A novel recursive formulation for dynamic modeling and trajectory tracking control of multi-rigid-link robotic manipulators mounted on a mobile platform

Abstract

This article establishes an innovative and general approach for the dynamic modeling and trajectory tracking control of a serial robotic manipulator with n-rigid links connected by revolute joints and mounted on an autonomous wheeled mobile platform. To this end, first the Gibbs–Appell formulation is applied to derive the motion equations of the mentioned robotic system in closed form. In fact, by using this dynamic method, one can eliminate the disadvantage of dealing with the Lagrange Multipliers that arise from nonholonomic system constraints. Then, based on a predictive control approach, a general recursive formulation is used to analytically obtain the kinematic control laws. This multivariable kinematic controller determines the desired values of linear and angular velocities for the mobile base and manipulator arms by minimizing a point-wise quadratic cost function for the predicted tracking errors between the current position and the reference trajectory of the system. Again, by relying on predictive control, the dynamic model of the system in state space form and the desired velocities obtained from the kinematic controller are exploited to find proper input control torques for the robotic mechanism in the presence of model uncertainties. Finally, a computer simulation is performed to demonstrate that the proposed algorithm can dynamically model and simultaneously control the trajectories of the mobile base and the end-effector of such a complicated and high-degree-of-freedom robotic system.

WITHDRAWN: Analyzing governing equations of multibody dynamic systems through kinematic properties of joints and effects of kinematic chains on closed-form mechanism

“…Two sets of simulations were executed to measure the effects of the suggested methodology on the total efficiency of the CPU usage time. The first simulations (DAE) were run using the conventional methodology based on (Hollerbach 1980, Walker and Orin 1982, Korayem and Shafei 2007, Shafei and Mirzaeinejad 2021, in which λ was solved before q¨ followed by the numerical integrations. The second simulations were executed through the methodology based on (2-14), (2-16), (2-19), (2-25), and the recursive algorithm of ODE.…”

“…A typical procedure for the forward dynamic of closed-loop mechanisms is dividing the mechanism into multiple open architectures, which is accomplished by cutting the mechanism at suitable joints. The Newton-Euler formulation (Walker and Orin 1982), energy-based Euler-Lagrange method (Hollerbach 1980), or Gibbs-Appell technique (Korayem andShafei 2007, Shafei andMirzaeinejad 2021) is employed to derive the Lagrange multipliers, which indicate constraint forces and moments. Afterward, these Lagrange multipliers and state variables are simultaneously calculated (Blajer 2009).…”

Determining equations governing multibody dynamic systems through joint kinematics and kinematic chain effects in closed-form mechanisms

“…Two sets of simulations were executed to measure the effects of the suggested methodology on the total efficiency of the CPU usage time. The first simulations (DAE) were run using the conventional methodology based on (Hollerbach 1980, Walker and Orin 1982, Korayem and Shafei 2007, Shafei and Mirzaeinejad 2021, in which λ (Lagrangr multiplier) was solved before q¨ followed by the numerical integrations. The second simulations were executed through the methodology based on (2-30), (2-32), (2-35), (2-36), and the recursive algorithm of ODE.…”

Linear manipulator: Motion control of an n-link robotic arm mounted on a mobile slider

“…Experimenting on the position of the center of percussion of the last link as the linearizing output, the results showed that swing-up maneuvers and smooth trajectories for any initial and desired final state of the robotic arm under gravity could be easily obtained. Shafei et al [46] utilized a multivariable kinematic controller to obtain the trajectory tracking control and dynamic modeling of a robotic manipulator consisting of n -rigid links connected by revolute joints installed on an autonomous mobile platform. A predictive control process was taken to determine appropriate input control torques and optimum velocities for the robotic system in the existence of model uncertainties.…”