1、 Designing approach on trajectory-tracking control of mobile robotAbstract Based on differential geometry theory, applying the dynamic extension approach of relative degree, the exact feedback linearization on the kinematic error model of mobile robot is realized. The trajectory-tracking controllers
2、 are designed by pole assignment approach. When angle speed of mobile robot is permanently nonzero, the local asymptotically stable controller is designed. When angle speed of mobile robot is not permanently nonzero, the trajectory-tracking control strategy with globally tracking bound is given. The
3、 algorithm is simple and applied easily. Simulation results show their effectiveness. Keywords: Trajectory tracking; Dynamic extension approach; Exact feedback linearization; Globally tracking bound1. Introduction Recently, interest in the tracking control of mobile robots has increased with various
4、 theoretical and practical contributions being made. Particularly, feedback linearization has attracted a great deal of research interest in recent nonlinear control theory, and some techniques have been employed in mobile robot control Path tracking problems of several types of mobile robots have b
5、een investigated by means of linearizing the static and dynamic state feedback in 1. The local and global tracking problems via time-varying state feedback based on the back stepping technique have been addressed in 2. Since the wheel-driven mobile robot has nonholonomic constraints that arise from
6、constraining the wheels of the mobile robot to roll without slipping and the linearized mobile robot with nonholonomic constraints has a controllability deficiency, it is difficult to control them. The point stabilization problem can be regarded as the generation of control inputs to drive the robot
7、 from any initial point to target point. The crucial problem in this stabilization question centers on the fact that the mobile robot model does not meet Brocketts well-known necessary smooth feedback stabilization condition, so the mobile robot cannot be stabilized with smooth state feedback, which
8、 leads to the limitation in application. Therefore some discrete time-invariant controllers, time-varying controllers and hybrid controllers based on Lyapunov control theories have been proposed in 4. The global trajectory-tracking problem to reference mobile robot is discussed based on the back ste
9、pping technique in 5. The trajectory-tracking problem to reference mobile robot is discussed based on the terminal sliding-mode technique in 6, but it requires the nonzero speed of rotation. Point stabilization of mobile robot via state-space exact feedback linearization based on dynamic extension a
10、pproach is proposed in 7. The point stabilization problem in polar frame can be exactly transformed into the problem of controlling a linear time-invariant system. But its disadvantage is to require the verification of the complex involution. And the point stabilization problem is only discussed but
11、 the trajectory tracking is not solved. In the present paper, the trajectory tracking to reference mobile robot as 5 and 6 is addressed based on dynamic extension approach in 7. The exact feedback linearization on the kinematic error model of mobile robot is realized. Its proof is simple and differe
12、nt from 7 since the complex process of verifying involution is avoided. By linearization, the nonlinear system is transferred to linear time-invariance system, which is equivalent to two reduced-order linear time-invariance systems that can be controlled easily. If angle speed of mobile robot is per
13、manently nonzero, the local asymptotically stable controller is designed. If anglespeed of mobile robot is not permanently nonzero, the trajectory-tracking control strategy with globally tracking bound is given. The algorithm is simple and applied easily.2. Preliminaries and problem formulation Cons
14、ider a class of nonlinear systems described asDefinition (Slotine and Li 8 and Feng and Fei9.) Given X is an n-dimension differentiable manifold if there exists a neighborhood V of x0 and integer vector er1; r2;y; rmT such thatis nonsingular 8xAV; we say that system (1)(2) has vector relative degree
15、 er1; at point x0: Lemma (Feng and Fei 9). The necessary and sufficient condition of exact feedback linearization at x0 for system (1) is that there exists a neighborhood V of x0 and smooth real-valued functionssuch that system (1)(2) has vector relativeedegreeat the point,The kinematic model of whe
16、el-driven mobile robot as follows: where (x; y) is the position of mobile robot and y is the heading angle. The control variables of mobile robot are the linear velocity v and the angular velocity o: Here, the trajectory-tracking problem is to track reference mobile robot with the known posture yr; yrT and velocities vr; as shown in Fig. 1. We have the posture error equation of mobile robot 5,6Hence we have
