Ti-Chung Lee

Tracking control of unicycle-modeled mobile robots using a saturation feedback controller

The tracking control problem with saturation constraint for a class of unicycle-modeled mobile robots is formulated and solved using the backstepping technique and the idea from the LaSalles invariance principle. A global result is presented in which several constraints on the linear and the angular velocities of the mobile robot from recent literature are dropped. The proposed controller can simultaneously solve both the tracking and regulation problems of a unicycle-modeled mobile robot. With the proposed control laws, the robot can globally follow any path specified by a straight line, a circle or a path approaching the origin using a single controller. As demonstrated, the circular and parallel parking control problem are solved using the proposed controller. Computer simulations are presented which confirm the effectiveness of the proposed tracking control law. Practical experimental results validate the simulations.

Reliable control of nonlinear systems

In this paper, we extend Veillettes results (1995) to the study of reliable linear-quadratic regulator problem for nonlinear systems. This is achieved by employing the Hamilton-Jacobi inequality in the nonlinear case instead of algebraic Riccati equation in the linear one. The proposed state-feedback controllers are shown to be able to tolerate the outage of actuators within a prespecified subset of actuators. Both the gain margins of guaranteeing system stability and retaining a performance bound are estimated.

Uniform Asymptotic Stability of Nonlinear Switched Systems With an Application to Mobile Robots

This paper is concerned with the study of, both local and global, uniform asymptotic stability for general nonlinear and time-varying switched systems. Two concepts of Lyapunov functions are introduced and used to establish uniform Lyapunov stability and uniform global stability. With the help of output functions, an almost bounded output energy condition and an output persistent excitation condition are then proposed and employed to guarantee uniform local and global asymptotic stability. Based on this result, a generalized version of Krasovskii-LaSalle theorem in time-varying switched systems is proposed. For switched systems with persistent dwell-time, the output persistent excitation condition is guaranteed to hold under a zero-state observability condition. It is shown that several existing results in past literature can be covered as special cases using the proposed criteria. Interestingly, as opposed to previous work, the main results of this paper are applicable to the situation where some switching systems are not asymptotically stable at the origin. The robust practical regulation problem of nonholonomic mobile robots is studied as a way of demonstrating the power of the proposed new criteria. A novel switching controller is proposed with guaranteed robustness to orientation error and unknown parameters in mobile robots.

A generalization of Krasovskii-LaSalle theorem for nonlinear time-varying systems: converse results and applications

This paper presents a practically applicable characterization of uniform (global) asymptotic stability (UAS and UGAS) for general nonlinear time-varying systems, under certain output-dependent conditions in the spirit of the Krasovskii-LaSalle theorem. The celebrated Krasovskii-LaSalle theorem is extended from two directions. One is using the weak zero-state detectability property associated with reduced limiting systems of the system in question to generalize the condition that the maximal invariance set contained in the zero locus of the time-derivative of the Lyapunov function is the zero set. Another one is using an almost bounded output-energy condition to relax the assumption that the time derivative of the Lyapunov function is negative semi-definite. Then, the UAS and UGAS properties of the origin can be guaranteed by employing these two improved conditions related to certain output function for uniformly Lyapunov stable systems. The proposed conditions turn out to be also necessary under some mild assumptions and thus, give a new characterization of UGAS (and UAS). Through an equivalence relation, the proposed detectability condition can also be verified in terms of usual PE condition. To validate the proposed results, the obtained stability criteria are applied to a class of time-varying passive systems and to revisit a tracking control problem of nonholonomic chained systems. For the latter, under certain persistency of excitation conditions, the K-exponential stability is achieved based on our approach.

Brief paper: Adaptive control in robotic systems with H ∞ tracking performance

The problem of the adaptive model reference tracking control with a guaranteed H^~ performance is solved for rigid robotic systems with unknown parameters and external disturbances. A novel model for disturbance signals is introduced to improve the ability of disturbance rejection in the proposed robotic adaptive tracking control design. The proposed H^~ adaptive tracking control design consists of an adaptive disturbance attenuation algorithm and an adaptive internal model compensation algorithm so that the tracking error can asymptotically converge to zero in the presence of disturbances. The proposed H^~ adaptive tracking control is smooth as well as global, and suitable for practical robotic control design. Finally, a simulation example is given to exhibit the tracking performance of a two-link robotic manipulator with the proposed H^~ adaptive control algorithm.

Fast parking control of mobile robots: a motion planning approach with experimental validation

This paper presents a solution to the general parking problem of nonholonomic mobile robots based on motion planning and tracking controller design. A new global tracking controller is first proposed to achieve global uniformly asymptotic stability and local exponential convergence. The parking problem is then transformed into a tracking one by adding a redesigned virtual trajectory to the original trajectory, thus guaranteeing practical stability with exponential convergence. Further improvement in parking performance is obtained through linearization and pole-placement methods. One feature of our approach is that fast convergence in parking and tracking can be treated at the same time without switching between two controllers. Moreover, a tuning function is used to enhance parking performance. With the proposed framework, various tracking controllers given in the literature can be adopted to handle parking problems. The effectiveness of the proposed methods is verified by several interesting experiments including parallel parking and back-into-garage parking.

On Uniform Global Asymptotic Stability of Nonlinear Discrete-Time Systems With Applications

This paper presents new characterizations of uniform global asymptotic stability for nonlinear and time-varying discrete-time systems. Under mild assumptions, it is shown that weak zero-state detectability is equivalent to uniform global asymptotic stability for globally uniformly stable systems. By employing the notion of reduced limiting systems, another characterization of uniform global asymptotic stability is proposed on the basis of the detectability for the reduced limiting systems associated with the original system. As a by-product, we derive a generalized, discrete-time version of the well-known Krasovskii-LaSalle theorem for general time-varying, not necessarily periodic, systems. Furthermore, we apply the obtained stability results to analyze uniform asymptotic stability of cascaded time-varying systems, and show that some technical assumptions in recent papers can be relaxed. Through a practical application, it is shown that our results play a similar role to the classic LaSalle invariance principle in guaranteeing attractivity, noting that reduced limiting systems are used instead of the original system. To validate the conceptual characterizations, we study the problem of sampled-data stabilization for the benchmark example of nonholonomic mobile robots via the exact discrete-time model rather than approximate models. This case study also reveals that in general, sampled-data systems may become non-periodic even though their original continuous-time system is periodic. A novel sampled-data stabilizer design is proposed using the new stability results and is supported via simulation results

New cascade approach for global /spl kappa/-exponential tracking of underactuated ships

This note investigates the fast tracking control problem of underactuated ships via persistent excitation (PE) conditions. By combining a novel transformation with the computed torque method, a decoupling controller related to the surge force is given first to decompose the error model into two cascade subsystems. Then, a stabilizing controller involving the yaw moment is designed. With the help of the proposed cascaded structure, a weaker PE condition than those given in past literature can be used to verify an integral detectability and guarantee global /spl kappa/-exponential convergence by employing several newly developed stability criteria. A new feature of the obtained results is that only one of these reference signals is needed to satisfy the usual PE condition. Simulation results are provided to validate the effectiveness of the proposed scheme.

A general stability criterion for time-varying systems using a modified detectability condition

Uniform asymptotic stability for general nonlinear time-varying systems is investigated from the output-to-state viewpoint. A unified criterion is proposed using a modified detectability condition and certain integral inequalities. The criterion extends the Krasovskii-LaSalle theorem to nonperiodic time-varying systems. An example taken from the tracking control of mobile robots is given to illustrate that, much as the invariance principle of LaSalle is used in studying the stability of time-invariant systems, our results can be used to study the stability of nonperiodic time-varying systems by checking the modified detectability condition.

Tracking control of mobile robots using saturation feedback controller

A general tracking control problem with saturation constraint for nonholonomic mobile robots is proposed and solved using the backstepping technique. A global result is given in which some artificial assumptions about the linear and the angular velocities of mobile robots from recent literature are dropped. The proposed controller can simultaneously solve both the tracking problem and the regulation problem of mobile robots. With the proposed control laws, mobile robots can now globally follow any path such as a straight line, a circle and the path approaching to the origin using a single controller. Computer simulations are presented which confirm the effectiveness of the tracking control laws. Moreover, practical experimental results concerning the tracking control are reported with saturation constraint for mobile robots.