On the Reliable Computation of Optimal Motions for Underactuated Manipulators

In this paper we develop a numerical solution to optimal control problems for underactuated manipulators. Our approach finds a local solution to the nonlinear optimal control problem using an SQP approach with exact gradients of the cost function. We show that a dramatic improvement in computation times can be obtained if one computes the required gradient using the adjoint equations and a backward integration standard in optimal control theory. We demonstrate the the algorithm on a 19 dof model high-diver for various initial conditions and performance criteria.