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Discrete Time Control of a Mobile Robot
Abstract
To control the same process in discrete time, this control design methodology is applied in this chapter. Several models and discretization approaches for the same process are considered. The simpler the model is, the easier the controller results, and its tuning also becomes easier. The advantages and drawbacks of designing the control by using more complicated models are outlined and the results compared in a practical experiment. This comparison includes the CT controller developed in the previous chapter. The chapter is structured as follows: first, the kinematic model previously used is discretized, following different approximations. Then, the dynamic model is introduced. If the process model order is increased, additional sacrificed variables appear, and their reference should be computed. A practical experiment confirms the expected results, and some conclusions are drafted.
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In this work, a controller design technique called linear algebra based controller (LABC) is presented. The controller is obtained following a systematic procedure that is summarized in this work. In addition, the influence of additive uncertainty on the tracking error is analyzed, and a solution using integrators is proposed. A mobile robot is used as a benchmark to test the performance of the proposed algorithms. In addition, implementation to other systems such as marine vessel is referenced. In this work, the design of controllers in continuous and discrete time is included and experimental and simulation results are shown in a Pioneer 3AT mobile robot. Comparisons are also shown with other controllers proposed in the literature.
A design of sliding mode controllers (SMC) with adaptive capacity is presented. This control technique is formed by two cascaded SMC controllers, one of them having an adaptive neural compensator (ANC); both are put on a WMR (wheeled mobile robot). The mobile robot is divided into a kinematics and a dynamics structure; the first SMC controller acts only on the kinematic structure and the SMC with neural adaptive compensator on the other one. The dynamic SMC was designed applying an inverse dynamic controller and using the model dynamics of the WMR. The adaptive neural compensation (ANC) was used in order to reduce the control error caused by the dynamics variations but it conveys a residual approximation error, so a sliding part was designed to cancel such error. This technique allows achieving the control objective despite parameter variations and external disturbances that take place in the dynamics; on the other hand, the ANC can adjust its neural parameters to reduce the dynamics variations of the WMR and thus improve the trajectory tracking control. Problems of convergence and stability are treated and design rules based on Lyapunov’s theorem are given.
A new approach for navigation of mobile robots in dynamic environments by using Linear Algebra Theory, Numerical Methods, and a modification of the Force Field Method is presented in this paper. The controller design is based on the dynamic model of a unicycle-like nonholonomic mobile robot. Previous studies very often ignore the dynamics of mobile robots and suffer from algorithmic singularities. Simulation and experimentation results confirm the feasibility and the effectiveness of the proposed controller and the advantages of the dynamic model use. By using this new strategy, the robot is able to adapt its behavior at the available knowing level and it can navigate in a safe way, minimizing the tracking error.
This paper addresses the problem of trajectory tracking control in mobile robots under velocity limitations. Following the results reported in ref. [1], the problem of trajectory tracking considering control actions constraint is focused and the zero convergence of the tracking errors is demonstrated. In this work, the original methodology is expanded considering a controller that depends not only on the position but also on the velocity. A simple scheme is obtained, which can be easily implemented in others controllers of the literature. Experimental results are presented and discussed, demonstrating the good performance of the controller.
This paper is a continuation of a previous work of authors, Scaglia et al. [G. J. E. Scaglia, L. M. Quintero, V. Mut and F. Di Sciascio, “Numerical methods based controller design for mobile robots,” Robotica
27(2), 269–279 (2009)]. A method is presented to choose the controller parameters such that, the values of the control actions do not exceed the maximum allowable and the tracking errors tend to zero. In addition, the analysis of the controller design parameters is included. The experimental results (laboratory experiments and a real world application) demonstrate the efficiency of the controller.
This paper presents the design of four controllers for a mobile robot such that the system may follow a pre-established trajectory. To reach this aim, the kinematic model of a mobile robot is approximated using numerical methods. Then, from such approximation, the control actions to get a minimal tracking error are calculated. Both simulation and experimental results on a PIONEER 2DX mobile robot are presented, showing a good performance of the four proposed mobile robot controllers.
This work presents a novel linear interpolation based methodology to design control algorithms for the trajectory tracking of mobile robotic systems. Particularly, a typical nonlinear multivariable system—a mobile robot—is analysed. The methodology is simple and can be applied to the design of a large class of control systems. Simulation and experimental results are presented and discussed, demonstrating the good performance of the proposed methodology.
SUMMARY This work presents, first, a complete dynamic model of a unicycle-like mobile robot that takes part in a multi- robot formation. A linear parameterization of this model is performed in order to identify the model parameters. Then, the robot model is input-output feedback linearized. On a second stage, for the multi-robot system, a model is obtained byarrangingintoasingleequationallthefeedbacklinearized robot models. This multi-robot model is expressed in terms of formation states by applying a coordinate transformation. The inverse dynamics technique is then applied to design a formation control. The controller can be applied both to positioning and to tracking desired robot formations. The formation control can be centralized or decentralized and scalable to any number of robots. A strategy for rigid formation obstacle avoidance is also proposed. Experimental results validate the control system design.