Schooling for Multiple Underactuated AUVs

In the past few decades, autonomous underwater vehicles (AUVs) have been playing one of most important roles in the applications ranging from scientific research, survey to industry and military operations. Today, there is an apparent trend that more and more underwater tasks are carrying out by cooperative operations of multiple AUVs instead of traditional method of using single AUV (Soura & Pereira, 2002; Edwards et al., 2004; Guo et al., 2004; Watanabe & Nakamura, 2005; Fiorelli et al., 2006). Multiple AUVs have cost-effective potential. However, a number of research efforts are still remained to be done before this advanced technology can be fully applied in the practice. And one of the efforts is about the efficient schooling scheme for these multiple underwater vehicles. The history of the formation or cooperative control of multiple agent systems can be traced back to the 1980’s. Reynolds (1987) introduced a distributed behavioural model for flocks of birds, herds of land animals, and schools of fishes. This model can be summarized as three heuristic rules: flock centring, collision avoidance and velocity matching. In the formation algorithm (Reynolds, 1987), each dynamic agent was modelled as certain particle system – a simple double-integrator system. This kind of agent model has been inherited in most of the following research works (Leonard & Fiorelli, 2001; Olfati-Saber & Murray, 2002, 2003; Fiorelli et al., 2006; Olfati-Saber, 2006; Do, 2007). Besides these works, another type of linear model was used in Smith et al. (2001), and certain nonlinear model was applied for underwater vehicles (Dunbar & Murray, 2002) and for wheel robots with terminal constraints (Fax & Murray, 2004). In both of Dunbar & Murray (2002) and Fax & Murray (2004), the nonlinear dynamics were all fully actuated. In this chapter, we consider the schooling problem for multiple underactuated AUVs, where only three control inputs surge force, stern plane and rudder are available for each vehicle’s six degrees of freedom (DOF) motion. For these torpedo-type underwater flying vehicles, since there are non-integrable constraints in the acceleration dynamics, the vehicles do not satisfy Brockett’s necessary condition (Brockett et al., 1983), and therefore, could not be asymptotically stabilizable to an equilibrium point using conventional time-invariant continuous feedback laws (Reyhanoglu, 1997; Bacciotti & Rosier, 2005). Moreover, these vehicles’ models are not transformable into a drift-less chained form (Murray & Sastry, 1993), so the tracking method proposed in Jiang & Nijmeiner (1999) cannot be directly applicable to these vehicles. Recently, quite a number of research works have been carried out on the tracking of underactuated surface ships (Jiang, 2002; Do et al., 2002a, 2002b, 2004, 2005; Pettersen & Nijmeijer, 2001; Fredriksen & Pettersen, 2006). However, the presented O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg