Impact of External Disturbance and Discontinuous Input on the Redundant Manipulator Robot Behaviour using the Linear Parameter Varying Modelling Approach

Abstract

Abstract-This paper is concerned with the synthesis of dynamic model of the redundant manipulator robot based on Linear Parameter Varying approach. To evaluate its behavior and in presence of external disturbance several motions profiles are developed using a new algorithm which produce smooth trajectories in optimal time. The main advantages of this proposed approach are its robustness and its simplicity with respect to the flexibility structure, to the motion profile and mass load variations. Numerical simulations with several tasks show that in presence of mass load variation the desired trajectory is more efficiently followed by the LPV model than the dynamic model of the studied mechanism. Its performances are ensured using the smoothest trajectory designed by the Eighth-degree polynomial profile than the Fifth-degree polynomial one and the trapezoidal one.

Smooth motion profile for trajectory planning of a flexible manipulator

“…The dynamic modelling of the considered mechanism presented by the Bernoulli-Euler beam is performed using the Euler-Lagrange formulation and the finite elements approach ( [11][12][13][14][15][16]). Remember that in all expressions, a number between parentheses in the power of such a function means a time derivative.…”

Dynamic Modelling of Flexible Manipulator based on a Large Number of Finite Elements

“…A (3946 L + 305 M ( 4,4 ) ,M( 4,5 ) 50000 ( 4,6 ) ,M ( 4,7 ) ,M ( 4,8 ) (6,9 ) ,M (7,1) (7,5 ) ,M (7,6 ) (7,8 ) ,M(7,9 ) 5000 100000 25000 ( 8,6 ) ,M ( 8,7 ) ,M ( 8,8 ) ( 9,7 ) ,M ( 9,8 ) ,M( 9,9 ) 2m 25000 50000 5000 3 2 3 3 1 2 3 3 1 2 3 3 1 2 3 3 3 2 1 2…”

“…-4608 E I K (7,8 ) , ( 8,6 ) , ( 8,8 ) , ( 8,4 ) 0 ,K ( 8,5 ) 0 27648 E I -59520 E I K ( 8,6 ) , ( 8,8 ) ,K ( 8,9 ) ,…”

“…As it is introduced by [5], [6], the finite element method (FE) has proven to be one of the best methods to obtain a good description of the dynamics of the system because it is able to function with irregularities in the structure of the arm with managing mixed boundary conditions and it makes allowance for interaction between the gross motion and the flexible dynamics of the manipulator, which is not possible with use of methods based on frequency domain analysis. Unfortunately, the major disadvantage of the FE method is the computational complexity and the difficult software coding involved, this is the primary reason several works such as [7], [8] have been limited to two or three finite elements.…”

Improvement of Ultra-local Model Control Using the Auto-tuning PID Control Applied to Redundant Manipulator Robot

“…In previous research works and as the first step, the interest was focused on the importance of motion profile that must satisfy some requirements such as the motion flexibility and its optimality in terms of energy consumption and time for the period of its operation ( [7], [8]). In the second step, the improvement of the dynamic model of the flexible mechanism was achieved using the Linear Parameter Varying approach [9]. In this research work, instead of dealing with the trajectory planning or the dynamic model development, an improvement of the control strategy presents the main interest which considers the redundancy of mechatronic systems.…”