ $(i = 1, ? 2, ? ..., ? 7)$	Joint angle of the SRS manipulator
$θ 2 −$ and $θ 2 +$	$θ 2$ calculated by Eqs. (4) and (5)
$θ 4 −$ and $θ 4 +$	Formulas of the negative and positive values in accordance with $θ 4$ calculated by Eq. (8)
$θ 6 −$ and $θ 6 +$	Formulas of the negative and positive values in accordance with $θ 6$ calculated by Eq. (6)
$Δ θ$	Stride of $θ 1$
$ε$	Iteration termination condition
$Σ i$ $(i = 0, ? 1, ? ..., ? 7, ? EE)$	Coordinate system of the manipulator

1	R Yoshimitsu, Y Yuguchi, A Kobayashi, et al.. Dynamic simulator for HTV capture with Space Station Remote Manipulator System. In: Proceedings of the 12th International Symposium on Artificial Intelligence, Robotics and Automation in Space. Montreal: CSA, 2014, 1–8
2	R Rembala, C Ower. Robotic assembly and maintenance of future space stations based on the ISS mission operations experience. Acta Astronautica, 2009, 65(7–8): 912–920 https://doi.org/10.1016/j.actaastro.2009.03.064
3	A Flores-Abad, O Ma, K Pham, et al.. A review of space robotics technologies for on-orbit servicing. Progress in Aerospace Sciences, 2014, 68: 1–26 https://doi.org/10.1016/j.paerosci.2014.03.002
4	M Sabatini, P Gasbarri, R Monti, et al.. Vibration control of a flexible space manipulator during on orbit operations. Acta Astronautica, 2012, 73(4–5): 109–121 https://doi.org/10.1016/j.actaastro.2011.11.012
5	S B Nokleby. Singularity analysis of the Canadarm2. Mechanism and Machine Theory, 2007, 42(4): 442–454 https://doi.org/10.1016/j.mechmachtheory.2006.04.004
6	E Coleshill, L Oshinowo, R Rembala, et al.. Dextre: Improving maintenance operations on the International Space Station. Acta Astronautica, 2009, 64(9–10): 869–874 https://doi.org/10.1016/j.actaastro.2008.11.011
7	R Boumans, C Heemskerk. The European robotic arm for the international space station. Robotics and Autonomous Systems, 1998, 23(1–2): 17–27 https://doi.org/10.1016/S0921-8890(97)00054-7
8	K Krukewich, J Sexton, K Cavin, et al.. The systems engineering approach to the integration of the Space Station Remote Manipulator System on the International Space Station (ISS). Space Technology (Oxford, England), 1996, 16(1): 31–48 https://doi.org/10.1016/0892-9270(96)00001-2
9	D Li, W Rao, C Hu, et al.. Overview of the Chinese Space Station manipulator. In: Proceedings of AIAA SPACE 2015 Conference and Exposition. Pasadena: AIAA, 2015, 1–6 https://doi.org/10.2514/6.2015-4540
10	H Liu, Z Li, Y Liu, et al.. Key technologies of TianGong-2 robotic hand and its on-orbit experiments. SCIENTIA SINICA Technologica, 2018, 48(12): 1313–1320 (in Chinese) https://doi.org/10.1360/N092018-00168
11	M A Diftler, J S Mehling, M E Abdallah, et al.. Robonaut 2—The first humanoid robot in space. In: Proceedings of the IEEE International Conference on Robotics and Automation. Shanghai: IEEE, 2011, 2178–2183 https://doi.org/10.1109/ICRA.2011.5979830
12	Y Fukazu, N Hara, Y Kanamiya, et al.. Reactionless resolved acceleration control with vibration suppression capability for JEMRMS/SFA. In: Proceedings of the IEEE International Conference on Robotics and Biomimetics. Bangkok: IEEE, 2009, 1359–1364 https://doi.org/10.1109/ROBIO.2009.4913198
13	T Imaida, Y Yokokohji, T Doi, et al.. Ground-space bilateral teleoperation of ETS-VII robot arm by direct bilateral coupling under 7-s time delay condition. IEEE Transactions on Robotics and Automation, 2004, 20(3): 499–511 https://doi.org/10.1109/TRA.2004.825271
14	H Liu, Z Jiang, Y Liu. Review of space manipulator technology. Manned Spaceflight, 2015, 21(5): 435–443 (in Chinese)
15	J Baillieul. Avoiding obstacles and resolving kinematic redundancy. In: Proceedings of the IEEE International Conference on Robotics and Automation. San Francisco: IEEE, 1986, 1698–1704 https://doi.org/10.1109/ROBOT.1986.1087464
16	D Guo, Y Zhang. Acceleration-level inequality-based MAN scheme for obstacle avoidance of redundant robot manipulators. IEEE Transactions on Industrial Electronics, 2014, 61(12): 6903–6914 https://doi.org/10.1109/TIE.2014.2331036
17	R Stevenson, B Shirinzadeh, G Alici. Singularity avoidance and aspect maintenance in redundant manipulators. In: Proceedings of the 7th International Conference on Control, Automation, Robotics and Vision. Singapore: IEEE, 2002, 857–862
18	W Xu, J Zhang, B Liang, et al.. Singularity analysis and avoidance for robot manipulators with nonspherical wrists. IEEE Transactions on Industrial Electronics, 2016, 63(1): 277–290 https://doi.org/10.1109/TIE.2015.2464176
19	J M Hollerbach, K C Suh. Redundancy resolution of manipulators through torque optimization. In: Proceedings of the IEEE International Conference on Robotics and Automation. St. Louis: IEEE, 1985, 1016–1021
20	Y Zhang, W Li, X Yu, et al.. Encoder based online motion planning and feedback control of redundant manipulators. Control Engineering Practice, 2013, 21(10): 1277–1289 https://doi.org/10.1016/j.conengprac.2013.06.001
21	K N Groom, A A Maciejewski, V Balakrishnan. Real-time failure-tolerant control of kinematically redundant manipulators. IEEE Transactions on Robotics and Automation, 1999, 15(6): 1109–1115 https://doi.org/10.1109/70.817673
22	R S Jamisola, A A Maciejewski, R G Roberts. Failure-tolerant path planning for kinematically redundant manipulators anticipating locked-joint failures. IEEE Transactions on Robotics, 2006, 22(4): 603–612 https://doi.org/10.1109/TRO.2006.878959
23	Y She, W Xu, H Su, et al.. Fault-tolerant analysis and control of SSRMS-type manipulators with single-joint failure. Acta Astronautica, 2016, 120: 270–286 https://doi.org/10.1016/j.actaastro.2015.12.012
24	G K Singh, J Claassens. An analytical solution for the inverse kinematics of a redundant 7DoF manipulator with link offsets. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Taipei: IEEE, 2010, 2976–2982 https://doi.org/10.1109/IROS.2010.5649095
25	H Seraji. Configuration control of redundant manipulators: Theory and implementation. IEEE Transactions on Robotics and Automation, 1989, 5(4): 472–490 https://doi.org/10.1109/70.88062
26	R V Dubey, J A Euler, S M Babcock. Real-time implementation of an optimization scheme for seven-degree-of-freedom redundant manipulators. IEEE Transactions on Robotics and Automation, 1991, 7(5): 579–588 https://doi.org/10.1109/70.97869
27	M Shah, R V Patel. Inverse Jacobian based hybrid impedance control of redundant manipulators. In: Proceedings of the IEEE International Conference Mechatronics and Automation. Niagara Falls: IEEE, 2005, 55–60 https://doi.org/10.1109/ICMA.2005.1626522
28	A Colomé, C Torras. Closed-loop inverse kinematics for redundant robots: Comparative assessment and two enhancements. IEEE/ASME Transactions on Mechatronics, 2015, 20(2): 944–955 https://doi.org/10.1109/TMECH.2014.2326304
29	S Lee, A K Bejczy. Redundant arm kinematic control based on parameterization. In: Proceedings of the IEEE International Conference on Robotics and Automation. Sacramento: IEEE, 1991, 458–465 https://doi.org/10.1109/ROBOT.1991.131621
30	D Zu, Z Wu, D Tan. Efficient inverse kinematic solution for redundant manipulators. Chinese Journal of Mechanical Engineering, 2005, 41(6): 71–75 (in Chinese) https://doi.org/10.3901/JME.2005.06.071
31	K Kreutz-Delgado, M Long, H Seraji. Kinematic analysis of 7-DOF manipulators. International Journal of Robotics Research, 1992, 11(5): 469–481 https://doi.org/10.1177/027836499201100504
32	M Shimizu, H Kakuya, W K Yoon, et al.. Analytical inverse kinematic computation for 7-DOF redundant manipulators with joint limits and its application to redundancy resolution. IEEE Transactions on Robotics, 2008, 24(5): 1131–1142 https://doi.org/10.1109/TRO.2008.2003266
33	W Xu, L Yan, Z Mu, et al.. Dual arm-angle parameterisation and its applications for analytical inverse kinematics of redundant mani-pulators. Robotica, 2016, 34(12): 2669–2688 https://doi.org/10.1017/S0263574715000284
34	D Zhou, L Ji, Q Zhang, et al.. Practical analytical inverse kinematic approach for 7-DOF space manipulators with joint and attitude limits. Intelligent Service Robotics, 2015, 8(4): 215–224 https://doi.org/10.1007/s11370-015-0180-3
35	S Dereli, R Koker. 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. Inverse Problems in Science and Engineering, 2020, 28(5): 601–613 https://doi.org/10.1080/17415977.2019.1602124
36	M Faroni, M Beschi, N Pedrocchi. Inverse kinematics of redundant manipulators with dynamic bounds on joint movements. IEEE Robotics and Automation Letters, 2020, 5(4): 6435–6442 https://doi.org/10.1109/LRA.2020.3013879
37	M Gong, X Li, L Zhang. Analytical inverse kinematics and self-motion application for 7-DOF redundant manipulator. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 18662–18674 https://doi.org/10.1109/ACCESS.2019.2895741
38	M Kelemen, I Virgala, T Liptak, et al.. A novel approach for a inverse kinematics solution of a redundant manipulator. Applied Sciences, 2018, 8(11): 2229 https://doi.org/10.3390/app8112229
39	C D III Crane, J Duffy, T Carnahan. A kinematic analysis of the space station remote manipulator system (SSRMS). Journal of Robotic Systems, 1991, 8(5): 637–658 https://doi.org/10.1002/rob.4620080505
40	C Yu, M Jin, H Liu. An analytical solution for inverse kinematic of 7-DOF redundant manipulators with offset-wrist. In: Proceedings of the IEEE International Conference on Mechatronics and Automation. Chengdu: IEEE, 2012, 92–97 https://doi.org/10.1109/ICMA.2012.6282813
41	V Abbasi, B Azria, E Tabarah, et al.. Improved 7-DOF control of ISS robotic manipulators. In: Proceedings of AIAA Space OPS 2004 Conference. Montreal: AIAA, 2004 https://doi.org/10.2514/6.2004-610-407
42	S Lu, Y Gu, J Zhao, et al.. An iterative calculation method for solve the inverse kinematics of a 7-DOF robot with link offset. In: Huang Y, Wu H, Liu H, et al., eds. Intelligent Robotics and Applications. ICIRA 2017. Lecture Notes in Computer Science, vol 10464. Cham: Springer https://doi.org/10.1007/978-3-319-65298-6_65
43	M Jin, Q Liu, B Wang, et al.. An efficient and accurate inverse kinematics for 7-DOF redundant manipulators based on a hybrid of analytical and numerical method. IEEE Access: Practical Innovations, Open Solutions, 2020, 8: 16316–16330 https://doi.org/10.1109/ACCESS.2020.2966768
44	W Xu, J Zhang, L Yan, et al.. Parameterized inverse kinematics resolution method for a redundant space manipulator with link offset. Journal of Astronautics, 2015, 36(1): 33–39 (in Chinese)
45	J J Craig. Introduction to Robotics: Mechanics and Control. 4th ed. New York: Pearson Education Inc., 2005

Viewed

Full text

Abstract

Cited

Shared

Discussed