Motion Control of Holonomic Wheeled Mobile Robot with Modular Actuation

This thesis proposes a control scheme for a new holonomic wheeled mobile robot. The platform, which is called C3P (Caster 3 wheels Platform), is designed and built by the Automation Lab., University of Heidelberg. The platform has three driven caster wheels, which are used because of their simple construction and easy maintenance. The C3P has modular actuators and sensors configurations. The robot’s actuation scheme produces singularity difficulties for some wheel steering configuration, described as the following: When all wheels yield the same steering angle value, the C3P cannot be actuated in the direction perpendicular to the wheel velocity vector. The C3P has a modular sensing scheme defined by sensing the steering angle and the wheel angular velocity of each caster wheel. This work has four main contributions 1- developing a controller based on an inverse kinematics solution to handle motion commands in the singular configurations; 2- modeling the C3P’s forward dynamics of the C3P for the simulation purpose; 3- developing a motion controller based on an inverse dynamics solution; and 4- comparing the C3P with other standard holonomic WMRs. In order to escape singularity condition, the actuated inverse kinematics solution is developed based on the idea of coupling any two wheel velocities to virtually actuate the steering angular velocity of the third wheel. The solution is termed as the Wheel Coupling Equation (WCE). The C3P velocity controller consists of two parts: a) the WCE regulator to avoid singularities and adjust the steering angles to the desired value, and b) the regular PID controller to maintain the reference robot velocities with respect to the floor frame of coordinates. The solution reaches acceptable performance in the simulation examples and in the practical experiments. However, it generates relatively large displacement errors only during the steering angles adjustment period. The Euler-Lagrangian method is used for obtaining the forward dynamic and the inverse dynamic models. The forward dynamic model consists of two equations of motion: the WTD (Wheel Torque Dynamics) to calculate the wheel angular velocities with respect to the actuated wheels’ torques, and the DSE (Dynamic Steering Estimator) for calculating the steering angles and steering angular velocities corresponding to the angular wheels’ velocities and accelerations. The inverse dynamics solution defines the forces and torques acting on each actuator and joint. The solution is used in the development of the C3P velocity and position controllers. In comparison to the proposed inverse kinematics solution, the inverse dynamics solution yields less displacement errors. Lyapunov stability analysis is carried out to investigate the system stability for different steering angles’ combinations. The steering angles’ values are considered as the disturbances affecting the platform. Finally, a comparison is made between the C3P and three other holonomic wheeled mobile robots configurations. The comparison is based on the simulation results in relation to the following aspects: a) mobility, b) total energy consumed by each robot in a finite interval of time and c) hardware complexity. The C3P platform shows its advantage in the aspects “b” and “c”