OPTIMAL TRAJECTORIES OF OPEN-CHAIN ROBOT SYSTEMS - A NEW SOLUTION PROCEDURE WITHOUT LAGRANGE MULTIPLIERS

For an n d.o.f. robot system, optimal trajectories using Lagrange mult ipliers are characterized by 4n first-order nonlinear differential equ ations with 4n boundary conditions at the two end time. Numerical solu tion of such two-point boundary value problems with shooting technique s 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 satis fies n fourth-order differential equations. Due to absence of Lagrange multipliers, the two-point boundary-value problem can be solved effic iently and accurately using classical weighted residual methods.