Optimal Trajectories of Open-Chain Robot Systems: A New Solution Procedure Without Lagrange Multipliers
1998 ◽
Vol 120
(1)
◽
pp. 134-136
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Keyword(s):
For an n d.o.f. robot system, optimal trajectories using Lagrange multipliers are characterized by 4n first-order nonlinear differential equations with 4n boundary conditions at the two end time. Numerical solution of such two-point boundary value problems with shooting techniques is hard since Lagrange multipliers can not be guessed. In this paper, a new procedure is proposed where the dynamic equations are embedded into the cost functional. It is shown that the optimal solution satisfies n fourth-order differential equations. Due to absence of Lagrange multipliers, the two-point boundary-value problem can be solved efficiently and accurately using classical weighted residual methods.
1996 ◽
Vol 26
(4)
◽
pp. 1499-1515
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1977 ◽
Vol 7
(1)
◽
pp. 103-110
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1990 ◽
Vol 20
(4)
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pp. 899-907
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2003 ◽
pp. 977-989
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1996 ◽
Vol 11
(3)
◽
pp. 335-348
2010 ◽
Vol 1
(1)
◽
pp. 105-118
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1978 ◽
Vol 29
(2)
◽
pp. 205-213
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