Energy Based Indexes for Manipulator Dynamics Improvement

Several indexes for evaluation of nonlinear effects during the motion of rigid multi-body systems are proposed in this paper. All of them are based on the kinetic energy and arise from an analysis of equations of motion expressed in terms of inertial quasi-velocities (IQV). Such equations are first-order and have a diagonal mass matrix of the system. The IQV depend on configuration of the system and take into consideration also its geometrical and inertial parameters. The indexes enable to detect deformation of joint velocity as a consequence of manipulator motion, the kinetic energy resulting from dynamical couplings and the energy transferred by each link individually. Because calculation of these indexes allow to determine influence of couplings on behavior of the manipulator then they can be used in the design phase for analysis and reduction of nonlinear effects in any motion. Simulation and experimental results demonstrate that the proposed indexes are significant for evaluation of nonlinear effects and kinetic energy reduction during the manipulator motion.     

On the robust control of robot manipulators including actuator dynamics

A robust nonlinear control law that incorporates the manipulator dynamics as well as dynamics of actuators is developed in this article. The inertial parameters of the manipulator and the electrical parameters of the actuators are considered to be of uncertain values. In contrast to the known methods, the presented design procedure is based on less restrictive assumptions regarding the characteristics of uncertainties. We just assume that unknown parameters are bounded, which is evidently true for any robotic system. Exponential stability of the developed controller is proved by the Lyapunov method. © 1996 John Wiley & Sons, Inc.     

Compliance control safety: An architecture-independent analysis

Safe manipulator/task interaction is defined and quantified based on interaction forces resulting from manipulator motion commands. H¹ and H^*** safety bounds are introduced for evaluation of compliance control designs deriving from any control architecture or design method. Compliance control design examples are presented to demonstrate the use of these bounds, and to demonstrate the need to consider safety bounds of the type proposed. © 1994 John Wiley & Sons, Inc.     

带滑移铰空间机械臂的非完整运动规划遗传算法

本文讨论带滑移铰空间机械臂非完整运动规划的最优控制问题。利用系统的非完整特性,将带滑移铰空间机械臂运动规划转化为非线性系统最优控制问题。提出基于遗传算法的非完整运动规划最优控制方法。通过仿真计算,验证了该方法的有效性和可行性。     

Uncertainty compensation for a flexible-link manipulator using nonlinear H control

In a flexible-link manipulator, in general the effect of some parameters such as payload, friction amplitude and damping coefficients cannot be exactly measured. One possibility is to consider the above as parameters with uncertainty. In this paper, constant as well as L₂-bounded deviations of parameters from their nominal values are considered as uncertainties. These uncertainties make it difficult for a linear controller to achieve desired closed-loop performance. To remedy this problem, a nonlinear dynamical model of a flexible-link manipulator which has a constant input vector field (g in [xdot]=f(x) + g(x)u) is obtained. Based on recent results in nonlinear robust regulation with an H∞ constraint a nonlinear controller is designed for the flexible-link manipulator. The contribution of this paper is in demonstrating that the nonlinear controller has a larger domain of attraction than the linearized controller. In fact, for the single-link flexible manipulator considered in this paper, the linear H∞ controller results in instability for step changes in the desired output of greater than 3.6 rad, whereas the nonlinear H∞ controller yields desired step changes of 2π rad. Simulation results demonstrating the advantages and superiority of the nonlinear H∞ controller over the linear H∞controller are presented.     

PD Controller for Manipulator with Kinetic Energy Term

A kinetic energy approach to PD control in joint space of a manipulator in terms of the eigenfactor quasi-coordinate velocity (EQV) vector is considered in this paper. The modified PD controller which contains quantities resulting from decomposition of a manipulator mass matrix is proposed. The obtained equations of motion are based on the eigenvalues and eigenvectors of the mass matrix (Junkins, J. L. and Schaub, H. [7]. It is shown that utilizing the EQV vector one can determine directly the kinetic energy of the manipulator and at the same time realize PD control in its joint space. This energy-based strategy gives an interesting insight into position control. The controller presented here was tested in simulation on a 3 d.o.f. direct drive arm manipulator and via experiment on a 2 d.o.f. manipulator. The results confirmed that one can directly determine the kinetic energy for the total manipulator as well for its each joint. Additionally, time response of the system under EQV controller is faster than for the classical controller if mechanical coupling are strong.     

Nonlinear adaptive control of master–slave system in teleoperation

This paper is devoted to the nonlinear control design problem to achieve stability of master–slave manipulators in teleoperation system and its transparency in the sense of motion/force tracking. Nonlinear adaptive controllers are bilaterally designed for both master and slave sites to guarantee the stability of whole system and motion tracking performance. Global boundedness of the overall adaptive system and asymptotic motion (velocity/position) tracking are established. Especially, the concept of “virtual master manipulator” is introduced to increase degree of freedom of control design for force tracking performance. The resulting force tracking error depends only on the acceleration of the designed virtual master manipulator. Accurate dynamic parameters of manipulators, their acceleration information as well as models of human operator and environment are not required in the control design. Another important feature of our approach is the relaxation for the trade-off between motion and force tracking performances.     

Design and kinetostatic analysis of a new parallel manipulator

This paper proposes an innovative design for a parallel manipulator that can be applied to a machine tool. The proposed parallel manipulator has three degrees of freedom (DOFs), including the rotations of a moving platform about the x and y axes and a translation of this platform along the z-axis. A passive link is introduced into this new parallel manipulator in order to increase the stiffness of the system and eliminate any unexpected motion. Both direct and inverse kinematic problems are investigated, and a dynamic model using a Newton–Euler approach is implemented. The global system stiffness of the proposed parallel manipulator, which considers the compliance of links and joints, is formulated and the kinetostatic analysis is conducted. Finally, a case study is presented to demonstrate the applications of the kinematic and dynamic models and to verify the concept of the new design.     

A Frequency-Dependent Direct Adaptive Scheme for Robot Manipulators: A Case of Model-Following Motion Control

This paper presents a new frequency-dependent direct adaptive scheme for the optimal and/or suboptimal tracking of the motion of a prescribed model. The idea is based on a closed-loop control scheme in which an _{2 H} optimal/suboptimal controller is applied in parallel with a direct adaptive technique to guide a robot manipulator to follow a certain prescribed trajectory. The H ₂ compensators have to be proper and positively bounded with respect to all dynamic frequencies. Robustness issues are addresses in the paper by lumping all the nonlinear dynamic terms such as the centrifugal and Coriolis effects as well as the mechanical and electrical friction forces of the robot arm, into a general unstructured uncertainty term.     

Hypersurfaces of special configurations of serial manipulators and related concepts. part I: Theory and development of the hypersurfaces of special configurations

This article is the first of three companion papers which introduce some novel concepts useful in the kinetmatic design, analysis, motion planning, control, and performance evaluation of serial manipulators. Here an efficient methodology is developed to classify the special configurations of an N DOF manipulator. This classification yields hyper-surfaces in the joint space on each of which the manipulator loses a certain number of its degrees of freedom. The efficiency of the methodology is based on a theorem proved in Appendix B and the utilization of the minimal reference frames. These frames are obtained and tabulated for all possible types of manipulators. Furthermore the adaptability of a manipulator to a common control algorithm is quantified via an index. The numerical values of these indices are listed for all types of manipulators.     

基于小波逼近的空间机械臂非完整运动最优规划的遗传算法

本文讨论了空间机械臂非完整运动规划问题．将空间机械臂非完整运动规划问题转化 为非线性系统最优控制问题．在控制算法中用小波函数逼近控制输入规律．提出了空间机械 臂非完整运动规划最优控制的遗传算法．数值仿真表明,小波逼近和遗传算法联合求解最优 控制问题是有效的．     

Global stability of trajectory tracking of robot underPD control

It is shown for the first time that, even if there exist nonlinear unknown dynamics, aPD feedback control without higher-order nonlinear compensation can guarantee global stability for the trajectory following problem of a robot manipulator. ThePD control under investigation is a position and velocity feedback control with a time-varying gain, and does not contain any higher-order nonlinearity. The proposed control is in general continuous and does not require any knowledge of robotic systems except size bounding function on nonlinear dynamics. Asymptotic stability of velocity tracking error and arbitrarily small position tracking error are guaranteed. Another novel and interesting result shown in this paper is that a measure on protection against saturation of actuators has been incorporated into consideration of control design and robustness analysis.This work is supported in part by U.S. National Science Foundation under grant MSS-9110034.     

Error recovery in the assembly of a Self-Organizing Manipulator by using active visual and force sensing

This paper deals with the assembly of aSelf-OrganizingManipulator (SOM) by using the method ofActive Sensing. We set a 6-axis force/torque sensor in the wrist of a manipulator and a CCD camera in the hand of another manipulator. By cooperation of hand and eye, human beings can do a variety of versatile work. The eyes guide the motion of the hand, while the hand moves to make the object easy to see. We try to construct a system working in the same way as a human being. We integrate a vision system, a manipulator, and a force/torque sensor into a hand-eye working system. The scene simplification is based on the controlled motion of camera and manipulator. A method of theAverage Visible Ratio (AVR) is proposed to evaluate the viewpoint of the movable camera. A strategy for planning the assembly is presented. The efficiency of the system is illustrated by experiments.     

New optimization method to solve motion planning of dynamic systems: application on mechanical manipulators

In this paper, a new method is proposed to solve a nonlinear optimal control problem and determine the Dynamic Load-Carrying Capacity (DLCC) of fixed and mobile manipulators in point-to-point motion. Solution methods for designing nonlinear optimal controller in closed loop form are usually based on indirect methods, but the proposed method is a combination of direct and indirect methods. The optimal control law with state feedback form, for nonlinear dynamic systems, is given by the solution to the nonlinear Hamilton–Jacobi–Bellman (HJB) equation. The Galerkin procedure and a nonlinear optimization algorithm are used to solve this equation numerically. Another innovation of this paper is optimal trajectory planning, which is done simultaneously with the controller design procedure. Finally, a new algorithm is developed to find DLCC of manipulators and the related optimal trajectory using proposed method. The validity of the method is demonstrated via simulation and experimental tests for a fixed manipulator and two-link wheeled mobile manipulator named Scout.     

Improving the absolute positioning accuracy of robot manipulators

The absolute positioning accuracy of robot manipulator can be increased substantially by updating the nominal link parameters in the control software. This paper presents a general method to estimate the link parameter errors for any serial link manipulator (i.e., n links, and any combination of revolute and prismatic joints). The parameters are estimated through a linear kinematic model which relates the link bias errors to the end-effector positioning error. Only end-effector measurements are required instead of individual link measurements to implement this method.     

Obstacle Modelling Oriented to Safe Motion Planning and Control for Planar Rigid Robot Manipulators

Trajectory planning and tracking are crucial tasks in any application using robot manipulators. These tasks become particularly challenging when obstacles are present in the manipulator workspace. In this paper a n-joint planar robot manipulator is considered and it is assumed that obstacles located in its workspace can be approximated in a conservative way with circles. The goal is to represent the obstacles in the robot configuration space. The representation allows to obtain an efficient and accurate trajectory planning and tracking. A simple but effective path planning strategy is proposed in the paper. Since path planning depends on tracking accuracy, in this paper an adequate tracking accuracy is guaranteed by means of a suitably designed Second Order Sliding Mode Controller (SOSMC). The proposed approach guarantees a collision-free motion of the manipulator in its workspace in spite of the presence of obstacles, as confirmed by experimental results.     

Stability and control aspects of flexible link robot manipulators during constrained motion tasks

The effect of robotic manipulator structural compliance on system stability and trajectory tracking performance and the compensation of this structural compliance has been the subject of a number of publications for the case of robotic manipulator noncontact task execution. The subject of this article is the examination of dynamics and stability issues of a robotic manipulator modeled with link structural flexibility during execution of a task that requires the robot tip to contact fixed rigid objects in the work environment. The dynamic behavior of a general n degree of freedom flexible link manipulator is investigated with a previously proposed nonlinear computed torque constrained motion control applied, computed based on the rigid link equations of motion. Through the use of techniques from the theory of singular perturbations, the analysis of the system stability is investigated by examining the stability of the “slow” and “fast” subsystem dynamics. The conditions under which the fast subsystem dynamics exhibit a stable response are examined. It is shown that if certain conditions are satisfied a control based on only the rigid link equations of motion will lead to asymptotic trajectory tracking of the desired generalized position and force trajectories during constrained motion. Experiments reported here have been carried out to investigate the performance of the nonlinear computed torque control law during constrained motion of the manipulator. While based only on the rigid link equations of motion, experimental results confirm that high-frequency structural link modes, exhibited in the response of the robot, are asymptotically stable and do not destabilize the slow subsystem dynamics, leading to asymptotic trajectory tracking of the overall system. © 1992 John Wiley & Sons, Inc.     

Nonlinear control with end-point acceleration feedback for a two-link flexible manipulator: Experimental results

Experimental results for end-point positioning of multi-link flexible manipulators through end-point acceleration feedback are presented in this article. The advocated controllers are implemented on a two-link flexible arm developed at the Control/Robotics Research Laboratory at Polytechnic University. The advocated approach in this article is based on a two-stage control design. The first stage is a nonlinear (1) feedback linearizing controller corresponding to the rigid body motion of the manipulator. Because this scheme does not utilize any feedback from the end-point motion, significant vibrations are induced at the end effector. To this effect, and to enhance the robustness of the closed-loop dynamics to parameter variations, the inner loop is augmented with an outer loop based on a linear output LQR design that utilizes an end-point acceleration feedback. The forearm of the manipulator is significantly more flexible as compared with the upper arm. Experimental and simulation results validate the fact that the end-effector performance is significantly better with the proposed (1) feedback linearizing control as compared with the linear independent joint PD control. In addition, the nonlinear control offers other advantages in terms of smaller and smoother actuator torques and reducing the effects of nonlinearities. Close conformation between simulation and experimental results validates the accuracy of the model.     

Efficient manipulator collision avoidance by dynamic programming

This paper describes a research effort in the area of collision avoidance path planning for robotic manipulators. A robotic arm with known geometry is to perform a spatial manipulation in the presence of known obstacles in its workspace. The task is to generate a series of waypoints for its path to pass through which will guarantee a safe, collision-free trajectory from its predefined starting point to its predefined goal position.This is an important topic in the area of automated manufacturing. Automated factories are becoming increasingly important for the goals of greater manufacturing efficiency, better equipment utilization, and lower overall manufacturing costs. Robotic devices, including manipulator arms and assembly devices, are finding more uses in these factories.The approach is to discretize the robot's workspace into a transition network. The optimal path through this network, in terms of angular displacement of the manipulator's joints, is generated by dynamic programming. While this approach has been used previously, this paper adds the innovation of variable-node spacing, with the node density in various parts of the network reflecting the need for precise position control in each local area of the workspace. In this way, precise motion control is possible without an undue computational burden.