Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism

Micro-Robot Management

“…The first one shows the trajectory planning of the first joint of robot derived using four different times and the second one shows the torque history for the first joint and a comparison between the four times of the first joint of robot in terms of the orientation, velocity, acceleration and the torque history to select the best time that can be used to derive the trajectory planning and torque history for all joints of robot model. Figures 19 and 20 show comparisons between the orientation, velocity, acceleration, torque and four different time ranges (5,10,20 and 60 s) of the first joint of the surgical robot. It is clearly shown in Figure 19 that the orientation behaviour increases gradualy with the time from the initial angle to the final angle and as the time increases the velocity required decreases and also the acceleration i.e.…”

“…So it is more suitable to represent the angle-Time relation and velocity and acceleration -Time relations in two separate figures. Figures 22 and 23 show comparisons between the orientation, velocity, acceleration, and torque for four different time ranges (5,10,20 and 60 s) of the first joint of the robot. As is clearly shown in Figure 22 the orientation behaviour increases gradually with time from the initial angle to the final angle for the times (5, 10 and 20 s) only.…”

“…They finally presented and analyzed the results of real experiments, performed with an outdoor mobile robot. Abdellatif and Heimann [10] investigated the inverse dynamics equations of 6-DOF fully parallel manipulators using the Lagrangian formalism. With respect to a proposed set of generalized coordinates and velocities they obtained the final form with respect to the robot's active coordinates.…”

Inverse dynamics and trajectory tracking control of a new six degrees of freedom spatial 3-RPRS parallel manipulator

“…Further, the geometrical/physical parameters of the manipulator are also optimized for a given constant orientation workspace. The inverse dynamic model is obtained using the Lagrangian dynamic formulation method (Abdellatif and Heimann, 2009). The proposed robust task-space trajectory tracking controller is based on a centralized proportional-integral-derivative (PID) control along with a nonlinear disturbance observer.…”

Dynamic modelling of a 3-CPU parallel robot via screw theory

“…Due to its computational efficiency, such approach is often used when the dynamic modelling aims at the realization of model-based control algorithms. In fact, even if all methods lead to equivalent dynamic equations, these equations present different levels of complexity and associated computational loads; minimizing the number of operations involved in the computation of the manipulator dynamics model has been the main goal of recently proposed techniques (Abdellatif and Heimann, 2009;Yang et al, 2012): since by the use of the virtual work principle constraint forces and moments do not need to be computed, this approach leads to faster computational algorithms, which is a very important advantage for the purpose of robot control. Furthermore, the vector approach specific of the virtual work principle is particularly feasible for computer implementation.…”