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.

1.
Agrawal
S. K.
, and
Veeraklaew
T.
, “
A Higher-Order Method for Optimization of a Class of Linear Time-Invariant Dynamic Systems
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
118
, No.
4
,
1996
, pp.
786
791
.
2.
Agrawal
S. K.
,
Li
S.
, and
Fabien
B. C.
, “
Optimal Trajectories of Open-Chain Mechanical Systems: Explicit Optimality Equation with Multiple Shooting Solution
,”
Mechanics of Structures and Machines
, Vol.
25
, No.
2
,
1997
, pp.
163
177
.
3.
Bryson, A. E., and Ho, Y. C., Applied Optimal Control, Hemisphere Publishing Company, 1975.
4.
Claewplodtook, P., “Optimization of a Class of Nonlinear Dynamic Systems without Lagrange Multipliers,” M.S. thesis of Mechanical Engineering, Ohio University, 1996.
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