Optimal Motion Planning for Manipulator Arms Using Nonlinear Programming

Abstract

Industrial Robotics -Programming, Simulation and Applications solve them through parameter optimization Although this theory and its solutions are rigorous, it has been used to solve equations for the motions of 2-link or at most 3-link planar manipulators due to the complexity and the nonlinearity of the manipulator dynamics. Approximation methods have been studied to obtain the solutions for three or more DOF spatial manipulators; however, the solutions obtained have not been proved to be optimal. These approximation methods are roughly divided into two groups depending on whether or not they utilize gradients. Most algorithms based on nonlinear programming use gradients For stable convergence, the objective functions and constraints must be locally convex and their first derivatives must be continuous. Numerically calculated gradients have been used to find minimum time motions Subsequently, analytically calculated gradients were used to minimize actuator torques for various multibody systems However, torque or energy minimizations show more stable convergence properties than the minimum time motions because the motion time is fixed. Other approximation methods that do not utilize gradients are mainly based on (1) approximations in small time-intervals The former requires less CPU time but may accumulate numerical or modeling errors in small time-intervals and thus lower the accuracy of the results. The latter assures stable convergence but the CPU time may increase exponentially for the refinement of tessellation. Because of the complex dynamics and kinematics of robot manipulators, various assumptions or simplifications were introduced for the online implementation or simplification of the algorithms.