Flatness based cooperative control of multiple mobile robotic systems

Abstract

Cooperative multi-robotic systems can be more useful in numerous applications when compared to single-robotic systems. However, to ensure that cooperative systems execute tasks accurately, highly effective control architectures are vital. This study aims to improve the coordination control of a model based cooperative multiple mobile robotic system using differential flatness theory. To achieve this, a comprehensive analysis of literature on fundamentals of wheeled mobile robots and their cooperative systems was conducted. Then, mathematical modelling is performed for a cooperative robotic system composed of differential drive wheeled robots. First the kinematic model is presented to describe the motion of a robot without consideration of the forces causing it. Following that, the dynamic model is presented to describe the robot's motion in relation to forces applied to it. These models allowed for better design of a control system and paved way for the differential flatness characterisation of the mobile robotic system. Next, the robot differential flatness characterisation and analysis were performed, and the flatness properties were exploited to design a flatness-based control algorithm for motion planning and to generate trajectories and track them. Thereafter, the formation model was derived using a leader-follower formation. In this approach, three similar robots were modeled. Among the robots, one is selected as leader, and it is followed by two follower robots. Only the leader robot has access to information about the desired tracking path and all follower robots rely on it to coordinate their motion. Also, each follower must maintain a constant defined distance and orientation from the leader. Lastly, a flatness-based formation controller was developed. Tests were conducted to compare the flatness-based controller with the conventional PID controller. According to the results, Flatness-based controllers significantly reduce tracking errors of the cooperative system, whereas PID controllers have slightly higher tracking errors. This is because increasing the gains of the PID controller beyond a certain threshold causes it to get saturated, whereas the Flatness controller can be adjusted without any concern for saturation. The key findings of this study was that differential flatness allows for the whole system to be represented by a reduced number of variables and thus the computational cost is significantly reduced especially when dealing with multiple robots that could otherwise entail solving large robotic model differential equations. This significantly simplifies the motion planning problem of the cooperative system. Also, a differential flatness characterisation of the robotic formation enabled the linearisation of the system to a stable linear equivalent system. Furthermore, in flat output space a simple polynomial-based trajectory planning can be used, that is simplifying the trajectory generation problem. Additionally, trajectories are solved without integrating robot model differential equations. Thus, it is concluded from this study that differential flatness theory improves coordination control of cooperative multiple mobile robotic systems.