Maximum payload path planning for redundant manipulator using indirect solution of optimal control problem

• Published in: International journal of advanced manufacturing technology Vol. 44; no. 7-8; pp. 725 - 736
• Main Authors: Korayem, M. H., Nikoobin, A.
• Format: Journal Article
• Language: English
• Published: London Springer-Verlag 01.10.2009; Springer Nature B.V
• Subjects: Actuators; Algorithms; Bearing strength; Boundary value problems; CAE) and Design; Computer simulation; Computer-Aided Engineering (CAD; End effectors; Engineering; Hamiltonian functions; Industrial and Production Engineering; Load carrying capacity; Manipulators; Mathematical analysis; Mechanical Engineering; Media Management; Optimal control; Optimization; Original Article; Path planning; Product design; Redundancy; Two-point boundary value problem; Path planning; Maximum payload; Redundant manipulator; Optimal control
• ISSN: 0268-3768; 1433-3015
• DOI: 10.1007/s00170-008-1862-1

The aim of this paper is to determine the maximum load-carrying capacity and the corresponding joint optimal path for kinematically redundant manipulators to track a given end effector path, subject to actuator torque limits. The path-planning problem is solved by using the indirect solution of open-loop optimal control problem and the scheme makes full use of redundancy to increase the load-carrying capacity. In this method, after decomposing the joint coordinates into redundant and nonredundant parts, dynamic equations are derived and the inverse kinematic is solved in terms of the redundant terms. Then, the Hamiltonian function is formed and the necessary conditions for optimality are derived from Pontryagin’s minimum principle. The obtained equations establish a two-point boundary value problem (TPBVP) which is solved by numerical techniques. An efficient algorithm based on the TPBVP solution is presented to determine the maximum payload and the corresponding joint optimal path. Simulations are performed for two types of mobile base manipulator in order to show how the proposed method is applied to find the maximum payload of redundant manipulator and how extra degrees of freedom are used to increase the maximum payload value.