Two-link Planar Robot Manipulator Research Articles

Adaptive Admittance Control for Safety-Critical Physical Human Robot Collaboration

Physical human-robot collaboration requires strict safety guarantees, due to the fact that robots and humans work in a shared workspace. This paper presents a novel control framework to handle safety-critical position-based constraints for human-robot physical interaction. The proposed methodology is based on admittance control, exponential control barrier functions (ECBFs), and quadratic program (QP) to achieve compliance during the force interaction between human and robot, while simultaneously guaranteeing safety constraints. In particular, the formulation of admittance control is formulated as a second-order nonlinear control system, and the interaction forces between humans and robots are regarded as the control input. A virtual force feedback for admittance control is provided in real-time by using the ECBFs-QP framework as a compensator of the external human forces. A safe trajectory is therefore derived from the proposed adaptive admittance control scheme for a low-level controller to track. The main innovation of the proposed approach is the ability to enable the robot to naturally comply with human forces without violating any safety constraints, even when external human forces incidentally force the robot to do so. The effectiveness of our approach is demonstrated in simulation studies on a two-link planar robot manipulator.

Optimal Tuning of the SMC Parameters for a Two-Link Manipulator Co-Simulation Control

This paper presents the trajectory tracking control of a two-link planar robot manipulator using MSC Adams and MATLAB co-simulation which enables the innovative virtual prototyping of the systems without any mathematical expressions. Firstly, the tracking control performance of the planar manipulator is investigated using the Sliding Mode Control (SMC) controller and the Proportional Integral Derivative (PID) controller in terms of the performance analysis. As a result, the SMC demonstrates effective control performances compared to the PID controller according to the required trajectory, settling time, and end position of the system. Then, the SMC controller parameters are determined using the different optimization methods offered as open source by MATLAB/Response Optimization Toolbox and compared to each other. In the virtual co-simulation, the trajectory tracking control performance is observed to be improved by optimizing the parameters of the SMC controller using Simplex Search (SS) method. All control results are examined and presented with graphics and international error standards.

Exponentially convergence for the regressor-free adaptive fuzzy impedance control of robots by gradient descent algorithm

Having the capability to estimate parametric and non-parametric uncertainties, this paper investigates a regressor-free adaptive model-reference scheme for impedance control of robotic systems interacting with an environment. Using the gradient descent algorithm for designing a fuzzy estimator makes the tune of controller’s parameters possible in different physical situations and uncertainties. Thanks to the voltage control strategy and fuzzy systems, there is no need for designers to have the knowledge of robots and actuators’ dynamics. In addition, the force feedback is not employed in the structure of control law. Using the Lyapunov-like stability analysis, not only the exponential convergence of error signal and its time derivative to zero are guaranteed in the decentralised form but also the boundedness of all signals is ensured. To confirm the efficiency of proposed control algorithm, several simulations as well as a comparison with a positioned-based impedance controller and a regressor-based adaptive impedance controller are conducted on a two-link planar robot manipulator considering a tunable desired trajectory and different stiffness of environment. Additionally, the proposed adaptive impedance controller is applied to a six degree of freedom revolute-joint manipulator to provide better evaluation.

A convex optimization based solution for the robotic manipulator control design problem subject to input saturation

This paper proposes a state-feedback design procedure for robotic manipulator systems with saturating actuators, a solution which is based on convex optimization subject to constraints in the form of linear matrix inequalities. Our fundamental idea is to express the system dynamics in a novel differential-algebraic representation with state-derivative components. This approach allows us to provide a systematic control design framework with formal theoretical guarantees, such as the asymptotic stabilization of the manipulator attitude reference error within a prescribed exponential decay-rate. Our method is capable of dealing with the nonlinearities of a mechanical manipulator system, including the input saturation effect, without relying on any kind of linearization or approximation. A two-link planar robotic manipulator example is employed in order to illustrate the proposed approach.

Trajectory tracking control for robot manipulators using only position measurements

ABSTRACTIn the paper, the trajectory tracking control problem is investigated for robotic manipulators which are not equipped with the tachometers. Our contribution consists in establishing uniform asymptotic stability in closed-loop system by using the dynamic position-feedback controller with feedforward. Using Lyapunov vector function and comparison principle, we construct the non-linear controller with variable gain matrices and first-order linear dynamic compensator such that the origin of the closed-loop system is uniformly asymptotically stable. The controller is shown to be robust with respect to parameters incertainties. We illustrate the utility of our result by simulation tests with reference to a two-link planar elbow robot manipulator.

Guidance and Control of a Planar Robot Manipulator Used in a Mounting Line

AbstractIn this study, the guidance and control of a two-link planar robot manipulator which is utilized to put the considered parts or components into the relevant slots on a moving belt of a mounting line is dealt with. In this extent, first the kinematic analysis of the robot manipulator is completed and its dynamic model is derived. Then, an indirect control scheme is built regarding the link angles of the manipulator as the control variables based on the mentioned dynamic model. Afterwards, the part carried by the end effector of the robot manipulator from the considered container is tried to be inserted to the relevant slot on the moving belt in accordance with the commands generated by the linear homing guidance law and the performance of the designed guidance and control algorithm is investigated through the computer simulations using the constructed models under different initial conditions.

A new perturbation estimator in a sliding mode control system with application to robot control

In this work, a new perturbation estimator associated with a sliding mode controller is proposed to enhance control performance of linear or non-linear systems under perturbations such as parameter uncertainties and extraneous disturbances. The estimator is designed by adopting an integrated average value of the imposed perturbation over a certain sampling period. Subsequently, in order to improve control performance, a so-called perturbation filtering condition (PFC) is introduced for the estimator. By applying the PFC in which useful components of the imposed perturbations are kept, control performance can be substantially improved without additional control input. Some benefits of the proposed methodology are demonstrated on a two-link planar robotic manipulator. The position tracking control performances of the manipulator are evaluated in the time domain and a comparative work between the proposed methodology and conventional scheme for the perturbation estimation is undertaken.

Integral Nested Sliding Mode Control for Robotic Manipulators

An Integral Nested Sliding Mode Control (INSMC) is proposed for n-link robotic manipulators tracking problem by employing Integral Sliding Mode (ISM) and Nested Sliding Mode (NSM) concepts. This controller has the robustness of NSM against matched and no matched perturbations, and the capability of ISM to reduce the sliding functions gains. Application to a two-link planar robot manipulator is presented as a simulation example.

Nonlinear programming-based sliding mode control with an application in the stabilization of an Acrobot

A new approach to compute optimal forcing functions for nonlinear dynamic systems expressed by differential equations and stemming from the sliding mode control (SMC) problems is presented. SMC input achieves generation of a desired trajectory in two phases. In the first phase, the input is designed to steer the state of the nonlinear dynamic system towards a stable (hyper) surface (in practice, it is generally a subspace) in the state space. The second phase starts once the state enters a prespecified neighbourhood of the surface. In this phase, the control input is required to drive the system state towards the origin while keeping it in this neighbourhood. It is shown that by appropriate selection of the objective functions and the constraints, it is possible to model both phases of this problem in the form of constrained optimization problems, which provide an optimal solution direction and thus improve the chattering. Generally, these problems are not convex and therefore require a special solution approach. The modified subgradient algorithm, which serves for solving a large class of nonconvex optimization problems, is used here for solving the optimization problems so constructed. This article also proposes a generalized optimization problem with a unified objective function by taking a weighted sum of two objectives representing the two stages. Validity of the approach of this work is illustrated by stabilizing a two-link planar robot manipulator.

Design of Adaptive Robot Control System Using Recurrent Neural Network

The use of a new Recurrent Neural Network (RNN) for controlling a robot manipulator is presented in this paper. The RNN is a modification of Elman network. In order to solve load uncertainties, a fast-load adaptive identification is also employed in a control system. The weight parameters of the network are updated using the standard Back-Propagation (BP) learning algorithm. The proposed control system is consisted of a NN controller, fast-load adaptation and PID-Robust controller. A general feedforward neural network (FNN) and a Diagonal Recurrent Network (DRN) are utilised for comparison with the proposed RNN. A two-link planar robot manipulator is used to evaluate and compare performance of the proposed NN and the control scheme. The convergence and accuracy of the proposed control scheme is proved.

Tip Dynamic Response of Elastic Joint Manipulators Subjected to a Stochastic Base Excitation

An approach to study of the tip dynamic response (displacement and velocity) of elastic joint manipulators subjected to a vertical stochastic excitation of the base is presented. The crossing analysis of maximum displacement of the manipulator tip along a determined path is also investigated. Dynamic equations of motion of an n-link articulated elastic joint manipulator subjected to a vertical stochastic base excitation are derived by using the Euler-Lagrange equations and then extended by Taylor series expansion. The resulting dynamic equations are linearized with respect to links vibration. The power spectral density representation is used to compute the second moment matrix of angular displacement and velocity of the links and also to compute the second moment matrix of manipulator tip dynamic response. Then the crossing analysis and also the probability that any maximum peak displacement value of manipulator tip exceeds from a determined level along a path are investigated. Finally, some of simulation results for a two-link planar robot manipulator subjected to a vertical stochastic excitation of the base are presented.

Adaptive control of robot manipulator using fuzzy compensator

This paper presents two kinds of adaptive control schemes for robot manipulator which has the parametric uncertainties. In order to compensate these uncertainties, we use the FLS (fuzzy logic system) that has the capability to approximate any nonlinear function over the compact input space. In the proposed control schemes, we need not derive the linear formulation of robot dynamic equation and tune the parameters. We also suggest the robust adaptive control laws in all proposed schemes for decreasing the effect of approximation error. To reduce the number of fuzzy rules of the FLS, we consider the properties of robot dynamics and the decomposition of the uncertainty function. The proposed controllers are robust not only to the structured uncertainty such as payload parameter, but also to the unstructured one such as friction model and disturbance. The validity of the control scheme is shown by computer simulations of a two-link planar robot manipulator.

Implementation of Adaptive Hyperplanes for the Determination of Robust Control

This paper deals with the problem of identifying and controlling nonlinear time varying plants. The algorithm is defined to reach the following objectives. First, to achieve a quick and efficient identification, the plant is represented by a linear model defined with hyperplanes. They are found by minimizing errors between the last measures and their estimations. Secondly, to obtain a smooth control and a good accuracy, control law is derived from the optimization of a quadratic criteria defined to minimize outputs errors and the successive derivatives of the control. This identification and control law overcome the problems met in adaptive control based on neural networks, for which learning is often long, and where an important number of neurons and weights is required to get accurate results. Finally the proposed approach is applied to control a two-link planar robot manipulator and a PUMA 560 robot.

Applications of Kinematic/Kinetic Performance Tools in Synthesis of Multi-DOF Mechanisms

Analytical and graphical performance synthesis tools for multi-DOF mechanisms are developed in the companion of this two-part paper [1]. Various performance indices derived from the Jacobian matrix for analyzing performance characteristics of multi-DOF mechanisms were proposed. These performance indices are the local kinematic coupling index (inner product of the Jacobian column vectors), the local directional mobility index (ratio of the Jacobian’s eigenvalues), and the local efficiency index (product of the Jacobian’s eigenvalues). In this paper, effort is placed on the applicability of the proposed analytical and graphical synthesis tools used to aid the design of multi-DOF mechanisms. Two examples representing open and closed chain mechanisms will be used to illustrate the effectiveness and efficiency of the proposed method. First, a two-link planar robotic manipulator is used to apply the proposed method. Following that, a two DOF parallel drive road simulator illustrates applicability of the suggested tools. Through these examples, geometric parameters and joint range limits of the mechanism are optimized through the evaluation of performance indices, eigen-ellipse and intersection angle between trajectory contours.