The recently developed bio-inspired virtual motion camouflage (VMC) method can be used to rapidly solve nonlinear constrained optimal trajectory problems. However, the optimality of VMC solution is affected by the dimension reduced search space. Compared with the VMC method, the B-spline augmented VMC (BVMC) method studied in this paper improves the optimality of the solution, while the computational cost will not be significantly increased. Two simulation examples, the Snell's river problem and a robotic minimum time obstacle avoidance problem, are used to show the advantages of the algorithm.
Issue Section:
Technical Briefs
References
1.
Nusyirwan
, I. F.
, and Bil
, C.
, 2007
, “Effect of Uncertainties on UAV Optimisation Using Evolutionary Programming
,” IEEE Information, Decision, and Control Conference
, Feb. 11–14, Adelaide, Australia
, pp. 219
–223
.2.
Kaneshige
, J.
, and Krishnakumar
, K.
, 2007
, “Artificial Immune System Approach for Air Combat Maneuvering
,” Intelligent Computing: Theory and Applications
, K. L.
Priddy
and E.
Ertin
, eds., Society of Photo Optical, New York.3.
Merchan-Cruz
, E. A.
, and Morris
, A. S.
, 2006
, “Fuzzy-GA-Based Trajectory Planner for Robot Manipulators Sharing a Common Workspace
,” IEEE Trans. Rob.
, 22
(4
), pp. 613
–624
.10.1109/TRO.2006.8787894.
Hristu-Varsakelis
, D.
, and Shao
, C.
, 2004
, “Biologically-Inspired Optimal Control: Learning From Social Insects
,” Int. J. Control
, 77
(18
), pp. 1549
–1566
.10.1080/002071704123313300985.
Lawden
, D. F.
, 1991
, “Rocket Trajectory Optimization: 1950–1963
,” J. Guid. Control Dyn.
, 14
(4
), pp. 705
–711
.10.2514/3.207036.
Ocampo
, C.
, 2004
, “Finite Burn Maneuver Modeling for a Generalized Spacecraft Trajectory Design and Optimization System
,” Ann. N. Y. Acad. Sci.
, 1017
, pp. 210
–233
.10.1196/annals.1311.0137.
Pontryagin
, L. S.
, Boltyanskii
, V. G.
, Gamkrelidze
, R. V.
, and Mishchenko
, E. F.
, 1962
, The Mathematical Theory of Optimal Processes
, Wiley-Interscience
, New York
.8.
Betts
, J.
, 2001
, Practical Methods for Optimal Control Using Nonlinear Programming
, SIAM
, Philadelphia
.9.
Fahroo
, F.
, and Ross
, I. M.
, 2001
, “Costate Estimation by a Legendre Pseudospectral Method
,” J. Guid. Control Dyn.
, 24
(2
), pp. 270
–275
.10.2514/2.470910.
Hager
, W.
, 2000
, “Runge-Kutta Methods in Optimal Control and the Transformed Adjoint System
,” Numer. Math.
, 87
(2
), pp. 247
–282
.10.1007/s00211000017811.
Milam
, M.
, Mushambi
, K.
, and Murray
, R.
, 2000
, “A Computational Approach to Real-Time Trajectory Generation for Constrained Mechanical Systems
,” IEEE Conference on Decision and Control
, Dec. 12–15, Sydney, Australia
, pp. 845
–851
.12.
Dai
, R.
, “B-Splines Based Optimal Control Solution
,” 2010 AIAA Guidance, Navigation, and Control Conference
, Aug. 2–5, Toronto, ON
, Paper No. AIAA-2010-7888.13.
Jackiewicz
, Z.
, and Welfert
, B. D.
, 2003
, “Stability of Gauss-Radau Pseudospectral Approximations of the One-Dimensional Wave Equation
,” J. Sci. Comput.
, 18
(2
), pp. 287
–313
.10.1023/A:102112100809114.
Kameswaran
, S.
, and Biegler
, L. T.
, 2008
, “Convergence Rates for Direct Transcription of Optimal Control Problems Using Collocation at Radau Points
,” Comput. Optim. Appl.
, 41
(1
), pp. 81
–126
.10.1007/s10589-007-9098-915.
Jacobson
, D. H.
, and Lele
, M. M.
, 1969
, “A Transformation Technique for Optimal Control Problems With a State Variable Inequality Constraint
,” IEEE Trans. Autom. Control
, 14
(5
), pp. 457
–464
.10.1109/TAC.1969.109928316.
Mehra
, R. K.
, and Davis
, R. E.
, 1972
, “A Generalized Gradient Method for Optimal Control Problems With Inequality Constraints and Singular Arcs
,” IEEE Trans. Autom. Control
, 17
(1
), pp. 69
–79
.10.1109/TAC.1972.109988117.
Betts
, J.
, 1998
, “Survey of Numerical Methods for Trajectory Optimization
,” J. Guid. Control Dyn.
, 21
(2
), pp. 193
–207
.10.2514/2.423118.
Goerzen
, C.
, Kong
, Z.
, and Mettler
, B.
, 2010
, “A Survey of Motion Planning Algorithms From the Perspective of Autonomous UAV Guidance
,” J. Intell. Robotic Syst.
, 57
, pp. 65
–100
.10.1007/s10846-009-9383-119.
Xu
, Y.
, 2007
, “Motion Camouflage and Constrained Suboptimal Trajectory Control
,” 2007 AIAA Guidance, Control, and Dynamics Conference
, Aug. 20–23, Hilton Head, SC
.20.
Xu
, Y.
, 2010
, “Analytical Solutions to Formation Flying System Trajectory Guidance Via the Virtual Motion Camouflage Approach
,” J. Guid. Control Dyn.
, 33
(5
), pp. 1376
–1386
.10.2514/1.4869121.
Kumar
, R. R.
, and Seywald
H.
, 1996
, “Should Controls be Eliminated While Solving Optimal Control Problems Via Direct Methods?
,” J. Guid. Control Dyn.
, 19
(2
), pp. 418
–423
.10.2514/3.2163422.
Piegl
, L.
, and Tiller
, W.
, 1997
, The NURBS Book: Second Edition
, Springer-Verlag
, New York
.23.
Benson
, D. A.
, Huntington
, G. T.
, Thorvaldsen
, T. P.
, and Rao
, A. V.
, 2006
, “Direct Trajectory Optimization and Costate Estimation Via an Orthogonal Collocation Method
,” J. Guid. Control Dyn.
, 29
(6
), pp. 1435
–1440
.10.2514/1.2047824.
Rao
, C. V.
, Wright
, S. J.
, and Rawlings
, J. B.
, 1998
, “Application of Interior-Point Methods to Model Predictive Control
,” J. Optim. Theory Appl.
, 99
(3
), pp. 723
–757
.10.1023/A:102171140272325.
Xu
, Y.
, and Basset
, G.
, 2010
, “Real-Time Optimal Coherent Phantom Track Generation Via the Virtual Motion Camouflage Approach
,” 2010 AIAA Guidance, Navigation, and Control Conference
, Aug. 2–5, Toronto, ON, Canada
, Paper No. AIAA-2010-7714.26.
Hartl
, R. F.
, Sethi
, S. P.
, and Vickson
, R. G.
, 1995
, “A Survey of the Maximum Principles for Optimal Control Problems With State Constraints
,” SIAM Rev.
, 37
(2
), pp. 181
–218
.10.1137/103704327.
Srinivasan
, M. V.
, and Davey
, M.
, 1995
, “Strategies for Active Camouflage Motion
,” Proc. R. Soc. London
, 259
(1354
), pp. 19
–25
.10.1098/rspb.1995.000428.
Gong
, Q.
, Kang
, W.
, and Ross
, I. M.
, 2006
, “A Pseudospectral Method for the Optimal Control of Constrained Feedback Linearizable Systems
,” IEEE Trans. Autom. Control
, 51
(7
), pp. 1115
–1129
.10.1109/TAC.2006.87857029.
Gong
, Q.
, Ross
, I. M.
, Kang
, W.
, and Fahroo
, F.
, 2008
, “Connections Between the Covector Mapping Theorem and Convergence of Pseudospectral Methods for Optimal Control
,” Comput. Optim. Appl.
, 41
(3
), pp. 307
–335
.10.1007/s10589-007-9102-430.
Ferrante
, A.
, and Ntogramatzidis
, L.
, 2006
, “A Unified Approach to the Finite-Horizon LQ Regulator—Part I: The Continuous Time
,” 45th IEEE Conference on Decision and Control
, Dec. 13–15, San Diego, CA
, pp. 5651
–5656
.31.
Bryson
, A. E.
, Jr., and Ho
, Y. C.
, 1975
, Applied Optimal Control: Optimization, Estimation, and Control
, Taylor & Francis
, Washington, DC
.32.
Laumond
, J. P.
, Sekhavat
, S.
, and Lamiraux
, F.
, 1998
, Guidelines in Nonholonomic Motion Planning for Mobile Robots (Lecture Notes in Control and Information Sciences), LNCIS 229, Springer-Verlag, New York, pp. 1
–44
.Copyright © 2013 by ASME
You do not currently have access to this content.