Screening of factors influencing the performance of manipulator using combined array design of experiment approach

A robot must manipulate objects with high accuracy and repeatability to perform precise tasks. However, deviation in performance is attributed to uncertainties and improper selection of control, noise, and process factors. The information regarding the effect of these factors on performance is almost non-existent. A probabilistic approach has been used to model and simulate the performance of manipulator. The combined array fractional factorial design of experiment approach has been employed to identify the significant factors and their interactions. This approach helps in screening of the manipulator factors and focus on those that are important. To explore further, two indices, viz. link length ratio and link mass ratio, have been proposed and impact of these indices on manipulator performance is investigated. A two degree of freedom (2-DOF) RR planar manipulator performing a task with cubic and quintic trajectory has been used to illustrate the approach. It has been observed that the statistically significant factors are different for different tasks in workspace. It has also been observed that for the same task, factors responsible for performance variations are different for cubic and quintic trajectories. Finally, it has been demonstrated that the link length ratio change has significant influence on performance compared to link mass ratio.     

Parametric design optimization of 2-DOF R–R planar manipulator—A design of experiment approach

This work illustrates simulation approach for optimizing the parametric design and performance of a 2-DOF R–R planar manipulator. Using dynamic and kinematic models of a manipulator different performance measures for the manipulator are obtained for different combination of parameters with effect of noise incorporated to imitate the real time performance of the manipulator. A novel approach has been proposed to model, the otherwise difficult to model, noise effects. The data generated during simulation for various parameter combinations are utilized to analyze the statistical significance of kinematic and dynamic parameters on performance of manipulator using ANOVA technique. The parameter combinations, which give optimum performance measures obtained for different points in workspace, are compared and reported.     

Simultaneous selection of optimal parameters and tolerance of manipulator using evolutionary optimization technique

For precise industrial applications, a manipulator must have high positioning accuracy and repeatability. However, variations in performance of the manipulator are attributed to improper selection of dimensions of design and process parameters and its tolerance. There have been almost no attempts to optimize these parameters and tolerance of the manipulator, by which performance variations will be minimum. This paper presents an offline approach to select optimal parameters and tolerance simultaneously which minimizes the manufacturing cost and delivers the target performance level. To determine the optimal parameters and tolerances, a modification in differential evolution algorithm is proposed, which helps in incorporating the effect of uncertainty in optimization process. Proposed approach has been illustrated by selecting optimal parameters and tolerance of a 2-DOF RR planar manipulator. The performance of this approach has been compared with modified genetic algorithm. It is observed that differential evolution algorithm provides optimal results with lesser computations compared to genetic algorithm.     

Laser interferometry-based guidance methodology for high precision positioning of mechanisms and robots

Laser interferometry-based sensing and measurement (LISM) technique was originally investigated to perform dynamic measurements of the end effector of a robot manipulator in motion. This technique can provide dynamic position measurements in real time and has high accuracy, large working space, high sampling rate and automatic target tracking. In this paper, a methodology using LISM technique is proposed to perform laser interferometry-based guidance (LIG) for accurate positioning of a robot manipulator in high precision manufacturing operations. The methodology utilizes the LISM apparatus to guide the robot's end effector to a desired location or along a desired path by directing the robot to follow the trajectory mapped by the laser beam. This is accomplished through the establishment of techniques for path generation, sensing and data acquisition and guidance error determination and compensation in the control algorithm. The algorithms for this methodology, together with the measurement and analysis techniques are described. A number of experiments are carried out to examine and validate the proposed LIG technique. Experimental results show that the established technique can effectively improve the positioning accuracy of the robot manipulator.     

Optimum design of a three-dimensional serial robot manipulator

A systematic and mathematical optimization methodology is presented for the optimal design of a three link, revolute joint, three-dimensional manipulator which must perform specific prescribed tasks. The objective of interest is the minimization of average torque requirement. In particular circular and eccentric closed task paths are considered. The optimization is carried out with the link lengths and the positional coordinates of the base taken as the five design variables, and subject to assembly and geometric constraints imposed on the system. In particular restrictions are placed on the joint angle between the links and on the link lengths. The minimization is successfully performed by the application of Snymans robust dynamic trajectory method for unconstrained optimization, to a penalty function formulation of the constrained problem.     

Tolerance specification of robot kinematic parameters using an experimental design technique—the Taguchi method

This paper presents the tolerance specification of robot kinematic parameters using the Taguchi method. The concept of employing inner and outer orthogonal arrays to identify the significant parameters and select the optimal tolerance range for each parameter is proposed. The performance measure based on signal-to-noise ratios (S/N) using the Taguchi method is validated by Monte Carlo simulations. Finally, a step-by-step tolerance specification methodology is developed and illustrated with a planar two-link manipulator and a five-degree-of-freedom Rhino robot.     

Position control of very lightweight single-link flexible arms with large payload variations by using disturbance observers

In this article, a robust control scheme for trajectory tracking of very lightweight single-link flexible arms is discussed. Since the payload is one of the most variable parameters in a manipulator, the control is designed to achieve an accurate tracking of the desired tip trajectory for any value of the robot tip mass, or even for a tip mass changing during the maneuver. The proposed controller also guarantees stability for small uncertainties in parameters such as stiffness or motor friction. In addition, the effect of spillover on the performance of the controlled system is analyzed, and it is proven that stability and a good performance are preserved independently from the non-modeled high-order dynamics. The control scheme is based on a two nested loops structure. Each of these loops implements a Generalized Proportional Integral (GPI) controller. Moreover, the outer loop includes a disturbance compensation term based on a disturbance observer, which achieves the required insensitivity to payload changes. The theoretical analysis is supported by an extensive set of numerical simulations which shows controlled system response when variations in the robot payload, or dynamics neglected in the controller design, are considered. Finally, some experiments have been carried out in order to test the performance of the tip trajectory tracking of the proposed control system.     

Evolving an interval type-2 fuzzy PID controller for the redundant robotic manipulator

Robotic manipulators are a multi-input multi-output, dynamically coupled, highly time-varying, complex and highly nonlinear systems wherein the external disturbances, parameter variations, and random noise adversely affects the performance of the robotic system. Therefore, in order to deal with such complexities, however, an intriguing task for control researchers, these systems require an efficient and robust controller. In this paper, a novel application of genetic algorithms (GA) optimization approach to optimize the scaling factors of interval type-2 fuzzy proportional derivative plus integral (IT2FPD+I) controllers is proposed for 5-DOF redundant robot manipulator for trajectory tracking task. All five controllers' parameters are optimized simultaneously. Further, a procedure for selecting appropriate initial search space is also demonstrated. In order to make a fair comparison between different controllers, the tuning of each of the controllers' parameters is done with GA. This optimization technique uses the time domain optimal tuning while minimizing the fitness function as the sum of integral of multiplication of time with square error (ITSE) for each joint. To ascertain the effectiveness of IT2FPID controller, it is compared against type-1 fuzzy PID (T1FPID) and conventional PID controllers. Furthermore, robustness testing of developed IT2FPID controller for external disturbances, parameter variations, and random noise rejection is also investigated. Finally, the experimental study leads us to claim that our proposed controller can not only assure best trajectory tracking in joint and Cartesian space, but also improves the robustness of the systems for external disturbances, parameter variations, and random noise.     

Multi-objective robust design of helical milling hole quality on AISI H13 hardened steel by normalized normal constraint coupled with robust parameter design

Helical milling is a hole-making process which has been applied in hardened materials. Due to the difficulties on achieving high-quality boreholes in these materials, the influence of noise factors, and multi-quality performance outcomes, this work aims the multi-objective robust design of hole quality on AISI H13 hardened steel. Experiments were carried out through a central composite design considering process and noise factors. The process factors were the axial and tangential feed per tooth of the helix, and the cutting velocity. The noise factors considered were the tool overhang length, the material hardness and the borehole height of measurement. Response models were obtained through response surface methodology for roughness and roundness outcomes. The models presented good explanation of data variability and good prediction capability. Mean and variance models were derived through robust parameter design for all responses. Similarity analysis through cluster analysis was performed, and average surface roughness and total roundness were selected to multi-objective optimization. Mean square error optimization was performed to achieve bias and variance minimization. Multi-objective optimization through normalized normal constraint was performed to achieve a robust Pareto set for the hole quality outcomes. The normalized normal constraint optimization results outperformed the results of other methods in terms of evenness of the Pareto solutions and number of Pareto optimal solutions. The most compromise solution was selected considering the lowest Euclidian distance to the utopia point in the normalized space. Individual and moving range control charts were used to confirm the robustness achievement with regard to noise factors in the most compromise Pareto optimal solution. The methodology applied for robust modelling and optimization of helical milling of AISI H13 hardened steel was confirmed and may be applied to other manufacturing processes.     

Unconstrained and constrained motion control of a planar two-link structurally flexible robotic manipulator

Unconstrained and constrained motion control of a planar two-link structurally-flexible robotic manipulator are considered in this study. The dynamic model is obtained by using the extended Hamilton's principle and the Galerkin criterion. A method is presented to obtain the linearized equations of motion in Cartesian space for use in designing the control system. The approach to solving the control problem is to use feedforward and feedback control torques. The feedforward torques maneuver the flexible manipulator along a nominal trajectory and the feedback torques minimize any deviations from the nominal trajectory. The feedforward and feedback torques are obtained by solving the inverse dynamics problem for the rigid manipulator and designing linear quadratic Gaussian with loop transfer recovery (LQG/LTR) compensators, respectively. The LQG/LTR design methodology is exploited to design a robust feedback control system that can handle modeling errors and sensor noise, and operate on Cartesian space trajectory errors. Computer simulated results are presented for an example planar, two-link, structurally flexible robotic manipulator. © 1994 John Wiley & Sons, Inc.     

Application of genetic algorithms to conceptual design of a micro-air vehicle

This paper investigates the feasibility of automating the conceptual design of a micro-air vehicle on a personal computer system. The proposed design methodology adopts the use of genetic algorithms as the search engine in the design process. The multidisciplinary optimization problem here is to maximize the lift-to-drag ratio subjected to static longitudinal stability, performance and physical constraints. The six design parameters chosen are angle of attack, main wing twist angle, winglet span, main wing chord length, main wing taper ratio and winglet taper ratio. A case study has been carried out to compare the performance of using genetic algorithms with well-established non-linear optimization method based on sequential quadratic programming.     

Sensor Fusion for Joint Kinematic Estimation in Serial Robots Using Encoder,Accelerometer and Gyroscope

Open-chain manipulator robots play an important role in the industry, since they are utilized in applications requiring precise motion. High-performance motion of a robot system mainly relies on adequate trajectory planning and the controller that coordinates the movement. The controller performance depends of both, the employed control law and the sensor feedback. Optical encoder feedback is the most used sensor for angular position estimation of each joint in the robot, since they feature accurate and low noise angular position measurements. However, it cannot detect mechanical imperfections and deformations common in open chain robots. Moreover, velocity and acceleration cannot be extracted from the encoder data without adding phase delays. Sensor fusion techniques are found to be a good solution for solving this problem. However, few works has been carried out in serial robots for kinematic estimation of angular position, velocity and acceleration, since the delays induced by the filtering techniques avoids its use as controller feedback. This work proposes a novel sensor-fusion-based feedback system capable of providing complete kinematic information from each joint in 4-degrees of freedom serial robot, with the contribution of a proposed methodology based on Kalman filtering for fusing the information from optical encoder, gyroscope and accelerometer appended to the robot. Calibration and experimentation are carried out for validating the proposal. The results are compared with another kinematic estimation technique finding that this proposal provides more information about the robot movement without adding state delays, which is important for being used as controller feedback.     

Design and Analysis of a Novel 3D Decoupled Manipulator Based on Compliant Pantograph for Micromanipulation

A novel 3D compliant manipulator for micromanipulation is introduced based on pantograph linkage. The proposed manipulator provides decoupled 3DOF translational motions. The key design feature is the use of parallelograms, which maintain the orientation of the end-effector fixed. The proposed manipulator provides advantages over its counterparts in the literature. It has significantly higher workspace to size ratio if its pantograph acts as a magnification device. On the other hand, it has higher resolution if its pantograph acts as a miniaturizing device. This provides great flexibility in the design process to account for the limited variety of the micro-actuators and the large variety of the micro-scale tasks in terms of workspace and resolution. Thus, the proposed system possesses the characteristics of gearing (speed up or speed down). A suitable choice of flexure hinges and material is done. The position and velocity kinematic analysis are carried out. Analytical expressions are derived for singularity-free-workspace boundaries in terms of physical constraints of the flexure joints. Dexterity analysis is performed to evaluate the design performance. A synthesis methodology of the proposed manipulator is developed. A finite element analysis is carried out and a prototype is manufactured to validate the conceptual design. Simulation and experimental results have successfully demonstrated the linearity and consistency between input and output displacements with acceptable parasitic motions. Moreover, the manipulability of the proposed manipulator is found to be configuration independent. Also, the manipulator could have isotropic performance over its workspace for certain actuator setup.     

Performance analysis of fractional order fuzzy PID controllers applied to a robotic manipulator

A two-link robotic manipulator is a Multi-Input Multi-Output (MIMO), highly nonlinear and coupled system. Therefore, designing an efficient controller for this system is a challenging task for the control engineers. In this paper, the Fractional Order Fuzzy Proportional-Integral-Derivative (FOFPID) controller for a two-link planar rigid robotic manipulator for trajectory tracking problem is investigated. Robustness testing of FOFPID controller for model uncertainties, disturbance rejection and noise suppression is also investigated. To study the effectiveness of FOFPID controller, its performance is compared with other three controllers namely Fuzzy PID (FPID), Fractional Order PID (FOPID) and conventional PID. For tuning of parameters of all the controllers, Cuckoo Search Algorithm (CSA) optimization technique was used. Two performance indices namely Integral of Absolute Error (IAE) and Integral of Absolute Change in Controller Output (IACCO) having equal weightage for both the links are considered for minimization. Numerical simulation results clearly indicate the superiority of FOFPID controller over the other controllers for trajectory tracking, model uncertainties, disturbance rejection and noise suppression.     

A Fast and Unified Method to Find a Minimum-Jerk Robot Joint Trajectory Using Particle Swarm Optimization

In robot trajectory planning, finding the minimum-jerk joint trajectory is a crucial issue in robotics because most robots are asked to perform a smooth trajectory. Jerk, the third derivative of joint position of a trajectory, influences how smoothly and efficiently a robot moves. Thus, the minimum-jerk joint trajectory makes the robot control algorithm simple and robust. To find the minimum-jerk joint trajectory, it has been formulated as an optimization problem constrained by joint inter-knot parameters including initial joint displacement and velocity, intermediate joint displacement, and final joint displacement and velocity. In this paper, we propose a fast and unified approach based on particle swarm optimization (PSO) with K-means clustering to solve the near-optimal solution of a minimum-jerk joint trajectory. This work differs from previous work in its fast computation and unified methodology. Computer simulations were conducted and showed the competent performance of our approach on a six degree-of-freedom robot manipulator.     

Force control of a two-linke planar manipulator with one flexible link

Force control of a two-link planar manipulator with one flexible link is considered in this study. The equations of motion are derived using the extended Hamilton's principle with only structural flexibility effects included in the dynamic model. The linear quadratic Gaussian/loop transfer recovery (LQG/LTR) design methodology is exploited to design a robust feedback control system that can handle modelling errors and sensor noise, and operate on Cartesian space trajectory errors. The LQG/LTR compensator together with a feedforward loop is used to simultaneously control the force exerted by the flexible manipulator normal to the environment and the position of the end-point in a direction tangent to the environment. Simulated results are presented for a numerical example.     

Dimensioning problems in system design using bicausal bond graphs

System inversion techniques and bond graph representations are used here to present a methodology for the dimensioning of actuating components for the proper operation of the overall system based on dynamic and energy criteria associated to some prescribed specifications. The proposed methodology to deal with the so-called sizing problem is then illustrated by the validation of the actuators of a two-link manipulator for a specified end-effector trajectory. The study shows that the components imposing limitations to the system performance and the causes of their inappropriateness can conveniently be identified and analysed.     

Neural network-based adaptive controller design of roboticmanipulators with an observer

A neural network (NN)-based adaptive controller with an observer is proposed for the trajectory tracking of robotic manipulators with unknown dynamics nonlinearities. It is assumed that the robotic manipulator has only joint angle position measurements. A linear observer is used to estimate the robot joint angle velocity, while NNs are employed to further improve the control performance of the controlled system through approximating the modified robot dynamics function. The adaptive controller for robots with an observer can guarantee the uniform ultimate bounds of the tracking errors and the observer errors as well as the bounds of the NN weights. For performance comparisons, the conventional adaptive algorithm with an observer using linearity in parameters of the robot dynamics is also developed in the same control framework as the NN approach for online approximating unknown nonlinearities of the robot dynamics. Main theoretical results for designing such an observer-based adaptive controller with the NN approach using multilayer NNs with sigmoidal activation functions, as well as with the conventional adaptive approach using linearity in parameters of the robot dynamics are given. The performance comparisons between the NN approach and the conventional adaptation approach with an observer is carried out to show the advantages of the proposed control approaches through simulation studies     

The influence of joint angle constraints on the optimum design of a planar robot manipulator following a complicated prescribed path

The application of a general optimization methodology, previously proposed by the authors, is extended here to the design of a three link revolute-joint planar manipulator performing a complicated prescribed task. In particular the end effector follows a “figure-of-eight” path. The minimization of average torque required for execution of the task is addressed and the optimization is carried out with the link lengths and base coordinates taken as the five design variables. In addition to simple physical bounds placed on the variables, the maximum deliverable torques of the driving motors represent further constraints on the system. Joint angle constraints, which are severe for this problem, are also imposed. This results in a challenging optimization problem. Two different approaches are used in the application of torque and joint angle constraints. The complications arising from lock-up and nonassembly are handled by specially devised procedures. The optimization is carried out via a penalty function formulation of the constrained problem to which Snyman's unconstrained trajectory optimization algorithm is applied in a special way. Without joint angle constraints feasible designs with low objective function values are obtained. With the imposition of joint angle constraints the method yields good, but compromised, solutions.     

Optimal design of nonlinear model predictive controller based on new modified multitracker optimization algorithm

The controller design for the robotic manipulator faces different challenges such as the system's nonlinearities and the uncertainties of the parameters. Furthermore, the tracking of different linear and nonlinear trajectories represents a vital role by the manipulator. This paper suggests an optimal design for the nonlinear model predictive control (NLMPC) based on a new improved intelligent technique and it is named modified multitracker optimization algorithm (MMTOA). The proposed modification of the MTOA is carried out based on opposition-based learning (OBL) and quasi OBL approaches. This modification improves the exploration behavior of the MTOA to prevent it from becoming trapped in a local optimum. The proposed method is applied on the robotic manipulator to track different linear and nonlinear trajectories. The NLMPC parameters are tuned by the MMTOA rather than the trial and error method of the designer. The proposed NLMPC based on MMTOA is compared with the original MTOA, genetic algorithm, and cuckoo search algorithm in literature. The superiority and effectiveness of the proposed controller are confirmed to track different linear and nonlinear trajectories. Furthermore, the robustness of the proposed method is emphasized against the uncertainties of the parameters.