Eventos Anais de eventos
DINAME 2017
XVII International Symposium on Dynamic Problems of Mechanics
CONTROL OF MULTIPLE MOBILE ROBOTS IN DYNAMIC FORMATIONS
Submission Author:
Guilherme Rinaldo , SP
Co-Authors:
Guilherme Rinaldo, Elvira Rafikova, Marat Rafikov
Presenter: Guilherme Rinaldo
doi://10.26678/ABCM.DINAME2017.DIN17-0142
Abstract
The control of multiple mobile robots in formations has become the theme of several recent studies, due to its wide range of applications, both civilian and military. The idea is to control a robot so that it converges to a trajectory while maintaining a formation with other robots. The term swarm is often used in this context to describe robot formations that are synchronized in a geometric layout, which may or may not vary with time. This work deals with the control of multiple mobile robots in trajectory while maintaining dynamic formations, through the use of State-Dependent Riccati Equation control method. It has become popular in the first decade of this century because it allows non-linearities in the system states, providing the synthesis of non-linear feedback controls. The method parameterizes the nonlinearities of the system in a state vector and a matrix function dependent on the system’s state. Thus, it is able to account for all system nonlinearities [1, 2]. In this paper a control problem of synchronization of multiple robotic systems was formulated. The leader converges into a reference given in terms of linear and angular velocity, then, errors between leader and followers are minimized. Three robot models with differential drive were used in a leader-follower scheme such as in [3, 4], in which the follower robots receive information about the position of the leader and converge to a trajectory keeping a desired distance and orientation relative to the leader. One of the robot models is considered the leader and the other two are considered followers. The concept of mobile robots formation can be interpreted as physical distances in relation to the leader or adjacent agents that each follower robot must respect. By changing the formation parameters, it is possible to achieve any formation, but two of them are most common: V formation, in which the robots are arranged in a shape that resembles the letter V, and Echelon formation, in which the robots are disposed along a diagonal line, both very common in the military field. An digital interface is created and simulations are performed using the software LabVIEW, demonstrating the successful application of the control method in mobile robot tracking problems while maintaining formations. The SDRE control method was highly effective for the control of multiple mobile robots in formation. The computational cost of the control application is low because solving the equation of Hamilton-Jacobi-Bellman becomes unnecessary, instead it solves just one linear quadratic regulator. The proposed formations were achieved in all simulated trajectories. The stabilization of errors and control efforts proved to be quick, taking less than 1.5 seconds for all cases. References [1] - BANKS, H. T.; LEWIS, B. M.; TRAN, H. T. Nonlinear feedback controllers and compensators: A state-dependent Riccati equation approach. Computational Optimization and Applications, v. 37, n. 2, p. 177–218, 2007. [2] - ÇIMEN, T. State-Dependent Riccati Equation (SDRE) control: A survey. IFAC Proceedings Volumes (IFAC-PapersOnline), v. 17, n. 1 PART 1, p. 3761–3775, 2008. [3] - DAI, Y.; LEE, S.-G. The leader-follower formation control of nonholonomic mobile robots. International Journal of Control, Automation and Systems, v. 10, n. 2, p. 350–361, 2012. [4] - PARK, B. S.; YOO, S. J. Adaptive leader-follower formation control of mobile robots with unknown skidding and slipping effects. International Journal of Control, Automation and Systems, v. 13, p. 587–594, 2015.
Keywords
Nonlinear control, Robotics, Dynamic Systems
