Maximum Dynamic Load Determination of Mobile Manipulators via Nonlinear Optimal Feedback

Abstract

In this paper, a nonlinear optimal feedback control law is designed to nd the maximum load carrying capacity of mobile manipulators for a given trajectory task. The optimal state feedback law is given by the solution to the nonlinear Hamilton-Jacobi-Bellman (HJB) equation. An iterative procedure is used to nd a sequence of approximate solutions of the HJB equation. This is done by solving a sequence of Generalized HJB (GHJB) di erential equations. The Galerkin procedure is applied to nd a numerical solution to the GHJB equation. Using this method, a nonlinear feedback is designed for the mobile manipulator and, then, an algorithm is developed to nd the maximum payload. In mobile base manipulators, the maximum allowable load is limited by their joint actuator capacity constraints, nonholonomic constraints and redundancy that arise from base mobility and increased Dofs. To solve the extra Dofs of the system, an extended Jacobian matrix and additional kinematic constraints are used. The validity of the methodology is demonstrated via simulation for a two-link wheeled mobile manipulator and linear tracked Puma arm and the results are discussed.