Optimal Trajectories of Open-Chain Robot Systems: A New Solution Procedure Without Lagrange Multipliers

[+] Author and Article Information
Sunil K. Agrawal, Pana Claewplodtook

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716

Brian C. Fabien

Dept. of Mechanical Engineering, University of Washington, Seattle, WA 98195

J. Dyn. Sys., Meas., Control 120(1), 134-136 (Mar 01, 1998) (3 pages) doi:10.1115/1.2801309 History: Received May 15, 1995; Online December 03, 2007


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.

Copyright © 1998 by The American Society of Mechanical Engineers
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