Optimal planning of an under-actuated planar body using higher-order method

An optimal motion planning scheme for an under-actuated planar rigid body is presented. A higher-order method developed by the authors is used to construct the trajectories of this system. In this method, the explicit expressions for the states and inputs in terms of higher derivatives of a subset of states is used to change a constrained dynamic optimization problem into an unconstrained one, thereby, eliminating the need for Lagrange multipliers. The method is applied to a two input planar free-floating robot with three degrees-of-freedom and the numerical results are reported.