Singularity prediction of Jacobian is inherently related to the design of any manipulator. Optimization of Jacobian is known to improve the joint rates and joint torques for the same set of end-effector twists and wrenches. Any mathematical entity which is an estimator of Jacobian can be used as a manifestation of the stated two schemes. It is required that online computation of Jacobian be implemented so that singular poses can be avoided and performance is maximized. We present an algorithm that relates to the determinant of the Jacobian for robotic manipulators. The algorithm developed is quicker to compute, and a strategy is developed to synthesize the local estimator contour. The contours change dynamically, henceforth optimal motor torques (in case of presence of interaction fields or system requiring force control) and optimal joint rates can be defined, depending on the control algorithm. The algorithm developed is independent of the structure of the matrix and is generalized to any six DoF manipulator structure used.
HuQZhangJ.Dynamics and trajectory planning for reconfigurable space multibody robots. J Mech Des2015;
137: 092304-1–092304-12.
2.
ChuXHuQZhangJ.Path planning and collision avoidance for a multi-arm space maneuverable robot. IEEE Trans Aerosp Electron Syst2018;
54: 217–232.
3.
LiuFZhangJHuQ.A modified constraint force algorithm for flexible multibody dynamics with loop constraints. Nonlinear Dyn2017;
90: 1885–1906.
4.
ZanganehKEAngelesJ.Kinematic isotropy and the optimum design of parallel manipulators. Int J Robot Res1997;
16: 185–197.
5.
HuangTLiMLiZ, et al.
Optimal kinematic design of 2-DoF parallel manipulators with well-shaped workspace bounded by a specified conditioning index. IEEE Trans Robot Autom2004;
20: 538–543.
6.
GosselinCAngelesJ.Singularity analysis of closed-loop kinematic chains. IEEE Trans Robot Autom1990;
6: 281–290.
7.
StoughtonRSAraiT.A modified Stewart platform manipulator with improved dexterity. IEEE Trans Robot Automat1993;
9: 166–173.
8.
PaiDKLeuMC.Genericity and singularities of robot manipulators. IEEE Trans Robot Autom1992;
8: 545–559.
9.
MerletJP.Determination of the presence of singularities in 6D workspace of a Gough parallel manipulator. In: Lenarčič J and Husty ML (eds) Advances in robot kinematics: analysis and control.
Dordrecht:
Springer, 1998, pp. 39–48.
10.
MerletJP.Jacobian, manipulability, condition number, and accuracy of parallel robots. J Mech Des2006;
128: 199–206.
11.
HuntKH.Kinematic geometry of mechanisms.
Oxford:
Oxford University Press, 1978, vol. 7.
12.
HayesMJDHustyMLZsombor-MurrayPJ.Singular configurations of wrist-partitioned 6R serial robots: a geometric perspective for users. Trans Can Soc Mech Eng2002;
26: 41–55.
13.
PaulRPStevensonCN.Kinematics of robot wrists. Int J Robot Res1983;
2: 31–38.
14.
SciaviccoLSicilianoB.Modelling and control of robot manipulators. Berlin: Springer Science & Business Media, 2012.
15.
MerletJPDaneyD. A formal-numerical approach to determine the presence of singularity within the workspace of a parallel robot. In: 2nd Workshop on Computational Kinematics, Seoul, South Korea, May 2001, pp. 167–176.
16.
WangXZhangDZhaoC, et al.
Singularity analysis and treatment for a 7R 6-DOF painting robot with non-spherical wrist. Mech Mach Theory2018;
126: 92–107.
17.
KimDEParkDJParkJH, et al. Collision and singularity avoidance path planning of 6-DOF dual-arm manipulator. In: International Conference on Intelligent Robotics and Applications. Cham: Springer, 2018, pp. 195–207.
18.
BohigasOManubensMRosL.Singularities of robot mechanisms: numerical computation and avoidance path planning.
Cham:
Springer, 2016.
19.
ZhouCJinMHLiuYC, et al.
Singularity robust path planning for real time base attitude adjustment of free-floating space robot. Int J Autom Comput2017;
14: 169–178.
20.
WuJBinDFengX, et al.
GA based adaptive singularity-robust path planning of space robot for on-orbit detection. Complexity2018;
2018: 1–11.
21.
CorinaldiDCallegariMAngelesJ.Singularity-free path-planning of dexterous pointing tasks for a class of spherical parallel mechanisms. Mech Mach Theory2018;
128: 47–57.
22.
LiBWangKHanY, et al.
Singularity property and singularity-free path planning of the Gough–Stewart parallel mechanism. Int J Adv Robot Syst2017;
14: 1729881417734971.
23.
AgarwalANasaCBandyopadhyayS.Dynamic singularity avoidance for parallel manipulators using a task-priority based control scheme. Mech Mach Theory2016;
96: 107–126.
24.
BohigasOManubensMRosL. Singularity-free path planning. In: Singularities of robot mechanisms. Cham: Springer, 2017, pp. 111–136.
25.
CalzolariDLamparielloRGiordanoAM.Singularity maps of space robots and their application to gradient-based trajectory planning. In: Robotics: Science and Systems 2020 (Held Virtually), Corvalis, Oregon, USA, July 12-16 2020, http://www.roboticsproceedings.org/rss16/p015.pdf.
26.
RakitaDMutluBGleicherM. RelaxedIK: real-time synthesis of accurate and feasible robot arm motion. In: Robotics: Science and Systems, Pittsburgh, Pennsylvania, USA, 2018, pp. 26–30, http://www.roboticsproceedings.org/rss14/p43.pdf
27.
SixDBriotSChrietteA, et al.
A controller avoiding dynamic model degeneracy of parallel robots during singularity crossing. J Mechan Robot2017;
9: 051008-1–051008-8.
28.
KamaliKBonevIADesrosiersC. Real-time motion planning for robotic teleoperation using dynamic-goal deep reinforcement learning. In: 2020 17th Conference on Computer and Robot Vision (CRV). Piscataway: IEEE, 2020, pp. 182–189.
29.
KotlarskiJDe NijsRAbdellatifH, et al. 2009, May. New interval-based approach to determine the guaranteed singularity-free workspace of parallel robots. In: 2009 IEEE International Conference on Robotics and Automation. Piscataway: IEEE, pp. 1256–1261.
30.
GosselinCAngelesJ.Singularity analysis of closed-loop kinematic chains. IEEE Trans Robot Automat1990;
6: 281–290.
31.
LiWAngelesJ.A novel three-loop parallel robot with full mobility: kinematics, singularity, workspace, and dexterity analysis. J Mech Robot2017;
9: 051003-1–051003-10.
32.
ChengSJiP.Geometric algebra approach to analyzing the singularity of six-DOF parallel mechanism. J Adv Mech Des Syst Manuf2019;
13: JAMDSM0076–JAMDSM0076.
33.
GonzalezDJAsadaHH.Design and analysis of 6-dof triple scissor extender robots with applications in aircraft assembly. IEEE Robot Autom Lett2017;
2: 1420–1427.
34.
XuRAsadianANaiduAS, et al. 2013, May. Position control of concentric-tube continuum robots using a modified Jacobian-based approach. In 2013 IEEE International Conference on Robotics and Automation. Piscataway: IEEE, pp. 5813–5818.
35.
KimDChungWK.Analytic formulation of reciprocal screws and its application to nonredundant robot manipulators. Journal of Mechanical Design2003;
125: 158–164.
36.
SugimotoKDuffyJ.Application of linear algebra to screw systems. Mech Mach Theory1982;
17: 73–83.
KaltofenEVillardG.On the complexity of computing determinants. Comput Complex2005;
13: 91–130.
39.
PanV.Computing the determinant and the characteristic polynomial of a matrix via solving linear systems of equations. Inform Process Lett1988;
28: 71–75.
40.
RajeevlochanaCGSahaSKKumarS.Automatic extraction of DH parameters of serial manipulators using line geometry. In:The 2nd International Conference on Multibody System Dynamics, Stuttgart, Germany, May 29-June 1 2012.
41.
TeukolskySAFlanneryBPPressWH, et al.
Numerical recipes in C. SMR1992;
693: 59–70.
42.
FisherRA.Statistical methods for research workers.
Edinburgh:
Oliver and Boyd, 1958, 356 pp.
43.
KargerA.Singularity analysis of serial robot-manipulators. J Mech Des1996;
118: 520–525.
