Formation Control for Non-Holonomic Mobile Robots: A Hybrid Approach (invited paper)

MARCOS TOIBERO; FLAVIO ROBERTI; RICARDO CARELLI; PAOLO FIORINI

Recent Advances in Multi-Robot Systems

I-Tech Publication and Publishing, Austria

Lugar: Vienna; Año: 2008; p. 233 - 248

Many cooperative tasks in real world environments, such as exploring, surveillance, search and rescue, transporting large objects and capturing a prey, need the robots to maintain some desired formations when moving. Formation control refers to the problem of controlling the relative position and orientations of robots in a group, while allowing the group to move as a whole. Problems in formation control that have been investigated include assignment of feasible formations, moving into formation, maintenance of formation shape (Desai et al., 2001) and switching between formations (Desai et al., 1999; Fierro et al., 2002). A feasible solution to address these problems is by using hybrid control systems in formation control. In fact, several papers can be found in the literature using hybrid control systems: including a discrete event system at the supervisory level and continuous controllers to give the control actions (Desai et al., 1999; Ogren & Leonard, 2003; Chio & Tarn, 2003; Ogren, 2004; Shao et al., 2005). The work in (Das et al., 2002) is a very good example of the state of the art in robot formation control, in which it is presented a complete framework to achieve a stable formation for car-like and unicycle-like mobile robots. In this chapter, a hybrid approach for the autonomous navigation of a mobile robots team in a specified formation is developed considering a centralized leader-follower controller (Gava et al., 2007) (see e.g. (Shao et al., 2005) for a review on the leader-following method) and the non-holonomic constraint of the unicycle-like mobile robots (Gulec & Unel, 2005). In this last paper, the authors state that complicated coordinated tasks can be interpreted in terms of simpler coordinate tasks that are to be manipulated sequentially. The leader robot of the team, which navigate independently according to its own control laws, has a laser range-finder, odometry sensors and an omnidirectional camera, whereas the followers have odometry and collision (sonar) sensors. The laser range-finder and odometry sensors of the leader robot are used to carry out the leader robot controller (Toibero et al., 2007); and the omnidirectional camera is utilized to identify the follower postures relative to the leader coordinate system needed in the implementation of the centralized formation controller (Gava et al., 2007). This last assumption is not a constraint since the leader could get access to these positions using another absolute position sensor such as, for instance, a GPSs or odometry. This centralized control architecture, where the control actions for all the followers are generated by the leader (which has the main visual and laser sensors) could be decentralized by allowing the followers to estimate the leader movements (angular and translational velocities) and performing a minimal communication between the robots (Fredslund & Mataric, 2002). Due only to sensory limitation on our robot team we exposed experimental results that were obtained by using a centralized approach. Nevertheless, a decentralized control scheme could be supported by this strategy. Indeed, the focus of this chapter is not in the formation control framework, but in the way that a hybrid system can improve the performance of the formation controller in many applications by adding a few simple behaviors and a supervisor which generates switching signals while guaranteeing the asymptotic stability of the hybrid formation control system. The hybrid control strategy developed along this chapter involves mobile robot formation control when considering obstacles. Its main objectives are: i) place the follower robots at the desired positions in the given formation before starting the leader navigation, this is the so-called static formation problem (Antonelli et al., 2006); ii) reduce the temporary large formation errors during the autonomous navigation of the complete robot team; iii) avoid unknown obstacles while maintaining the formation geometry, instead of changing the formation geometry as in (Das et al., 2002). For this last objective, it is considered the obstacle contour-following strategy for the leader robot as presented in (Toibero et al., 2006). Regarding the others two major objectives, a hybrid approach based on a formation controller is proposed. The rest of the chapter includes: Section 2 presents a review of the stable leader-based formation controller. Then, in Section 3 it is described the hybrid control system including simulations results and stability considerations. In Section 4 some comparative simulation results are presented. Finally, in Section 5 experimental results are reported to state conclusions in Section 6.