Stable Inversion for Feedforward Control of Flexible Cooperative Manipulators

In this paper, the inverse dynamics solution for feedforward control of cooperative flexible manipulators is investigated. The internal dynamics of flexible manipulators are unstable, and to obtain a bounded solution to the inverse dynamics problem, the constrained nonlinear optimization method is used. In the optimization method, the aim is to minimize the elastic energy of the manipulators despite several constraints. These constraints include: 1) dynamic equations; 2) Spatial and force trajectory; 3) kinematic constraints limiting the movement of manipulators; 4) constraints related to superfluous variables and 5) constraints of the generalized α method for the stability of the solution. The method used for dynamic modeling is based on the Lagrange equation and finite element discretization. Lagrange multipliers have been used to control the internal forces applied to the payload, and to prevent the change of direction in force control, an inequality constraint has been added to the optimization constraints. This method is implemented on flexible cooperative manipulators and has the ability to control the path of the payload and the force applied to it.