In this paper, a numerical investigation of the Model Predictive Control strategy applied to flexible-link mechanisms is presented. The mechanisms used for all the tests are a planar five-link mechanisms. The tests are aimed at showing how the proposed control system can be used for the trajectory tracking and the vibration suppression. An analysis of the effects of the choice of tuning parameters is presented as well. The design of the predictive controller is based on a linearized version of an accurate nonlinear dynamic model. The effectiveness of the proposed approach is confirmed by extensive numerical results.

In this paper, a complete model of the elasto-kinematics is formulated in terms of a new kinematic notation, called the algebra of rotations. Based on this formulation, the elegant and concise expressions are derived for the displacement equation and especially the Jacobians governing the motion mapping between the manipulator tip and joint variables as well as link deflections. Introduction of the elasto-kinematics into the elasto-dynamics can directly take into consideration the nonlinear coupling between joint variables and link deflections, and thus improve the result of the elasto-dynamics.

The aim of this paper is to determine the optimal trajectory and maximum payload of flexible link manipulators in point-to-point motion. The method starts with deriving the dynamic equations of flexible manipulators using combined Euler–Lagrange formulation and assumed modes method. Then the trajectory planning problem is defined as a general form of optimal control problem. The computational methods to solve this problem are classified as indirect and direct techniques. This work is based on the indirect solution of open-loop optimal control problem. Because of the offline nature of the method, many difficulties like system nonlinearities and all types of constraints can be catered for and implemented easily. By using the Pontryagin's minimum principle, the obtained optimality conditions lead to a standard form of a two-point boundary value problem solved by the available command in MATLAB®. In order to determine the optimal trajectory a computational algorithm is presented for a known payload and the other one is then developed to find the maximum payload trajectory. The optimal trajectory and corresponding input control obtained from this method can be used as a reference signal and feedforward command in control structure of flexible manipulators. In order to clarify the method, derivation of the equations for a planar two-link manipulator is presented in detail. A number of simulation tests are performed and optimal paths with minimum effort, minimum effort-speed, maximum payload, and minimum vibration are obtained. The obtained results illustrate the power and efficiency of the method to solve the different path planning problems and overcome the high nonlinearity nature of the problems.