An approach to adaptive control of robotic manipulators

The control synthesis for the robotic systems in which parameters are partially unknown is considered. We propose synthesis of robust, non-adaptive, decentralized control which has to stabilize robots for all allowable variations of the parameters. If the robust non-adaptive control cannot withstand all expected variations of parameters, we propose synthesis of indirect adaptive control, i.e. the estimation of the robot parameters is performed first and then used for adjusting the decentralized control gains. The non-adaptive and adaptive control syntheses are illustrated by simulation of an industrial robot with unknown payload mass.     

Neural network approach to trajectory synthesis for robotic manipulators

The paper deals with the collision free trajectory synthesis for industrial robotic manipulators. A new efficient method is proposed that is based on a neural network collision model. The developed iterative transformation procedure provides small computing times for the C-space synthesis and yields sufficiently precise configuration space map for the manipulators with many degrees of freedom. A topologically ordered neural network model is proposed to find the path in the configuration space. The stability of this model is proved using the Lyapunov function technique. To generate the collision model, a modification of the Radial Basis Function Network (RBFN) is used. The developed technique is illustrated by an application example of designing a robotic manufacturing cell for the automotive industry.     

An algorithmic approach to resolutions

We provide an algorithmic method for constructing projective resolutions of modules over quotients of path algebras. This algorithm is modified to construct minimal projective resolutions of linear modules over Koszul algebras.     

An adaptive neural network switching control approach of robotic manipulators for trajectory tracking

In this paper, an adaptive neural network (NN) switching control strategy is proposed for the trajectory tracking problem of robotic manipulators. The proposed system comprises an adaptive switching neural controller and the associated robust compensation control law. Based on the Lyapunov stability theorem and average dwell-time approach, it is shown that the proposed control scheme can guarantee tracking performance of the robotic manipulators system, in the sense that all variables of the closed-loop system are bounded and the effect due to the external disturbance and approximate error of radical basis function (RBF) NNs on the tracking error can be converged to zero in an infinite time. Finally, simulation results on a two-link robotic manipulator show the feasibility and validity of the proposed control scheme.     

A design approach to adaptive model-following control of robotic manipulators

In this paper, the robot dynamics are represented by a nonlinear state-space model containing a disturbance term due to gravitational loading. Using a suitable linear time-invariant reference model, an adaptive model-following control problem is formulated which satisfies the matching conditions. The control input is designed to have two components: a nonadaptive linear component to do the task of model-following and a nonlinear unit-vector component based on hyperstability theory to do the adaptive task. An additional integral feedback term is further superimposed and then the overall asymptotic hyperstability is established. The simulation results on the first three joints of PUMA 560 robot manipulator indicate the potential of our design approach.Based on research supported by Kuwait University Research Administration under Grant No. EE 049.     

A dynamic programming approach to trajectory planning of robotic manipulators

This paper presents a solution to the problem of minimizing the cost of moving a robotic manipulator along a specified geometric path subject to input torque/force constraints, taking the coupled, nonlinear dynamics of the manipulator into account. The proposed method uses dynamic programming (DP) to find the positions, velocities, accelerations, and torques that minimize cost. Since the use of parametric functions reduces the dimension of the state space from2nfor ann- jointed manipulator, to two, the DP method does not suffer from the "curse of dimensionality." While maintaining the elegance of our previous trajectory planning method, we have developed the DP method for the general case where 1) the actuator torque limits are dependent on one another, 2) the cost functions can have an arbitrary form, and 3) there are constraints on the jerk, or derivative of the acceleration. Also, we have shown that the DP solution converges as the grid size decreases. As numerical examples, the trajectory planning method is simulated for the first three joints of the PACS arm, which is a cylindrical arm manufactured by the Bendix Corporation.     

An adaptive fuzzy sliding mode controller for robotic manipulators

This paper proposes an adaptive fuzzy sliding mode controller for robotic manipulators. An adaptive single-input single-output (SISO) fuzzy system is applied to calculate each element of the control gain vector in a sliding mode controller. The adaptive law is designed based on the Lyapunov method. Mathematical proof for the stability and the convergence of the system is presented. Various operation situations such as the set point control and the trajectory control are simulated. The simulation results demonstrate that the chattering and the steady state errors, which usually occur in the classical sliding mode control, are eliminated and satisfactory trajectory tracking is achieved.     

An algorithmic approach for fuzzy inference

To apply fuzzy logic, two major tasks need to be performed: the derivation of production rules and the determination of membership functions. These tasks are often difficult and time consuming. This paper presents an algorithmic method for generating membership functions and fuzzy production rules; the method includes an entropy minimization for screening analog values. Membership functions are derived by partitioning the variables into the desired number of fuzzy terms and production rules are obtained from minimum entropy clustering decisions. In the rule derivation process, rule weights are also calculated. This algorithmic approach alleviates many problems in the application of fuzzy logic to binary classification     

An algorithmic approach to combining belief functions

Methods of combination are used to synthesize pieces of evidence of equal standing that represent different aspects of a specific system about which a diagnosis is to be made. Combination is distinct from consensus, when complete diagnoses rendered by different knowledge sources require synthesis, and conditionalization, where pieces of evidence to be synthesized have dissymmetric relationships to each other. The Dempster-Shafer Rule is the quintessential combination method. However, it has been criticized for its inability to handle inconsistent pieces of evidence and for the way it focuses the weight of evidence. This article presents an alternative combination method that is capable of handling inconsistent evidence and relates evidence focusing to the amount of information resident in pieces of evidence. The method is capable of combining belief functions. Future research should address extending the method to the combination of a broad class of imprecise probability functions. © 1996 John Wiley & Sons, Inc.     

Nonlinear adaptive control of robotic manipulators - hyperstability approach

A nonlinear model reference adaptive controller based on hyperstability approach, is presented for the control of robot manipulators. Use of hyperstability approach simplifies the stability proof of the adaptive system. The unknown parameters of the system, as well as its variable payload, are estimated on line and are adaptive to their actual values; tending to reduce the system error. In addition, any sudden change in the system parameters or payload is detected by the proposed intelligent controller. Robot path tracking, with unknown parameter values and variable payload, is simulated to show the effectiveness of the proposed adaptive control algorithm. Both system output error and parameter estimation error vanish under the proposed parameter adaptation algorithm.     

Redundancy modelling and resolution for robotic mobile manipulators: a general approach

In this work the topic of kinematic redundancy modelling and resolution for robotic mobile manipulators is considered. A set of redundancy parameters is introduced to define a general inverse kinematic procedure for mobile manipulators. Then, redundancy is treated as a non-linear optimization problem with the purpose of finding robot configurations that maximize the designed metric measures. Some strategies to design the optimization objective function are introduced in order to achieve desirable redundant behaviours, such as obstacles avoidance, mobile base motions reductions and dexterity optimization. Moreover, the robot controller has been developed following an object-oriented software architecture principle that allows to keep it general and robot independent. As a prove of reliability and generality of our approach, the same controller has been used to control several different mobile manipulators in a simulation environment, as well as a real KUKA youBot robot.     

Robust neural control for robotic manipulators

A robust neural control scheme for mechanical manipulators is presented. The design basically consists of an adaptive neural controller which implements a feedback linearization control law for a generic manipulator with unknown parameters, and a sliding-mode control which robustifies the design and compensates for the neural approximation errors. It is proved that the resulting closed-loop system is stable and that the trajectory-tracking control objective is achieved. Some simulation results are also provided to evaluate the design.     

An algorithmic approach to discovering and provingq-series identities

An algorithmic method of producingq-series identities from any given power series is discassed. This recursive technique is then used to give new proofs of several classicalq-identities of Gauss and Rogers. Dedicated to the memory of John Knopfmacher, 1937–1999, the inventor of the Engel expansions for q-series. The first author was partially supported by National Science Foundation Grant DMS-9206993 and by The Centre for Applicable Analysis and Number Theory of the University of the Witwatersrand. He wishes to express his gratitude to the second author who provided the hospitality and support which made his participation possible This paper was presented at the fourth International Conference on Average-Case Analysis of Algorithms, Princeton, NJ, by the second author. Online publication September 6, 2000.     

Adaptive linear controller for robotic manipulators

This paper presents a new approach to the position and velocity control of a manipulator by using an adaptive controller of the self-tuning type for each joint. The complicated manipulator system is modeled by a set of time series difference equations. The parameters of the models are determined by on-line recursive algorithms, which result from minimizing the sum of the squared equation errors. The adaptive controller of each joint is designed on the basis of the difference equation model and a chosen performance criterion. The controller gains are calculated on-line using the model with the estimated values of system parameters. Simulation results are presented to demonstrate the applicability of the approach. Some aspects of the implementation are also discussed.     

Singularity avoidance in robotic manipulators: A differential form approach

We examine the avoidability property of singular configurations in redundant robot kinematics. Using a differential form approach a collection of so-called reduced self-motion dynamical systems is attributed to singular configurations distinguished by coranks. The problem of detecting avoidability/unavoidability is transformed to a stability study of the reduced self-motion systems. Sufficient conditions for avoidability and unavoidability are derived.     

A neuro-simulated annealing approach to the inverse kinematics solution of redundant robotic manipulators

The neural-network-based inverse kinematics solution is one of the recent topics in the robotics because of the fact that many traditional inverse kinematics problem solutions such as geometric, iterative and algebraic are inadequate for redundant robots. However, since the neural networks work with an acceptable error, the error at the end of inverse kinematics learning should be minimized. In this study, simulated annealing (SA) algorithm was used together with the neural-network-based inverse kinematics problem solution robots to minimize the error at the end effector. The solution method is applied to Stanford and Puma 560 six-joint robot models to show the efficiency. The proposed algorithm combines the characteristics of neural network and an optimization technique to obtain the best solution for the critical robotic applications. Three Elman neural networks were trained using separate training sets and different parameters, since one of them can give better results than the others can. The best result is selected within three neural network results by computing the end effector error via direct kinematics equation of the robotic manipulator. The decimal part of the neural network result was improved up to 10 digits using simulated annealing algorithm. The obtained best solution is given to the simulated annealing algorithm to find the best-fitting 10 digits for the decimal part of the solution. The end effector error was reduced significantly.     

A neural-network committee machine approach to the inverse kinematics problem solution of robotic manipulators

In robotics, inverse kinematics problem solution is a fundamental problem in robotics. Many traditional inverse kinematics problem solutions, such as the geometric, iterative, and algebraic approaches, are inadequate for redundant robots. Recently, much attention has been focused on a neural-network-based inverse kinematics problem solution in robotics. However, the result obtained from the neural network requires to be improved for some sensitive tasks. In this paper, a neural-network committee machine (NNCM) was designed to solve the inverse kinematics of a 6-DOF redundant robotic manipulator to improve the precision of the solution. Ten neural networks (NN) were designed to obtain a committee machine to solve the inverse kinematics problem using separately prepared data set since a neural network can give better result than other ones. The data sets for the neural-network training were prepared using prepared simulation software including robot kinematics model. The solution of each neural network was evaluated using direct kinematics equation of the robot to select the best one. As a result, the committee machine implementation increased the performance of the learning.     

基于模糊变结构的机械臂控制

现有的机械臂模糊变结构控制方法大都计算复杂或需要检测滑模面的微分信号.本文将机械臂模型分为确定部分和不确定部分进行研究,对确定部分采用一般反馈控制,对不确定部分采用变结构集中补偿控制,为了消除变结构控制器的抖震引入模糊控制方法,将滑模面作为模糊控制器的输入,补偿控制器权值作为输出.本方案不仅不需要检测滑模面微分信号,而且计算简单,易于实现.仿真结果表明,在存在模型误差和外部扰动的情况下,该方案既能达到快速跟踪,又能很好的消除控制器的抖震.     

LP-based velocity profile generation for robotic manipulators

In this paper we examine the minimum-time velocity profile generation problem which belongs to the second stage of the decoupled robot motion planning. The time-optimal profile generation problem can be translated to a convex optimal control task through a nonlinear change of variables. When the constraints of the problem have special structure, the time-optimal solution can be obtained by linear programming (LP). In this special case, the velocity of the robot along the path is maximised, instead of time minimising. The benefit of the LP solution is the lower computational time. Validation of the LP algorithm is also presented based on simulation results.     

Robust tracking control for rigid robotic manipulators

The problem of robust tracking control using a nominal feedback controller and a variable structure compensator for a rigid robotic manipulator with uncertain dynamics is addressed in this note. It is shown that the effects of large system uncertainties can be eliminated and asymptotic convergence of the output tracking error can be guaranteed by using a variable structure compensator in the closed loop feedback control system for the rigid robotic manipulator