The complex nature of robotic manipulator dynamic equations is well studied. Many different control algorithms have been developed; among them optimal control ones. However, most of them are either based on simplified equations of motion or are tedious to implement or set up.
In this work equations of motion are approximated using central difference technics and Taylor series expansion, while path of motion is divided in finite segments. The motion is assumed to have zero velocity at the beginning and at the end of the motion without loss of generality. Showing that Pontryagin principle is applicable and the optimal controller is bang bang. Actuator torques, iscolines, and switching points, can be calculated. The preparation time, problem set up and execution time are relatively small, and programming efforts are reasonably low.
The algorithm is implemented for a 2R planar robotic manipulator, and results are presented.