Download or read book Optimal Motion Planning for Manipulator Arms Using Nonlinear Programming written by Jong-keun Park and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, we present a practical and reliable method for finding the minimum torque, minimum energy, minimum overload, and minimum time motions for the manipulators moving in an obstacle field, subject to the limits of velocity-dependent actuator forces. Arbitrary point-to-point manipulator motions are represented by a point in a finitedimensional vector space parameterized by quintic B-splines. The novel idea in this work is the concept of the minimum overload trajectory, in which the actuator-overloads achieve their minimum values with the total motion time fixed. The minimum time motion is defined rigorously with this concept and it is obtained by successive searches for the minimum overload trajectory. There are various local minimal motions according to the directions in which the manipulator links bend. We can perform global searches in a certain obstacle field by adjusting the locations of the seed points of the obstacle models or the link models. In the resultant optimal motions, the manipulator turns with the last link bent inward in order to reduce the moment of inertia about the z1 axis and the moment arms of gravity about the z2 and z3 axes. In the resultant minimum time motions, 1) the manipulator maximizes the joint coupling effect by the overactions of underloaded joints to reduce the torques on the overloaded joints, and 2) almost all the actuators are close to saturation during the motion, which is consistent with Pontryagin's maximum principle.