This thesis presents a new model-based optimal control approach to 2D path tracking. The method is based on optimal control theory; I.e., by minimizing an appropriate cost functional the optimal trajectory of the control is obtained. The special composition of the cost functional leads to design parameters for constraining the solution so as to ensure that machine limitations are not violated. The cost functional is minimized via calculus of variations, or more precisely the Euler-Lagrange equations. The resulting set of equations is transformed into an augmented state space system describing the optimal tracking dynamics. A recently developed numerical method is used to compute the optimal solution from this state space system. The general control approach is demonstrated on an underactuated crane-like system, operating in a horizontal plane, with fixed load hoisting length. The potential of the proposed control scheme is proven by both simulation and experimental results. The multibody simulation is carried out with the software Simscape Multibody. The experimental validation was performed with a suspended load mounted to an industrial robot whose endeffector only moves in a horizontal plane to imitate the trolley of an overhead crane. The simulation and the experimental results confirm the good tracking accuracy. This method gives the best possible tracking accuracy in the least-squares sense without violating machine limits.