Time and energy optimal control by a new way based on centraldifference approximation of equation of motion with application to robotcontrol

摘要

The object of optimal control of robots is to determine thensignals or torques of its actuators that will cause a motion to satisfynthe constraints and at the same time minimize (or maximize) somenperformance criterion or functional. Optimal control of robotnmanipulator has a complex nature. In this paper the exact equations ofnmotion are approximated by the central difference technique and Taylornseries expansion in a new way, while the path of motion is divided intonfinite segments. The motion is assumed to have zero velocity at thenbeginning and at the end of the motion, without loss of generality. Innthe time optimal control, the Pontryagin principle is applied and thenoptimal controller is of bang bang type. the actuator torques, iscolinesnand switching points, can be calculated. As the maximum torques of thenactuators are fixed, the time optimal control problem is an optimalncontrol with bounded inputs. The problem of energy optimal control isnreduced to minimizing a scalar function of many but finite variablesnwith equality and inequality constraints. By applying the modified Hookenand Jeeves method, the actuator torques at any time are calculated. Thenalgorithm described is implemented on a 2R robot manipulator, andnresults are presented