Tracking Control of Omnidirectional Mobile Manipulator System with Disturbance and Friction

Abstract

Combining a three-wheeled omnidirectional mobile platform with a manipulator makes an omnidirectional mobile manipulator more powerful to move and do its tasks than a conventional mobile manipulator with regular wheels. However, until now, there are little researches about this system with disturbance and friction. Because it is very difficult to derive the dynamic modeling of an omnidirectional mobile manipulator with disturbance and friction and control it, obtaining modeling and motion control of the omnidirectional mobile manipulator are deeply needed. Objective of this dissertation is to present modeling and controlling of an omnidirectional mobile manipulator system (OMMS) with disturbance and friction. A tracking controller is designed for manipulator of the OMMS to track a desired trajectory with a desired angular velocities of links. Therefore, thefollowing tasks are implemented in this dissertation. First, the structure of the OMMS and the OMP used for experiment are proposed. Hardware configuration of the proposed systems are implemented. A control system is developed based on PIC18F452 microcontroller technology. One PIC18F452 is used as a master unit, and other PIC18F452s are used as slave units. The master unit is connected with other slave units through I2C communication. The master unit receives data from the sensors that are used for main controller, and then it sends the commands to the slave controllers via I2C communication, respectively. The slave controller integrates PIC18F452 with motor drivers, LMD18200, for the DC motor control. Second, an omnidirectional mobile manipulator system (OMMS), a SCARA type of the three-linked manipulator mounted on a mobile platform with three driving omnidirectional wheels, in the presence of disturbance and friction is presented. The OMMS is considered as two subsystems of an omnidirectional mobile platform (OMP) and a manipulator. A kinematic modeling of the OMP is presented, and a dynamic modeling of the OMP with disturbance and friction is derived based on the Newton’s second law of motion. The kinematic modeling and the dynamic modeling of the manipulator based on Euler-Lagrange formula are also presented. Based on the modeling of the system, the controllers are designed to control the manipulator of the OMMS tracking a desired trajectory. Third, a tracking controller that integrates a kinematic controller (KC) with an integral sliding mode dynamic controller (ISMC) of the OMP with disturbance and friction is designed to track a desired trajectory. A tracking error vector is defined, and a kinematic controller (KC) is designed to make the tracking error vector go to zero asymptotically. Then, an integral sliding surface vector is defined based on the velocity tracking error vector and its integral term. An integral sliding mode dynamic controller (ISMC) is designed to make the integral sliding surface vector and the tracking velocity error vector go to zero asymptotically. Stability of the system is guaranteed by Lyapunov stability theory. The simulation and experimental results are presented to illustrate the effectiveness of the proposed tracking controller. This concept is applied to control the manipulator of the OMMS and can be used for motion control of the OMP of the OMMS in Chapter 6. Fourth, a differential sliding mode controller (DSMC) of the OMP with disturbance and friction is designed to track a desired trajectory. A tracking error vector is defined as the difference between a tracking point of the OMP and a reference point, and then a differential sliding surface vector is chosen. A control law is designed to stabilize the sliding surface vector and make the tracking error vector go to zero asymptotically. Stability of the system is also guaranteed by Lyapunov stability theory. The simulation and experimental results are presented to illustrate the effectiveness of the proposed controllers. This controller is modified and applied for motion control of the OMP of the OMMS in Chapter 6. After that, the controllers in chapter 4 and chapter 5 are compared by simulation and experimental results in the same conditions. The concepts of two controllers in Chapter 4 and 5 are applied to control the manipulator and the OMP of the OMMS in Chapter 6, respectively. Fifth, a decentralized control strategy is applied for the OMMS with disturbance and friction. Two controllers are designed to control the OMP and the manipulator, respectively. A tracking error vector is defined as the difference between the end-effector and a reference point. Based on the tracking error vector and the kinematic modeling of the manipulator, a kinematic controller (KC) is designed using Lyapunov stability theory. The kinematic controller is a control law as a desired angular velocity vector of the manipulator. Next, an angular velocity error vector is defined as the difference between the real angular velocity vector and the desired angular velocity vector of the manipulator. An integral sliding surface vector is defined based on the angular velocity error vector and its integral term. Based on the dynamic modeling and the angular velocity error vector of the manipulator, an auxiliary control input vector is designed for the real angular velocity vector of the manipulator to track the desired angular velocity vector using Lyapunov stability theory. Also, a posture error vector is defined as the difference between a target point and the end-effector of the manipulator. A differential sliding surface vector is defined based on the posture error vector and its derivative. Based on the dynamic modeling of the OMP and the differential sliding surface vector, an auxiliary control input vector for the OMP is designed using Lyapunov stability theory. The auxiliary control input vector of the OMP is used to move the OMP so that the end-effector of the manipulator tracks a desired trajectory without its singulariry. The simulation and experimental results are presented to demonstrate the effectiveness of proposed control strategy. The effectiveness of the proposed system are shown through simulation and experimental results. The manipulator of the OMMS can track the desired trajectory with constant velocity as desired, without its singularity at the same time. So the system can be applicable and implemented in the applications.