Modeling and trajectory tracking control of non-holonomic mobile robot with revolute-prismatic joints

One of the main topics in the field of robotics is the modeling and control of the mobile robots intrajectory tracking problem. In this paper, the kinematic and dynamic models of a manipulator connetcted by revolute-prismatic joints and installed in a non-holonomic wheeled mobile platform are first derived by applying the recursive Gibbs-Appell method. Indeed, by employing this dynamic methodology, one gets rid of the difficulties of Lagrange Multipliers that originate from non-holonomic constraints. Then, a nonlinear predictive approach is applied to design the kinematic and dynamic control laws to generate trajectory tracking control commands of the non-holonomic robot. In this method, the nonlinear responses of the mobile robot are predicted using Taylor series. The optimal control laws are analytically developed by minimizing the difference between the predicted and the desired responses of the system outputs. The multivariable kinematic controller specifies the desired angular and linear velocities of the mobile base and the manipulator links. The obtained control inputs are then used as the desired values to be tracked by the dynamic controller. Finally, the results of numerical simulations are presented to emphasize the ability the proposed method in the mathematical modeling and simultaneous trajectory tracking control of the mobile base and end-effector of such complex robotic systems.