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A General Formulation for Managing Trajectory Tracking in Non-holonomic Moving Manipulators with Rotary-Sliding Joints

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Abstract

This article presents a general innovative technique for dynamically modeling and control of trajectory tracking in an industrial manipulator with multi-rigid links (connected by rotary-sliding (R-S) joints), which is installed on a non-holonomic moving platform on wheels. To accomplish this purpose, first the Gibbs-Appell (G-A) technique is used for getting the dynamic equations of the mentioned manipulator. Indeed, by employing the G-A methodology, one gets rid of the difficulties of Lagrange Multipliers that originate from non-holonomic constraints. To show the generality of the proposed technique, a recursive predictive control-based formulation is subsequently developed for the studied mechanism to systematically find the kinematic control rules. This multivariable kinematic controller specifies the desired angular and linear velocities of the moving base and manipulator links by finding the minimum tracking error between the system’s current position and reference trajectory from a point-wise quadratic objective function. Again, according to the predictive control approach, the system’s dynamic model in state space form and the desired velocities achieved from the kinematic controller are used to obtain the appropriate input torque and force controls while taking the existing uncertainties into consideration. Lastly, computer simulations are performed to emphasize that the suggested method is able to mathematically model the moving platform and end-effector of such complex robotic systems and also control their trajectory tracking.

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Shafei, A.M., Mirzaeinejad, H. A General Formulation for Managing Trajectory Tracking in Non-holonomic Moving Manipulators with Rotary-Sliding Joints. J Intell Robot Syst 99, 729–746 (2020). https://doi.org/10.1007/s10846-019-01143-6

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