Andrej Zdešar

Self-tuning of 2 DOF control based on evolving fuzzy model

Abstract In this paper we present a self-tuning of two degrees-of-freedom control algorithm that is designed for use on a non-linear single-input single-output system. The control algorithm is developed based on the Takagi-Sugeno fuzzy model, and it consists of two loops: a feedforward loop and feedback loop. The feedforward part of the controller should drive the system output to the vicinity of the reference signal. It is developed from the inversion of the T-S fuzzy model. To achieve accurate error-free reference tracking a feedback part of the controller is added. A time-varying error-model predictive controller is used in the feedback loop. The error-model is obtained from the T-S fuzzy model. The T-S fuzzy model of the system, required in the controller, is obtained with evolving fuzzy modelling, which is based on recursive Gustafson-Kessel clustering algorithm and recursive fuzzy least squares. It employs evolving mechanisms for adding, removing, merging and splitting the clusters. The presented control approach was experimentally validated on a non-linear second-order SISO system helio-crane in simulation and real environment. Several criteria functions were defined to evaluate the reference-tracking and disturbance rejection performance of the control algorithm. The presented control approach was compared to another fuzzy control algorithm. The experimental results confirm the applicability of the approach.

Fuzzy Control of a Helio-Crane

In this paper we present a comparison of two fuzzy-control approaches that were developed for use on a non-linear single-input single-output (SISO) system. The first method is Fuzzy Model Reference Learning Control (FMRLC) with a modified adaptation mechanism that tunes the fuzzy inverse model. The basic idea of this method is based on shifting the output membership functions in the fuzzy controller and in the fuzzy inverse model. The second approach is a 2 degrees-of-freedom (2 DOF) control that is based on the Takagi-Sugeno fuzzy model. The T-S fuzzy model is obtained by identification of evolving fuzzy model and then used in the feed-forward and feedback parts of the controller. An error-model predictive-control approach is used for the design of the feedback loop. The controllers were compared on a non-linear second-order SISO system named the helio-crane. We compared the performance of the reference tracking in a simulation environment and on a real system. Both methods provided acceptable tracking performance during the simulation, but on the real system the 2 DOF FMPC gave better results than the FMRLC.

Visual Trajectory-Tracking Model-Based Control for Mobile Robots

In this paper we present a visual-control algorithm for driving a mobile robot along the reference trajectory. The configuration of the system consists of a two-wheeled differentially driven mobile robot that is observed by an overhead camera, which can be placed at arbitrary, but reasonable, inclination with respect to the ground plane. The controller must be capable of generating appropriate tangential and angular control velocities for the trajectory-tracking problem, based on the information received about the robot position obtained in the image. To be able to track the position of the robot through a sequence of images in real-time, the robot is marked with an artificial marker that can be distinguishably recognized by the image recognition subsystem. Using the property of differential flatness, a dynamic feedback compensator can be designed for the system, thereby extending the system into a linear form. The presented control algorithm for reference tracking combines a feedforward and a feedback loop, the structure also known as a two DOF control scheme. The feedforward part should drive the system to the vicinity of the reference trajectory and the feedback part should eliminate any errors that occur due to noise and other disturbances etc. The feedforward control can never achieve accurate reference following, but this deficiency can be eliminated with the introduction of the feedback loop. The design of the model predictive control is based on the linear error model. The model predictive control is given in analytical form, so the computational burden is kept at a reasonable level for real-time implementation. The control algorithm requires that a reference trajectory is at least twice differentiable function. A suitable approach to design such a trajectory is by exploiting some useful properties of the Bernstein-Bézier parametric curves. The simulation experiments as well as real system experiments on a robot normally used in the robot soccer small league prove the applicability of the presented control approach.

Introduction to Mobile Robotics

This is an introductory chapter that presents the field of wheeled mobile robotics. Initially the words “robot,” “mobile,” and “wheel” that appear in the title of the book are explained. Then a brief classification of autonomous mobile systems is presented and an overview of various levels of autonomy is discussed. A short review of applications is followed by a list of important historical milestones that influenced the development of autonomous wheeled mobile robots.

Chapter 4 – Path Planning

This chapter defines path planning, lists possible fields of use, and states some additional terms that need to be met in the process of planning. Several possible ways to describe a planning problem and environment for the later path planning are given, such as graph representations, decomposition to cells, roadmaps, potential fields, and sampling-based path planning. Most commonly used search algorithms in path planning are described, starting with simple bug algorithms and continue with more advanced algorithms that can guarantee the optimal path and can include heuristics to narrow the search area or guarantee completeness. Also, some algorithms that do not require a fully known environment are introduced. For better understanding several illustrating examples and some implementations in Matlab scripts are given.

Homography estimation from circular motion for use in visual control

This paper presents a new method for estimation of the homography up to similarity from observing a single point that is rotating at constant velocity around a single axis. The benefit of the proposed estimation approach is that it does not require measurement of the points in the world frame. The homography is estimated based on the known shape of the motion and in-image tracking of a single rotating point. The proposed method is compared to the two known methods: the direct approach based on point correspondences and a more recently proposed method based on conic properties. The main advantages of the proposed method are that it also estimates the angular velocity and that it requires only a single circle. The estimation is made directly from the measurements in the image. Because of the advantages of the proposed method over the other methods, the proposed method should be simple to implement for calibration of visually guided robotic systems. All the approaches were compared in the simulation environment in some non-ideal conditions and in the presence of disturbances, and a real experiment was made on a mobile robot. The experimental results confirm that the presented approach gives accurate results, even in some non-ideal conditions.

A 2 DOF predictive control based on evolving fuzzy model

In this paper we present the design of a two degree-of-freedom (2 DOF) control algorithm, developed for a class of single-input multiple-output non-linear systems. The feedforward and feedback control loops are developed based on the known Takagi-Sugeno fuzzy model of the system. The fuzzy model is part of the control law and it is obtained by evolving fuzzy modelling. Although only a single system output is controlled, the clustering in evolving fuzzy model is made on multiple measurable system outputs. The control law is designed in a way that enables clustering in the evolving fuzzy model on multiple outputs. However, every input-output connection is described by a non-linear autoregressive system with exogenous inputs. The purpose of the feed-forward loop is to bring the controlled output close to the desired reference signal, and the feedback loop is used to eliminate the reference tracking error that may occur due to imprecise system modelling, noise or any other disturbances. Linearisation around the reference signal enables the design of an error-model predictive control in the feedback loop. The presented control approach was experimentally validated in simulation environment on a system of three water tanks. The experimental results confirm the applicability of the approach.

Design of the image-based satellite attitude control algorithm

This paper presents the design of the image-based control algorithm for interactive Earth observation. The image-based control algorithm is obtained from the modelling of the satellite pose in space. It is shown that the image-based control algorithm can be designed for two types of satellite attitude control problems: direction tracking and oriented-direction tracking. The reference target is not limited to the camera centre, but can be given anywhere in the image. The image-based control algorithm requires in-image tracking of one or two points on the Earths surface (depending on the type of the controller). To achieve robust image-based tracking, the general framework for tracking points on the Earths surface, which is assumed to be locally flat, is presented. The method is based on geometric local image features that are invariant to several image transformations and change in some environmental conditions. The presented methods are experimentally validated in simulation environment.

Optimum Velocity Profile of Multiple Bernstein-Bézier Curves Subject to Constraints for Mobile Robots

This article deals with trajectory planning that is suitable for nonholonomic differentially driven wheeled mobile robots. The path is approximated with a spline that consists of multiple Bernstein-Bézier curves that are merged together in a way that continuous curvature of the spline is achieved. The article presents the approach for optimization of velocity profile of Bernstein-Bézier spline subject to velocity and acceleration constraints. For the purpose of optimization, velocity and turning points are introduced. Based on these singularity points, local segments are defined where local velocity profiles are optimized independently of each other. From the locally optimum velocity profiles, the global optimum velocity profile is determined. Since each local velocity profile can be evaluated independently, the algorithm is suitable for concurrent implementation and modification of one part of the curve does not require recalculation of all local velocity profiles. These properties enable efficient implementation of the optimization algorithm. The optimization algorithm is also suitable for the splines that consist of Bernstein-Bézier curves that have substantially different lengths. The proposed optimization approach was experimentally evaluated and validated in simulation environment and on real mobile robots.

C2-continuous Path Planning by Combining Bernstein-Bézier Curves.

This work proposes fifth order Bernstein-Bézier (BB) curve segments to be used in path planning approaches. The combined path consists of BB spline sections with continuous second derivative in connections which means that the path curvature is continuous and feasible for wheeled robot to drive on. To further minimize the travelling time on this path a velocity profile is optimized by considering acceleration and velocity constraints.