Abstract
In this paper we develop an algorithm for solving optimal control problems for underactuated open chain manipulators. A local solution to the nonlinear optimal control problem is obtained using a constrained parameter optimization procedure. As part of the algorithm, a recursive dynamics formulation for underactuated serial chains is derived using matrix exponentials and the geometric framework provided by Lie groups and Lie algebras. The benefit of the matrix exponential formulation is the ability to derive explicit analytic gradients of the dynamics. These gradients are essential for our algorithm since the parameter optimization is ill-conditioned aid approximate numerical gradients do not produce meaningful solutions. Interesting example solutions are provided for a two dof acrobot, a simple branched chain and a 7 dof human diver.
