Branko Novaković

Global positioning of robot manipulators with mixed revolute and prismatic joints

The existing controllers for robot manipulators with uncertain gravitational force can globally stabilize only robot manipulators with revolute joints. The main obstacles to the global stabilization of robot manipulators with mixed revolute and prismatic joints are unboundedness of the inertia matrix and the Jacobian of the gravity vector. In this note, a class of globally stable controllers for robot manipulators with mixed revolute and prismatic joints is proposed. The global asymptotic stabilization is achieved by adding a nonlinear proportional and derivative term to the linear proportional-integral-derivative (PID) controller. By using Lyapunovs direct method, the explicit conditions on the controller parameters to ensure global asymptotic stability are obtained.

Tool wear monitoring using radial basis function neural network

This work considers the application of radial basis function neural network (RBFNN) for tool wear determination in the milling process. Tool wear, i.e., flank wear zone widths, have been estimated in two phases using two types of RBFNN algorithms. In the first phase, RBFNN pattern recognition algorithm is used in order to classify tool wear features in three wear level classes (initial, normal and rapid tool wear). On behalf of these results, in the second phase, RBFNN regression algorithm is utilized to estimate the average amount of flank wear zone widths. Tool wear features were extracted in time and frequency domain from three different types of signals: force, acoustic emission and nominal currents of feed drives.

Passive Finite-Dimensional Repetitive Control of Robot Manipulators

In this paper, a new class of finite-dimensional repetitive controllers for robot manipulators is proposed. The global asymptotic stability is proved for the unperturbed system. The passivity-based design of the proposed repetitive controller avoids the problem of tight stability conditions and slow convergence of the conventional, internal model-based, repetitive controllers. The passive interconnection of the controller and the nonlinear mechanical systems provides the same stability conditions as the controller with the exact feed-forward compensation of robot dynamics. The simulation results on a three degrees of freedom spatial manipulator illustrate the performances of the proposed controller.

Discrete time neural network synthesis using input and output activation functions

A new very fast algorithm for synthesis of a new structure of discrete-time neural networks (NN) is proposed. For this purpose the following concepts are employed: (i) combination of input and output activation functions, (ii) input time-varying signal distribution, (iii) time-discrete domain synthesis and (iv) one-step learning iteration approach. The problem of input-output mappings of time-varying vectors is solved. Simulation results based on the synthesis of a new structure of feedforward NN of an universal logical unit are presented. The proposed NN synthesis procedure is useful for applications to identification and control of nonlinear, very fast, dynamical systems. In this sense a feedforward NN for an adaptive nonlinear robot control is designed. Finally, a new algorithm for the direct inverse modeling of input/output nonquadratic systems is discussed.

Fuzzy logic control synthesis without any rule base

A new analytic fuzzy logic control (FLC) system synthesis without any rule base is proposed. For this purpose the following objectives are preferred and reached: 1) an introduction of a new adaptive shape of fuzzy sets and a new adaptive distribution of input fuzzy sets, 2) a determination of an analytic activation function for activation of output fuzzy sets, instead of using of min-max operators, and 3) a definition of a new analytic function that determines the positions of centers of output fuzzy sets in each mapping process, instead of definition of the rule base. A real capability of the proposed FLC synthesis procedures is presented by synthesis of FLC of robot of RRTR-structure.

A comparison of feed-forward and recurrent neural networks in time series forecasting

Forecasting performances of feed-forward and recurrent neural networks (NN) trained with different learning algorithms are analyzed and compared using the Mackey-Glass nonlinear chaotic time series. This system is a known benchmark test whose elements are hard to predict. Multi-layer Perceptron NN was chosen as a feed-forward neural network because it is still the most commonly used network in financial forecasting models. It is compared with the modified version of the so-called Dynamic Multi-layer Perceptron NN characterized with a dynamic neuron model, i.e., Auto Regressive Moving Average filter built into the hidden layer neurons. Thus, every hidden layer neuron has the ability to process previous values of its own activity together with new input signals. The obtained results indicate satisfactory forecasting characteristics of both networks. However, recurrent NN was more accurate in practically all tests using less number of hidden layer neurons than the feed-forward NN. This study once again confirmed a great effectiveness and potential of dynamic neural networks in modeling and predicting highly nonlinear processes. Their application in the design of financial forecasting models is therefore most recommended.

An analytic approach to fuzzy robot control synthesis

The main advantage of a fuzzy control system is the fact that no mathematical model of the controlled plant is required. Instead of that model, it is necessery to construct a fuzzy rule base for each particular application case. A vexing problem in fuzzy control, however, is the exponential growth in rules as the number of variables increases. This problem is avoided here by the introduction of a new, nonconventional analytic method for synthesising the fuzzy control. For this purpose a new analytic function is defined that determines the positions of the centres of the output fuzzy sets, instead of the definition of a fuzzy rule base. This function can be adapted to each concrete application case by changing the free fuzzy-set parameters. The proposed analytic approach to the synthesis of fuzzy control, has been tested by a numerical simulation of an analytic fuzzy control system for a robot with four degrees of freedom.

A conjugate gradient-based BPTT-like optimal control algorithm

The paper presents a gradient-based algorithm for optimal control of nonlinear multivariable systems with control and state vectors constraints. The algorithm has a backward-in-time recurrent structure similar to the backpropagation-through-time algorithm, which is mostly used as a learning algorithm for dynamic neural networks. Other main features of the algorithm include the use of higher order Adams time-discretization schemes, numerical calculation of Jacobians, and advanced conjugate gradient methods for favorable convergence properties. The algorithm performance is illustrated on an example of off-line vehicle dynamics control optimization based on a realistic high-order vehicle model. The optimized control variables are active rear differential torque transfer and active rear steering road wheel angle, while the optimization tasks are trajectory tracking and roll minimization for a double lane change maneuver.

Optimization of Global Chassis Control Variables

Abstract The paper presents a global chassis control (GCC) optimization approach using a gradient-based optimal control algorithm. The goal is to find optimal actions of various actuators such as active steering and active differential, which ensure satisfying the optimization criterion (e.g. trajectory following error minimization) subject to different equality and inequality constraints on state and control variables. The optimization algorithm is based on an exact gradient method, where the cost function gradient is calculated by using a backpropagation-through-time-like algorithm. The proposed GCC optimization approach is illustrated on an example of double lane change maneuver using rear active steering and/or rear active differential actuators.

An Algorithm for the Nonlinear Adaptive Robot Control Synthesis

This paper presents an unified approach to the nonlinear adaptive control synthesis of industrial robots. Following the ideas of the external linearization, the control problem of nonlinear industrial robot model (IRM) has been reduced to optimal control one of the equivalent linear IRM, with control and state constraints. Introducing the tracking error model of a full robot model (manipulator + actuators), the nonlinear control law has been derived, which guarantees the linear behaviour of the nonlinear IBM in the closed loop system. An unified direct adaptation procedure of the position and velocity regulator gains, has also been proposed, where desired stage of the relative and exponential stability have been preserved. In this sense a simple control synthesis procedure has been built.