Nonlinear Motion Control of Mobile Robot Dynamic Model

Abstract

The problem of motion planning and control of mobile robots has attracted the interest of researchers in view of its theoretical challenges because of their obvious relevance in applications. From a control viewpoint, the peculiar nature of nonholonomic kinematics and dynamic complexity of the mobile robot makes that feedback stabilization at a given posture cannot be achieved via smooth time-invariant control (Oriolo et al., 2002). This indicates that the problem is truly nonlinear; linear control is ineffective, and innovative design techniques are needed. In recent years, a lot of interest has been devoted to the stabilization and tracking of mobile robots. In the field of mobile robotics, it is an accepted practice to work with dynamical models to obtain stable motion control laws for trajectory following or goal reaching (Fierro & Lewis, 1997). In the case of control of a dynamic model of mobile robots authors usually used linear and angular velocities of the robot (Fierro & Lewis, 1997; Fukao et al., 2000) or torques (Rajagopalan & Barakat , 1997; Topalov et al., 1998) as an input control vector. The central problem in this paper is reduction of control torques during the reference position tracking. In the case of dynamic mobile robot model, the position control law ought to be nonlinear in order to ensure the stability of the error that is its convergence to zero (Oriollo et al., 2002). The most authors solved the problem of mobile robot stability using nonlinear backstepping algorithm (Tanner & Kyriakopoulos, 2003) with constant parameters (Fierro & Lewis, 1997), or with the known functions (Oriollo et al., 2002). In (Tanner & Kyriakopoulos, 2003) a combined kinematic/torque controller law is developed using backstepping algorithm and stability is guaranteed by Lyapunov theory. In (Oriollo et al., 2002) method for solving trajectory tracking as well as posture stabilization problems, based on the unifying framework of dynamic feedback linearization was presented. The objective of this chapter is to present advanced nonlinear control methods for solving trajectory tracking as well as convergence of stability conditions. For these purposes we developed a backstepping (Velagic et al., 2006) and fuzzy logic position controllers (Lacevic, et al., 2007). It is important to note that optimal parameters of both controllers are adjusted using genetic algorithms. The novelty of this evolutionary approach lies in automatic obtaining of suboptimal set of control parameters which differs from standard manual adjustment presented in (Hu & Yang, 2001; Oriolo et al., 2002). The considered motion control system of the mobile robot has two levels. The lower level subsystem deals with the