In the previous reports, analytical target cascading (ATC) is generally applied to product optimization. In this paper, the application area of ATC is expanded to trajectory optimization. Direct collocation method is utilized to convert a trajectory optimization into a nonlinear programing (NLP) problem. The converted NLP is a large-scale problem with sparse matrix of functional dependence table (FDT) suitable for the application of ATC. Three numerical case studies are provided to show the effects of ATC in solving trajectory optimization problems.

References

References
1.
Kober
,
J.
,
Bagnell
,
J. A.
, and
Peters
,
J.
,
2013
, “
Reinforcement Learning in Robotics: A Survey
,”
Int. J. Rob. Res.
,
32
(
11
), pp.
1238
1274
.
2.
Kulkarni
,
T. D.
,
Narasimhan
,
K. R.
, and
Saeedi
,
A.
,
2016
, “
Hierarchical Deep Reinforcement Learning: Integrating Temporal Abstraction and Intrinsic Motivation
,”
arXiv:1604.06057
.
3.
Betts
,
J. T.
,
2009
,
Practical Methods for Optimal Control and Estimation Using Nonlinear Programming
,
Society for Industrial and Applied Mathematics (SIAM) Press,
Philadelphia, PA
.
4.
Hull
,
D. G.
,
1997
, “
Conversion of Optimal Control Problems Into Parameter Optimization Problems
,”
J. Guid. Control Dyn.
,
20
(
1
), pp.
57
60
.
5.
Dolan
,
E. D.
, and
More
,
J. J.
,
2002
, “
Benchmarking Optimization Software With Performance Profiles
,”
Math. Program.
,
91
(
2
), pp.
201
213
.
6.
Dolan
,
E. D.
,
More
,
J. J.
, and
Munson
,
T. S.
,
2004
, “
Benchmarking Optimization Software With COPS 3.0
,” Argonne National Laboratory, Argonne, IL, Technical Report No.
ANL/MCS-TM-273
.
7.
Kim
,
H. M.
,
Rideout
,
D. G.
,
Papalambros
,
P. Y.
, and
Stein
,
J. L.
,
2003
, “
Analytical Target Cascading in Automotive Vehicle Design
,”
ASME J. Mech. Des.
,
125
(
9
), pp.
481
489
.
8.
Tosserams
,
S.
,
Kokkolaras
,
M.
,
Etman
,
L. F. P.
, and
Rooda
,
J. E.
,
2010
, “
A Nonhierarchical Formulation of Analytical Target Cascading
,”
ASME J. Mech. Des.
,
132
(
5
), p.
051002
.
9.
Guarneri
,
P.
,
Gobbi
,
M.
, and
Papalambros
,
P. Y.
,
2011
, “
Efficient Multi-Level Design Optimization Using Analytical Target Cascading and Sequential Quadratic Programming
,”
Struct. Multidiscip. Optim.
,
44
(
3
), pp.
351
362
.
10.
Tedford
,
N. P.
, and
Martins
,
J. R. R. A.
,
2010
, “
Benchmarking Multidisciplinary Design Optimization Algorithms
,”
Optim. Eng.
,
11
(
1
), pp.
159
183
.
11.
Braun
,
R.
,
1996
, “
Collaborative Optimization: An Architecture for Large-Scale Distributed Design
,”
Ph.D. thesis
, Stanford University, Stanford, CA.
12.
Kim
,
H. M.
,
2001
, “
Target Cascading in Optimal System Design
,”
Ph.D. dissertation
, University of Michigan, Ann Arbor, MI.
13.
Roth
,
B. D.
, and
Kroo
,
I. M.
,
2008
, “
Enhanced Collaborative Optimization: A Decomposition-Based Method for Multidisciplinary Design
,”
ASME
Paper No. DETC2008-50038.
14.
Tosserams
,
S.
,
Etman
,
L. F. P.
,
Papalambros
,
P. Y.
, and
Rooda
,
J. E.
,
2006
, “
An Augmented Lagrangian Relaxation for Analytical Target Cascading Using the Alternating Direction Method of Multipliers
,”
Struct. Multidiscip. Optim.
,
31
(
3
), pp.
176
189
.
15.
Wang
,
W.
,
Blouin
,
V. Y.
,
Gardenghi
,
M. K.
,
Fadel
,
G. M.
,
Wiecek
,
M. M.
, and
Sloop
,
B. C.
,
2013
, “
Cutting Plane Methods for Analytical Target Cascading With Augmented Lagrangian Coordination
,”
ASME J. Mech. Des.
,
135
(
10
), p.
104502
.
16.
Han
,
J.
, and
Papalambros
,
P. Y.
,
2010
, “
A Sequential Linear Programming Coordination Algorithm for Analytical Target Cascading
,”
ASME J. Mech. Des.
,
132
(
2
), p.
021003
.
17.
Li
,
X.
,
Liu
,
C.
,
Li
,
W.
, and
Shang
,
H.
,
2013
, “
Application of Collaborative Optimization to Optimal Control Problems
,”
AIAA J.
,
51
(
3
), pp.
745
750
.
18.
Michelena
,
N.
,
Park
,
H.
, and
Papalambros
,
P. Y.
,
2003
, “
Convergence Properties of Analytical Target Cascading
,”
AIAA J.
,
41
(
5
), pp.
897
905
.
19.
Kang
,
N.
,
Kokkolaras
,
M.
,
Papalambros
,
P. Y.
,
Yoo
,
S.
,
Na
,
W.
,
Park
,
J.
, and
Featherman
,
D.
,
2014
, “
Optimal Design of Commercial Vehicle Systems Using Analytical Target Cascading
,”
Struct. Multidiscip. Optim.
,
50
(
6
), pp.
1103
1114
.
20.
Wagner
,
T. C.
,
1993
, “
A General Decomposition Methodology for Optimal System Design
,”
Ph.D. dissertation
, University of Michigan, Ann Arbor, MI.
21.
Michalek
,
J. J.
, and
Papalambros
,
P. Y.
,
2005
, “
An Efficient Weighting Update Method to Achieve Acceptable Consistency Deviation in Analytical Target Cascading
,”
ASME J. Mech. Des.
,
127
(
2
), pp.
206
214
.
22.
Dormohammadi
,
S.
, and
Rais-Rohani
,
M.
,
2013
, “
Exponential Penalty Function Formulation for Multilevel Optimization Using the Analytical Target Cascading Framework
,”
Struct. Multidiscip. Optim.
,
47
(
4
), pp.
599
612
.
23.
Yokoyama
,
N.
, and
Suzuki
,
S.
,
2005
, “
Modified Genetic Algorithm for Constrained Trajectory Optimization
,”
J. Guid. Control Dyn.
,
28
(
1
), pp.
139
144
.
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