This paper presents a new parallel algorithm for the operational space dynamics of unconstrained serial manipulators, which outperforms contemporary sequential and parallel algorithms in the presence of two or more processors. The method employs a hybrid divide and conquer algorithm (DCA) multibody methodology which brings together the best features of the DCA and fast sequential techniques. The method achieves a logarithmic time complexity (O(log(n)) in the number of degrees of freedom (n) for computing the operational space inertia (Λe) of a serial manipulator in presence of O(n) processors. The paper also addresses the efficient sequential and parallel computation of the dynamically consistent generalized inverse (J¯e) of the task Jacobian, the associated null space projection matrix (Ne), and the joint actuator forces (τnull) which only affect the manipulator posture. The sequential algorithms for computing J¯e, Ne, and τnull are of O(n), O(n2), and O(n) computational complexity, respectively, while the corresponding parallel algorithms are of O(log(n)), O(n), and O(log(n)) time complexity in the presence of O(n) processors.

References

References
1.
Khatib
,
O.
,
1987
. “
A Unified Approach for Motion and Force Control of Robot Manipulators: The Operational Space Formulation
,”
IEEE J. Robotics and Automation
,
3
(
1
), pp.
43
53
.10.1109/JRA.1987.1087068
2.
Khatib
,
O.
,
Brock
,
O.
,
Chang
,
K.
,
Ruspini
,
D.
,
Sentis
,
L.
, and
Viji
,
S.
,
2003
, “
Robots for the Human and Interactive Simulations
,”
Proceedings of the 11th World Congress in Mechanism and Machine Science
, Tianjin, China, pp.
1572
1576
.
3.
Kreutz-Delgado
,
K.
,
Jain
,
A.
, and
Rodriguez
,
G.
,
1992
, “
Recursive Formulation of Operational Space Control
,”
Int. J. Robotics Res.
,
11
(
4
), pp.
320
328
.10.1177/027836499201100405
4.
Lilly
,
K.
, and
Orin
,
D.
,
1993
, “
Efficient o(n) Recursive Computation of the Operational Space Inertia Matrix
,”
IEEE Trans. Systems, Man and Cybernetics
,
23
(
5
), pp.
1384
1391
.10.1109/21.260669
5.
Chang
,
K.
, and
Khatib
,
O.
,
2000
, “
Operational Space Dynamics: Efficient Algorithms for Modeling and Control of Branching Mechanisms
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Vol.
1
, pp.
850
856
.
6.
Wensing
,
P.
,
Featherstone
,
R.
, and
Orin
,
D.
,
2012
, “
A Reduced-Order Recursive Algorithm for the Computation of the Operational-Space Inertia Matrix
,”
Proceedings of ICRA 2012. IEEE International Conference on Robotics and Automation
, pp.
4911
4917
.
7.
Featherstone
,
R.
,
2010
, “
Exploiting Sparsity in Operational-Space Dynamics
,”
Int. J. Robotics Res.
,
29
(
10
), pp.
1353
1368
.10.1177/0278364909357644
8.
Fijany
,
A.
,
1994
, “
Schur Complement Factorizations and Parallel O(logn) Algorithms for Computation of Operational Space Mass Matrix and its Inverse
,” Robotics and Automation, 1994,
Proceedings of the 1994 IEEE International Conference on IEEE
, pp.
2369
2376
.
9.
Jain
,
A.
,
2010
,
Robot and Multibody Dynamics: Analysis and Algorithms
,
Springer Verlag
,
Berlin
.
10.
Fijany
,
A.
, and
Featherstone
,
R.
,
2013
, “
A New Factorization of the Mass Matrix for Optimal Serial and Parallel Calculation of Multibody Dynamics
,”
Multibody System Dynamics
,
29
(
2
), pp.
169
187
.10.1007/s11044-012-9313-z
11.
Bhalerao
,
K. D.
,
Critchley
,
J.
, and
Anderson
,
K.
,
2012
, “
An Efficient Parallel Dynamics Algorithm for Simulation of Large Articulated Robotic Systems
,”
Mech. Mach. Theory
,
53
, pp.
86
98
.10.1016/j.mechmachtheory.2012.03.001
12.
Nakanishi
,
J.
,
Cory
,
R.
,
Mistry
,
M.
,
Peters
,
J.
, and
Schaal
,
S.
,
2008
, “
Operational Space Control: A Theoretical and Empirical Comparison
,”
Int. J. Robotics Res.
,
27
(
6
), pp.
737
757
.10.1177/0278364908091463
13.
Featherstone
,
R.
,
1999
, “
A Divide-and-Conquer Articulated Body Algorithm for Parallel O(log(n)) Calculation of Rigid Body Dynamics. Part 1: Basic Algorithm
,”
Int. J. Robotics Res.
,
18
(
9
), pp.
867
875
.10.1177/02783649922066619
14.
Featherstone
,
R.
,
1999
, “
A Divide-and-Conquer Articulated Body Algorithm for Parallel O(log(n)) Calculation of Rigid Body Dynamics. Part 2: Trees, Loops, and Accuracy
,”
Int. J. Robotics Res.
,
18
(
9
), pp.
876
892
.10.1177/02783649922066628
15.
Lathrop
,
R.
,
1985
, “
Parallelism in Manipulator Dynamics
,”
Int. J. Robotics Res.
,
4
(
2
), pp.
80
102
.10.1177/027836498500400207
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