Inverse Velocity and Singularity Analysis of Low‐DOF Serial Manipulators

This paper presents a method for exact inverse velocity analysis of low‐DOF (degrees of freedom n<6) serial manipulators. For a low‐DOF serial manipulator, the number of independently controllable variables in the Cartesian space is equal to the number of joint variables in the joint space, and the remaining 6?n variables are linearly dependent on these independent variables. This paper employs the theory of reciprocal screws to determine a mapping between the independent velocity components in the Cartesian space and the joint rates in the joint space. It is shown that singular conditions of a low‐DOF manipulator depend on choice of independent variables. A 5‐DOF and a 4‐DOF manipulator are analyzed, and a numerical example in which the end effector of a 4‐DOF manipulator is commanded to follow a straight line is used to demonstrate the methodology. © 2003 Wiley Periodicals, Inc.     

Robust trajectory planning for robotic manipulators under payload uncertainties

A number of trajectory planning algorithms are available for determining the joint torques, positions, and velocities required to move a manipulator along a given geometric path in minimum time. These schemes require knowledge of the robot's dynamics, which in turn depend upon the characteristics of the payload which the robot is carrying. In practice, the dynamic properties of the payload will not be known exactly, so that the dynamics of the robot, and hence the required joint torques, must be calculated for a nominal set of payload characteristics. But since these trajectory planners generate nominal joint torques which are at the limits of the robot's capabilities, moving the robot along the desired geometric path at speeds calculated for the nominal payload may require torques which exceed the robot's capabilities. In this paper, bounds on joint torque uncertainties are derived in terms of payload uncertainties. Using these bounds, a new trajectory planner is developed to incorporate payload uncertainties such that all the trajectories generated can be realized with given joint torques. Finally, the trajectory planner is applied to the first three joints of the Bendix PACS arm, a cylindrical robot to demonstrate its use and power.     

ACHIEVING MINIMUM PHASE TRANSFER FUNCTION FOR A NONCOLLOCATED SINGLE‐LINK FLEXIBLE MANIPULATOR

A noncollocated system has the potential of providing more precise tracking, improved disturbance rejection and increased bandwidth at the sensor location, but is considerably more difficult to stabilize than a collocated system due to its nonminimum phase nature. For a flexible manipulator, the problem becomes even more complicated because the system is inherently infinite dimensional. In this paper, a single‐link flexible manipulator having a tip payload and a noncollocated actuator and sensor is investigated using a linear distributed parameter model. With the joint torque as the input and the joint angle plus a weighted value of tip deflection as the measured output, an exact transfer function involving transcendental functions is derived. Using the methods of infinite product expansion, the root locus, and the asymptotic property of the roots of the transcendental equation, a necessary and sufficient condition in terms of the weighting factor of tip deflection is obtained such that the transfer function does not have any open right‐half plane zeros. This condition depends neither on the physical properties of the link nor on the mass properties of the tip payload. In order to correct the misinterpretation which has occurred in some closely‐related works concerning the stability of the infinite‐dimensional zero‐dynamics, the equivalence of the zeros of the transfer function and the eigenvalues of zero‐dynamics is also verified. Numerical results for the closed‐loop performance of a single‐link flexible arm using collocated and noncollocated PD controllers are given to show the efficacy of the proposed minimum phase transfer function approach.     

工业机器人在特殊位形下的瞬时运动

本文具体分析了工业机器人在特殊位形下的瞬时运动，以ＳＴＡＮＦＯＲＤ机器人为例，分析其在特殊位形下约束运动的性质及允许移动的方向和转动时轴线存在的子空间，得出反螺旋的螺距为零时，处地特殊位形的６种组合形成，并给出了每种特殊位形在参考价值 标的反螺旋及存在的运动螺旋的一般表达式和相应的运动图谱。     

Kinematic and dynamic models of hybrid robot manipulator for propeller grinding

In this article, we develop a hybrid robot manipulator for propeller grinding and derive its kinematic and dynamic models. The manipulator is constructed by combining a parallel mechanism and a serial one to increase high stiffness as well as workspace. Based on geometric constraints, inverse–direct kinematics and Jacobian are derived to be implemented in real time control. The velocity control is used to measure the surface of a propeller blade and the position control is conducted to grind the removal depth. The dynamic model, which is developed by a motor algebra, can compute the forces and moments acting at a passive joint and an active one. ©1999 John Wiley & Sons, Inc.     

Adaptive neural control for an uncertain robotic manipulator with joint space constraints

In this paper, adaptive neural tracking control is proposed for a robotic manipulator with uncertainties in both manipulator dynamics and joint actuator dynamics. The manipulator joints are subject to inequality constraints, i.e., the joint angles are required to remain in some compact sets. Integral barrier Lyapunov functionals (iBLFs) are employed to address the joint space constraints directly without performing an additional mapping to the error space. Neural networks (NNs) are utilised to compensate for the unknown robot dynamics and external force. Adapting parameters are developed to estimate the unknown bounds on NN approximations. By the Lyapunov synthesis, the proposed control can guarantee the semi-global uniform ultimate boundedness of the closed-loop system, and the practical tracking of joint reference trajectory is achieved without the violation of predefined joint space constraints. Simulation results are given to validate the effectiveness of the proposed control scheme.     

Design Strategy of Serial Manipulators With Certified Constraint Satisfaction

This paper presents the design strategy of serial manipulators with constraint satisfaction. The algorithm provides certified solutions to the range of values of the manipulator design parameters that satisfy the given constraints for all points inside a desired workspace. Alternatively, it can also be used to obtain the achievable workspace of a particular manipulator topology within which a set of given constraints are satisfied. This strategy can therefore be applied to the general case of a serial manipulator design problem, robots of adjustable parameters, or even reconfigurable robot strategy to obtain a suitable topology. The interval-based algorithm was implemented on an example serial anthropomorphic manipulator with joint displacement constraints and obtains the possible variations to the manipulator topology that allow the required workspace to be achievable under the given joint displacement constraints. Results are presented and discussed.      

Adaptive control of flexible manipulators carrying large uncertain payloads

An adaptive controller is presented for a manipulator with revolute joints and structurally flexible links which carries a rigid payload with unknown mass properties. Under the assumption that the payload mass is much greater than that of the manipulator, globally stable tracking of the Cartesian end-effector coordinates is established. Key ideas underlying the controller development are the passivity of a mapping involving the end-effector rates as part of the output and a fixed parameter feedforward which preserves this property. The concept of filtered error is borrowed from previous work on rigid arms and suitably modified in developing the adaptive law. Although measurements of the tip positions and rates are needed, there is no requirement for sensing of the elastic coordinates. A numerical example involving a six DOF manipulator with flexible links demonstrates excellent tracking with respect to a simulation based on the exact motion equations. © 1996 John Wiley & Sons, Inc.     

Hybrid Control Scheme for Robust Tracking of Two-Link Flexible Manipulator

The hybrid control scheme is proposed to stabilize the vibration of a two-link flexible manipulator while the robustness of Variable Structure Control (VSC) developed for rigid manipulators is maintained for controlling the joint angles. The VSC law alone, which is designed to accomplish only the asymptotic decoupled joint angle trajectory tracking, does not guarantee the stability of the flexible mode dynamics of the links. In order to actively suppress the flexible link vibrations, hybrid trajectories for the VSC are generated using the virtual control force concept, so that robust tracking control of the flexible-link manipulator can also be accomplished. Simulation results confirm that the proposed hybrid control scheme can achieve more robust tracking control of two-link flexible manipulator than the conventional control scheme in the presence of payload uncertainty.     

Hybrid Control Scheme for Robust Tracking of Two-Link Flexible Manipulator

A hybrid control scheme is proposed to stabilize the vibration of a two-link flexible manipulator while robustness of Variable Structure Control (VSC) developed for rigid manipulators is maintained for controlling the joint angles. The VSC law alone, which is designed to accomplish only the asymptotic decoupled joint angle trajectory tracking, does not guarantee the stability of the flexible mode dynamics of the links. In order to actively suppress the flexible link vibrations, hybrid trajectories for the VSC are generated using the virtual control force concept, so that robust tracking control of the flexible-link manipulator can also be accomplished. Simulation results confirm that the proposed hybrid control scheme can achieve more robust tracking control of two-link flexible manipulator than the conventional control scheme in the presence of payload uncertainty.     

线驱动模块化七自由度机器人轨迹跟踪控制

阐述了一种线驱动与常规串联驱动相结合的混合设计方法．这种设计方法融合了线驱动并联机构和模块化串联机构的优点,而且混合驱动机器人的工作空间大于完全线驱动机器人的工作空间．文章首先介绍了混合驱动机器人的机构设计,也就是机器人的肩关节采用模块化串联结构,而肘、腕关节采用线驱动结构．然后利用几何分析的方法来解机器人前向运动学问题．在分析驱动线长与关节角之间变换关系的基础上,分别利用速度法和关节角增量法来计算机器人逆向运动学解．最后,使用VC++实现混合驱动机器人对直线运动轨迹进行跟踪的仿真,从而证明了文章所描述的设计方法的正确性．     

Towards nonadaptive and adaptive control of manipulation robots

Control synthesis for robotic systems with a variable payload is considered. First, we synthesize a robust, nonadaptive decentralized control using an approximative system model. Then, we analyze the stability of an exact system model. We thus check whether the robotic manipulator is stabilized for all allowable payload variations. If the simple decentralized control cannot accommodate all expected payload variations we introduce additional load, nonadaptive, feedback loop. This global control requires force transducers to be implemented in manipulator joints. If such nonadaptive control cannot stabilize robotic manipulator trajectories we suggest another adaptive control scheme. This control scheme includes an algorithm for on-line identification of variable payload and adaptation of local gains.     

On controller tuning for a flexible-link manipulator with varying payload

In this article experimental results are presented for system identification and control of a single-link flexible manipulator carrying an unknown, varying payload. The control objective is to maintain endpoint position accuracy in the presence of flexure effects after rapid movement due to a rigid body slew-angle commanded position. Various time-domain parameter estimation techniques are used to identify ARMA model representations to be employed in controller tuning schemes for vibration compensation. Only endpoint acceleration measurements and motor shaft angle measurements are utilized in relatively simple PID control schemes, which are tuned as dictated by a varying, unknown payload.     

Adaptive control of a 3-DOF parallel manipulator considering payload handling and relevant parameter models

Model-based control improves robot performance provided that the dynamics parameters are estimated accurately. However, some of the model parameters change with time, e.g. friction parameters and unknown payload. Particularly, off-line identification approaches omit the payload estimation (due to practical reasons). Adaptive control copes with some of these structural uncertainties. Thus, this work implements an adaptive control scheme for a 3-DOF parallel manipulator. The controller relies on a novel relevant-parameter dynamic model that permits to study the cases in where the uncertainties affect: (1) rigid body parameters, (2) friction parameters, (3) actuator dynamics, and (4) a combination of the former cases. The simulations and experiments verify the performance of the proposed controller. The control scheme is implemented on the modular programming environment Open Robot Control Software (OROCOS). Finally, an experimental setup evaluates the controller performance when the robot handles a payload.     

Sensor Fusion for Compliant Robot Motion Control

Force feedback is necessary for accurate force control in robotic manipulators, and thus far, wrist force/torque (F/T) sensors have been used. But an important problem arises when only these types of sensors are used. In a dynamic situation where the manipulator moves in either free or constrained space, the interaction forces and moments at the contact point and also the noncontact ones are measured by the mentioned sensor. In this paper, an estimator based on a sensor fusion strategy integrating the measurements of three different sensors (a wrist F/T sensor, an inertial sensor, and joint sensors) was developed to determine the contact force and torque exerted by the manipulator to its environment. The resulting observer helps to overcome some difficulties of uncertain world models and unknown environments since it reduces the high-frequency and low-frequency spectral contents, i.e., the low-frequency component due to inertia of a heavy tool mass and the high-frequency component due to impacts. The new improvement was experimentally validated in a force/position impedance control loop applied to a Staubli RX60 industrial robotic platform.     

Adaptive control based on explicit model of robot manipulator

Adaptive and nonadaptive control algorithms, which make use of a fundamental mathematical property concerning positive definite matrices and Lyapunov stability theory, are proposed for the control of robot manipulators. Using the fact that the matrix dD(q)/dt-2C(q, dq/ dt) is skew symmetric, nonadaptive controllers which have a simplified structure with less computational burden are proposed. Using the dynamic equations for robot manipulators, parameter adaptation rules are developed for updating the controller's partially or totally unknown parameters, generalizing them to model reference adaptive controllers. To further take advantage of the simplified structure of the proposed adaptive controllers, a method for deriving the dynamic model of a robot manipulator which is linear in terms of its parameters is given. This dynamic model is also suitable for the pure identification of the parameters of links and payload of the manipulator     

Gravity compensation of spatial two‐DOF serial manipulators

This article presents the analysis of gravity compensation of a two‐DOF serial manipulator operating in three‐dimensional space by means of linear spring suspension. The physical configuration of the serial manipulator is assumed general. The analysis begins with gravity compensation of a one‐DOF manipulator in order to form the basis which is then extended to a two‐DOF manipulator. The approach taken in the analysis is that of conservation of potential energy. The goal is to seek the location and the stiffness of springs that provide complete compensation of gravity in the manipulator system. It has been found that complete compensation of gravity in a two‐DOF serial manipulator system is possible. Unlike many previous works on spring suspension of a rigid body, which assume that one end of the suspending spring is attached to ground, it is proven in this study that, for complete compensation in a two‐DOF manipulator, the spring that suspends the distal link cannot be connected to ground. Instead, it must be in certain motion relative to the proximal link. The discussion on how to provide such a motion for the spring is given. It is also explained how the problem of gravity compensation of a robot manipulator can be shifted to that of changing gravity environment within a manipulator system. The concept can be applied to simulation and testing of robot manipulators that will be sent to operate in a different gravity environment, such as space. © 2002 Wiley Periodicals, Inc.     

Task-based configuration control of redundant manipulators

This article establishes new goals for redundancy resolution based on manipulator dynamics and end-effector characteristics. These goals can be accomplished by employing the recently developed configuration control approach. Redundancy resolution is achieved by controlling the joint inertia matrix or the end-effector mass matrix that affect the inertial torques or by reducing the joint torques due to gravity loading and payload. The manipulator mechanical advantage and velocity ratio are also used as performance measures to be improved by proper utilization of redundancy. Furthermore, end-effector compliance, sensitivity, and impulsive force at impact are introduced as redundancy-resolution criteria. The new goals for redundancy resolution presented in this article allow a more efficient utilization of the redundant joints based on the desired task requirements. Simple case studies using computer simulations are described for illustration.     

Cartesian path generation of robot manipulators using continuous genetic algorithms

In this paper, the authors describe a novel technique based on continuous genetic algorithms (CGAs) to solve the path generation problem for robot manipulators. We consider the following scenario: given the desired Cartesian path of the end-effector of the manipulator in a free-of-obstacles workspace, off-line smooth geometric paths in the joint space of the manipulator are obtained. The inverse kinematics problem is formulated as an optimization problem based on the concept of the minimization of the accumulative path deviation and is then solved using CGAs where smooth curves are used for representing the required geometric paths in the joint space through out the evolution process. In general, CGA uses smooth operators and avoids sharp jumps in the parameter values. This novel approach possesses several distinct advantages: first, it can be applied to any general serial manipulator with positional degrees of freedom that might not have any derived closed-form solution for its inverse kinematics. Second, to the authors’ knowledge, it is the first singularity-free path generation algorithm that can be applied at the path update rate of the manipulator. Third, extremely high accuracy can be achieved along the generated path almost similar to analytical solutions, if available. Fourth, the proposed approach can be adopted to any general serial manipulator including both nonredundant and redundant systems. Fifth, when applied on parallel computers, the real time implementation is possible due to the implicit parallel nature of genetic algorithms. The generality and efficiency of the proposed algorithm are demonstrated through simulations that include 2R and 3R planar manipulators, PUMA manipulator, and a general 6R serial manipulator.