A simple PD controller for robots with elastic joints

The point-to-point control of manipulators having elastic joints is considered. It is shown that a simple PD (proportional plus derivative) controller, similar to that used for rigid robots, suffices to globally stabilize the elastic joint robots about a reference position. A robustness analysis is also given with respect to uncertainties on the robot parameters. The results of numerical simulation tests of a manipulator with three revolute elastic joints are presented     

Adaptive Regulation of Amplitude Limited Robot Manipulators With Uncertain Kinematics and Dynamics

Common assumptions in most of the previous robot controllers are that the robot kinematics and manipulator Jacobian are perfectly known and that the robot actuators are able to generate the necessary level of torque inputs. In this note, an amplitude-limited torque input controller is developed for revolute robot manipulators with uncertainty in the kinematic and dynamic models. The adaptive controller yields semiglobal asymptotic regulation of the task-space setpoint error. The advantages of the proposed controller include the ability to actively compensate for unknown parametric effects in the dynamic and kinematic model and the ability to ensure actuator constraints are not breached by calculating the maximum required torque a priori     

Feedback control of a flexible cylindrical manipulator

Flexible robotic manipulators have been the subject of numerous studies in the past few years. Past studies, however, have concentrated on flexible manipulators with only revolute joints. This paper considers the case of a structurally flexible manipulator with prismatic and revolute joints; specifically, an algorithm for controlling a structurally flexible three-degree-of-freedom cylindrical manipulator is presented. The control algorithm involves two steps. Using nonlinear feedback, the equations of motion are first decoupled into three subsystems representing the three rigid degrees of freedom together with their associated ‘flexible equations’, if any. Then, using linear optimal control theory, controllers are designed for the three subsystems independently. Computer simulated results for an example system are presented.     

Polynomial family of PD-type controllers for robot manipulators

This paper addresses the problem of position control for robot manipulators. A new polynomial family of PD-type controllers with gravity compensation for the global position of robots manipulators is presented. The previous results on the linear PD controller are extended to the proposed polynomial family. The classical PD controller can be found among this large class of controllers when its proportional gain is a diagonal matrix. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear robot dynamics and the proposed family of controllers is globally asymptotically stable in agreement with Lyapunov's direct method and LaSalle's invariance principle. Besides the theoretical results, a real-time experimental comparison is also presented to illustrate the performance of the proposed family with other well-known control algorithms such as PD and PID schemes on a three degrees of freedom direct-drive arm.     

Further results on adaptive iterative learning control of robot manipulators

Based on a combination of a PD controller and a switching type two-parameter compensation force, an iterative learning controller with a projection-free adaptive algorithm is presented in this paper for repetitive control of uncertain robot manipulators. The adaptive iterative learning controller is designed without any a priori knowledge of robot parameters under certain properties on the dynamics of robot manipulators with revolute joints only. This new adaptive algorithm uses a combined time-domain and iteration-domain adaptation law allowing to guarantee the boundedness of the tracking error and the control input, in the sense of the infinity norm, as well as the convergence of the tracking error to zero, without any a priori knowledge of robot parameters. Simulation results are provided to illustrate the effectiveness of the learning controller.     

Joint stick-slip friction compensation of robot manipulators by using smooth robust controllers

In this article, two new smooth robust nonlinear compensators have been developed, respectively, for positional regulation and trajectory tracking of rigid robot manipulators with internal joint stick-slip friction. The proposed controllers can improve not only the positioning accuracy but also the smoothness of motion. No exact knowledge of the friction models is required for the design of the controllers. Furthermore, the tracking controller is also robust with respect to the uncertain link parameters. Using Lyapunov's direct method, we can show that the time-invariant positional regulation controller guarantees the global boundedness stability of the closed-loop system, while the time-varying positional tracking controller guarantees the global asymptotic stability of the closed-loop system. The numerical simulations of the controllers on a two-link robot are presented as illustrations. © 1994 John Wiley & Sons, Inc.     

Distributively controlling two robots handling an object in thetask space without any communication

Two distributed cooperation controllers are presented for trajectory tracking of two manipulators which are cooperatively handling an object. The controllers control the positions of the robots distributively by using the trajectory error of the object in the task space. In the first controller, the internal force between the object and a manipulator is controlled only by a feedforward of the desired force. The second controller uses a force feedback. No communication is required between the manipulators in both the controllers. Their globally and exponentially asymptotic stabilities are guaranteed by Lyapunov functions     

A systematic formulation of dynamic equations for robot manipulators with elastic links

Although a variety of formulation schemes for the dynamic equations of robot manipulators with rigid links can be found in the literature, an efficient method of the formulation for robot manipulators with elastic links is not well known. Accordingly, this work presents the derivation of the equations of motion for application to mechanical manipulators with elastic links. The formulation is conducted analytically using Hamilton's principle. The resultant equations consist of the terms of inertial, Coriolis, centrifugal, gravitational, and exerted forces. They are expressed in terms of a set of independent generalized coordinates. In contrast to conventional variational approaches, the present method provides an efficient and systematic way for obtaining the compact symbolic equations of flexible manipulator systems. Two examples are presented to illustrate the proposed methodology. Firstly, a three-link flexible manipulator with three revolute joints is studied. A flexible manipulator consisting of a prismatic joint and a discrete mass is the second model.     

Analytical development of dynamic equations of motion for a three-dimensional flexible link manipulator with revolute and prismatic joints

In this paper, a mathematical model capable of handling a three-dimensional (3D) flexible n-degree of freedom manipulator having both revolute and prismatic joints is considered. This model is used to study the longitudinal, transversal, and torsional vibration characteristics of the robot manipulator and obtain kinematic and dynamic equations of motion. The presence of prismatic joints makes the mathematical derivation complex. In this paper, for the first time, prismatic joints as well as revolute joints have been considered in the structure of a 3D flexible n-degree of freedom manipulator. The kinematic and dynamic equations of motion representing longitudinal, transversal, and torsional vibration characteristics have been solved in parametric form with no discretization. In this investigation, in order to obtain an analytical solution of the vibrational equations, a novel approach is presented using the perturbation method. By solving the equations of motion, it is shown that mode shapes of the link with prismatic joints can be modeled as the equivalent clamped beam at each time instant. As an example, this method is applied to a three degrees of freedom robot with revolute and prismatic joints. The obtained equations are solved using the perturbation method and the results are used to simulate vibrational behavior of the manipulator.     

New tuning conditions for a class of nonlinear PID global regulators of robot manipulators

Several nonlinear proportional-integral-derivative (PID) controllers for robot manipulators that ensure global asymptotic stability have been proposed in the literature. However, the tuning criteria obtained are expressed in terms of conditions so restrictive that they have avoided, until now, carrying out experimental tests with such controllers. Tuning criteria of some PID controllers for robot manipulators with conditions more relaxed than those presented previously in the literature have been proposed in two recent works by the authors. This was achieved by setting the tuning conditions individually for each joint instead of general conditions for the whole robot. In this paper we extend these results to a class of nonlinear PID global regulators for robot manipulators. The obtained tuning criteria are given in terms of conditions so relaxed that they have allowed to carry out, for the first time, experimental essays with these controllers. Such experiments are presented in this paper using a two-degrees-of-freedom robot manipulator.     

A global adaptive learning control for robotic manipulators

This paper addresses the problem of designing a global adaptive learning control for robotic manipulators with revolute joints and uncertain dynamics. The reference signals to be tracked are assumed to be smooth and periodic with known period. By developing in Fourier series expansion the input reference signals of every joint, an adaptive learning PD control is designed which ‘learns’ the input reference signals by identifying their Fourier coefficients: global asymptotic and local exponential stability of the tracking error dynamics are obtained when the Fourier series expansion of each input reference signal is finite, while arbitrary small tracking errors are achieved otherwise. The resulting control is not model based and depends only on the period of the reference signals and on some constant bounds on the robot dynamics.     

A class of nonlinear PD-type controllers for robot manipulators

In this article we present the stability analysis of a class of PD-type controllers for position and motion control of robot manipulators. The main feature of this class of controllers is that the proportional and derivative gains can be nonlinear functions of the robot states. These controllers can be obtained from control strategies that adjust the controller gains depending on the robot states. It is shown that global asymptotic stability of the control system is achieved provided that the P and D gains have suitable structure. As an outcome, we propose a global regulator constrained to deliver torques within prescribed limits of the actuator's capabilities. Experimental results on a two degrees of freedom direct drive arm show the usefulness of the proposed scheme. © 1996 John Wiley & Sons, Inc.     

A novel global asymptotic stable set-point fuzzy controller with bounded torques for robot manipulators

This paper addresses the set-point control of robot manipulators with friction where avoiding saturation of the actuators is a major issue. The original contribution is a novel direct fuzzy control system dealing with both practical constraints in mechanical manipulators: saturation and friction. The control system is made by taking advantage of input-output properties of the so-called sectorial fuzzy controllers. When friction is considered, we prove, via Lyapunov theory, that the steady state position errors owing to static friction are inside of a global attractor, which can be arbitrarily reduced. In case of absence of friction, the closed-loop system becomes globally asymptotic stable. In both cases, the important theoretical and practical feature of maintaining the control actions always within prescribed limits according to the actuator torque capabilities is guaranteed. Experimental evaluation of the proposed direct fuzzy control system on a nonlinear direct-drive robot arm is presented to validate its effectiveness.     

Contril of rigid-link,flexible-joint robots:a survey of backstepping approaches

The purpose of this article is to show how the design procedure commonly referred to as integrator backstepping can be used to design globally stable trajectory tracking controllers for Rigid-Link Flexible-Joint (RLFJ) robot manipulators. Three different types of controllers are developed: (1) an exact model knowledge-based controller, (2) an adaptive controller that compensates for parametric uncertainty, and (3) a robust controller that compensates for parametric uncertainty and unknown bounded disturbances. All three controllers are based on previously published work but are presented here in a unifying framework. © 1995 John Wiley & Sons, Inc.     

An adaptive fuzzy strategy for motion control of robot manipulators

This paper makes an attempt to develop a self-tuned proportional-integral-derivative (PID)-type fuzzy controller for the motion control of robot manipulators. In recent past, it has been widely believed that static fuzzy controllers can not be suitably applied for controlling manipulators with satisfaction because the robot manipulator dynamics is too complicated. Hence more complicated and sophisticated neuro-fuzzy controllers and fuzzy versions of nonlinear controllers have been more and more applied in this problem domain. The present paper attempts to look back at this widely accepted idea and tries to develop a self-tuned fuzzy controller with small incremental complexity over conventional fuzzy controllers, which can yet attain satisfactory performance. The proposed controller is successfully applied in simulation to control two-link and three-link robot manipulators.     

PPR型平面欠驱动机械臂的点位控制

研究了PPR型平面欠驱动机械臂(第1个关节和第2个关节是移动关节且是受控的,第3个关节为被动的转动关节)在水平面运动的点位控制问题.首先,通过输入和坐标变换方法,系统的动力学方程被变换成二阶链式形式.其次,提出用反步法推导出保证系统指数渐近稳定的控制器.仿真结果表明,机械臂能够稳定地从任意初始位置运动到任意给定的位置,从而证明了控制器设计的有效性.     

Forward displacement analysis and uncertainty configurations of parallel manipulators with a redundant branch

The effect of adding a redundant branch in terms of reduction of the number of assembly modes and elimination of potential uncertainty configuration types is investigated for a class of parallel manipulators. Considered is a broad class that includes all three-branch manipulators where each branch is comprised of a serial arrangement of three main-arm joints supporting a common payload platform through a passive spherical branch end joint-group. The addition of a redundant branch effectively yields a four-branch manipulator class. Considered in particular is a 3–4 form of the manipulator where two branch ends meet at one point on the mobile platform. Symmetric main-arm joint sensing and actuation (two sensed/acutated main-arm joints per branch) is utilized. Synthetic geometry is used to study the number of assembly configurations of the resulting 3–4 four-branch parallel manipulators. It is presented that the number of assembly modes of three-branch parallel manipulators with passive spherical branch end joints can be reduced by utilizing a redundant branch. It is shown that there exist up to eight and up to four assembly modes when all unsensed joints are revolute and when all unsensed joints are prismatic, respectively. Combinations of unsensed prismatic and revolute joints are also investigated. It is determined that there are up to eight and up to four assembly modes when the unsensed main-arm joint of one of the concurrent branches is prismatic and when the unsensed joints of both concurrent branches are prismatic joints, respectively. Resolving the potential assembly modes require only the consideration of, at highest, second-order single-variable polynomials. In addition, kinematic design considerations allowing reduction of feasible assembly modes are discussed. The investigation of potential uncertainty configuration types is based on examining degeneracies of the screw systems formed by wrenches associated with the forces that the actuated-joints can apply. All linear dependency cases that could potentially cause uncertainties for the class of four-branch manipulators are identified. It is shown that while significantly reducing potential uncertainty configuration types, the addition of a redundant branch number cannot eliminate all potential dependency (uncertainty) cases completely. For the remaining potential uncertainty configuration types, the characteristics of the corresponding unconstrained instantaneous degrees of freedom are discussed. © 1996 John Wiley & Sons, Inc.     

An Adaptive Regulator of Robotic Manipulators in the Task Space

This note addresses the problem of position control of robotic manipulators both nonredundant and redundant in the task space. A computationally simple class of task space regulators consisting of a transpose adaptive Jacobian controller plus an adaptive term estimating generalized gravity forces is proposed. The Lyapunov stability theory is used to derive the control scheme. The conditions on controller gains ensuring asymptotic stability are obtained herein in a form of simple inequalities including some information extracted from both robot kinematic and dynamic equations. The performance of the proposed control strategy is illustrated through computer simulations for a direct-drive arm of a SCARA type redundant manipulator with the three revolute kinematic pairs operating in a two-dimensional task space.     

Adaptive explicit force control of position-controlled manipulators

This article presents a new adaptive outer-loop approach for explicit force regulation of position-controlled robot manipulators. The strategy is computationally simple and does not require knowledge of the manipulator dynamic model, the inner-loop position controller parameters, or the environment. It is shown that the control strategy guarantees global uniform boundedness of all signals and convergence of the position/force regulation errors to zero when applied to the full nonlinear robot dynamic model. If bounded external disturbances are present, a slight modification to the control scheme ensures that global uniform boundedness of all signals is retained and that arbitrarily accurate stabilization of the regulation errors can be achieved. Additionally, it is shown that the adaptive controller is also applicable to robotic systems with PID inner-loop position controllers. Computer simulation results are given for a Robotics Research Corporation (RRC) Model K-1207 redundant arm and demonstrate that accurate and robust force control is achievable with the proposed controller. Experimental results are presented for the RRC Model K-1207 robot and confirm that the control scheme provides a simple and effective means of obtaining high-performance force control. © 1996 John Wiley & Sons, Inc.     

Nonlinear Control of a Robot Manipulator with a Nonholonomic Jerk Constraint

We study the control of a prismatic‐prismatic‐revolute (PPR) robot manipulator subject to a nonholonomic jerk constraint, i.e., a third‐order nonintegrable design constraint. The mathematical model is obtained using the method of Lagrange multipliers. The control inputs are two forces and a torque applied to the prismatic joints and the revolute joint, respectively. The control objective is to control the robot end‐effector movement while keeping the transverse jerk component as zero. The main result of the paper is the construction of a feedback control algorithm that transfers the manipulator from any initial equilibrium configuration to the zero equilibrium configuration in finite time. The effectiveness of the algorithm is illustrated through a simulation example.