Igor Škrjanc

Tracking-error model-based predictive control for mobile robots in real time

In this paper, a model-predictive trajectory-tracking control applied to a mobile robot is presented. Linearized tracking-error dynamics is used to predict future system behavior and a control law is derived from a quadratic cost function penalizing the system tracking error and the control effort. Experimental results on a real mobile robot are presented and a comparison of the control obtained with that of a time-varying state-feedback controller is given. The proposed controller includes velocity and acceleration constraints to prevent the mobile robot from slipping and a Smith predictor is used to compensate for the vision-system dead-time. Some ideas for future work are also discussed.

Technical communique: Identification of dynamical systems with a robust interval fuzzy model

In this paper we present a new method of interval fuzzy model identification. The method combines a fuzzy identification methodology with some ideas from linear programming theory. On a finite set of measured data, an optimality criterion that minimizes the maximal estimation error between the data and the proposed fuzzy model output is used. The idea is then extended to modelling the optimal lower and upper bound functions that define the band that contains all the measurement values. This results in a lower and an upper fuzzy model or a fuzzy model with a set of lower and upper parameters. The model is called the interval fuzzy model (INFUMO). The method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed. We believe that the fuzzy interval model can be very efficiently used, especially in fault detection and in robust control design.

Time optimal path planning considering acceleration limits

A robot path planning technique is proposed in the paper. It was developed for robots with differential drive, but with minor modifications it could be used for all types of nonholonomic robots. The path was planned in the way to minimise the time of reaching the end point in desired direction and with desired velocity, starting from the initial state described by the start point, initial direction and initial velocity. The limitation was the grip of the tires that results in the acceleration limits. The path is presented as a spline curve and was optimised by placing the control points through which the curve should pass.

Recursive clustering based on a Gustafson–Kessel algorithm

In this paper an on-line fuzzy identification of Takagi Sugeno fuzzy model is presented. The presented method combines a recursive Gustafson–Kessel clustering algorithm and the fuzzy recursive least squares method. The on-line Gustafson–Kessel clustering method is derived. The recursive equations for fuzzy covariance matrix, its inverse and cluster centers are given. The use of the method is presented on two examples. First example demonstrates the use of the method for monitoring of the waste water treatment process and in the second example the method is used to develop an adaptive fuzzy predictive functional controller for a pH process. The results for the Mackey–Glass time series prediction are also given.

Recursive fuzzy c-means clustering for recursive fuzzy identification of time-varying processes.

In this paper we propose a new approach to on-line Takagi-Sugeno fuzzy model identification. It combines a recursive fuzzy c-means algorithm and recursive least squares. First the method is derived and than it is tested and compared on a benchmark problem of the Mackey-Glass time series with other established on-line identification methods. We showed that the developed algorithm gives a comparable degree of accuracy to other algorithms. The proposed algorithm can be used in a number of fields, including adaptive nonlinear control, model predictive control, fault detection, diagnostics and robotics. An example of identification based on a real data of the waste-water treatment process is also presented.

Globally stable direct fuzzy model reference adaptive control

Abstract In the paper a fuzzy adaptive control algorithm is presented. It belongs to the class of direct model reference adaptive techniques based on a fuzzy (Takagi–Sugeno) model of the plant. The plant to be controlled is assumed to be nonlinear and predominantly of the first order. Consequently, the resulting adaptive and control laws are very simple and thus interesting for use in practical applications. The system remains stable in the presence of unmodelled dynamics (disturbances, parasitic high-order dynamics and reconstruction errors are treated explicitly). The global stability of the overall system is proven in the paper, i.e. it is shown that all signals remain bounded while the tracking error and estimated parameters converge to some residual set that depends on the size of disturbance and high-order parasitic dynamics. The proposed algorithm is tested on a simulated three-tank system. Its performance is compared to the performance of a classical MRAC.

Optimal cooperative collision avoidance between multiple robots based on Bernstein-Bézier curves

In this paper a new cooperative collision-avoidance method for multiple, nonholonomic robots based on Bernstein-Bezier curves is presented. The main contribution focuses on an optimal, cooperative, collision avoidance for a multi-robot system where the velocities and accelerations of the mobile robots are constrained and the start and the goal velocity are defined for each robot. The optimal path of each robot, from the start pose to the goal pose, is obtained by minimizing the penalty function, which takes into account the sum of all the path lengths subjected to the distances between the robots, which should be larger than the minimum distance defined as the safety distance, and subjected to the velocities and accelerations, which should be lower than the maximum allowed for each robot. The model-predictive trajectory tracking is used to drive the robots on the obtained reference paths. The results of the path planning, real experiments and some future work ideas are discussed.

Direct fuzzy model-reference adaptive control

Intelligent systems may be viewed as a framework for solving the problems of nonlinear system control. The intelligence of the system in the nonlinear or changing environment is used to recognize in which environment the system currently resides and to service it appropriately. This paper presents a general methodology of adaptive control based on multiple models in fuzzy form to deal with plants with unknown parameters which depend on known plant variables. We introduce a novel model‐reference fuzzy adaptive control system which is based on the fuzzy basis function expansion. The generality of the proposed algorithm is substantiated by the Stone‐Weierstrass theorem which indicates that any continuous function can be approximated by fuzzy basis function expansion. In the sense of adaptive control this implies the adaptive law with fuzzified adaptive parameters which are obtained using Lyapunov stability criterion. The combination of adaptive control theory based on models obtained by fuzzy basis function expansion results in fuzzy direct model‐reference adaptive control which provides higher adaptation ability than basic adaptive‐control systems. The proposed control algorithm is the extension of direct model‐reference fuzzy adaptive‐control to nonlinear plants. The direct fuzzy adaptive controller directly adjusts the parameter of the fuzzy controller to achieve approximate asymptotic tracking of the model‐reference input. The main advantage of the proposed approach is simplicity together with high performance, and it has been shown that the closed‐loop system using the direct fuzzy adaptive controller is globally stable and the tracking error converges to the residual set which depends on fuzzification properties. The proposed approach can be implemented on a wide range of industrial processes. In the paper the foundation of the proposed algorithm are given and some simulation examples are shown and discussed.

Design and Stability Analysis of Fuzzy Model-based Predictive Control—A Case Study

In the paper a fuzzy model based predictive control algorithm is presented. The proposed algorithm is developed in the state space and is given in analytical form, which is an advantage in comparison with optimisation based control schemes. Fuzzy model-based predictive control is potentially interesting in the case of batch reactors, heat-exchangers, furnaces and all the processes with strong nonlinear dynamics and high transport delays. In our case it is implemented to a continuous stirred-tank simulated reactor and compared to optimal PI control. Some stability and design issues of fuzzy model-based predictive control are also given.

Fuzzy Predictive Functional Control in the State Space Domain

In the paper, a well-known predictive functional control strategy is extended to nonlinear processes. In our approach the predictive functional control is combined with a fuzzy model of the process and formulated in the state space domain. The prediction is based on a global linear model in the state space domain. The global linear model is obtained by the fuzzy model in Takagi–Sugeno form and actually represents a model with changeable parameters. A simulation of the system, which exhibits a strong nonlinear behaviour together with underdamped dynamics, has evaluated the proposed fuzzy predictive control. In the case of underdamped dynamics, the classical formulation of predictive functional control is no longer possible. That was the main reason to extend the algorithm into the state space domain. It has been shown that, in the case of nonlinear processes, the approach using the fuzzy predictive control gives very promising results.