On controlling robots with redundancy

Recently there has been considerable interest in increasing the applicability and utility of robots by developing manipulators which possess kinematic and/or actuator redundancy. This paper presents a unified approach to controlling these redundant robots. The proposed control system consists of two subsystems: an adaptive position controller which generates the Cartesian-space control force FR^m required to track the desired end-effector position trajectory, and an algorithm that maps this control input to a robot joint torque vector TRⁿ. The F → T map is constructed so that the robot redundancy (kinematic and/or actuator) is utilized to improve the performance of the robot. The control scheme does not require knowledge of the complex robot dynamic model or parameter values for the robot or the payload. As a result, the controller is very general and is computationally efficient for on-line implementation. Computer simulation results are given for a kinematically redundant robot, for a robot with actuator redundancy, and for a robot which possesses both kinematic and actuator redundancy. In each case the results demonstrate that accurate end-effector trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed scheme.     

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.     

Criteria optimization using self-motion of a 9-R redundant robot

Using inverse kinematic solutions for self-motion of a class of 9-R redundant robots, a conjugate-gradient based constrained optimization scheme for incremental trajectory planning is formulated. The proposed scheme has been evaluated and proved to be an efficient optimization method for redundancy utilization. It can also be used for studying 7-R and 8-R manipulators by simply restricting to one-variable and two-variable optimization, respectively. In contrast with other approaches which are based on the Jacobian, our scheme exploits the availability of closed-form inverse kinematic solutions to give more effective and accurate results.     

Null torque-based dynamic control for kinematically redundant manipulators

For the dynamic control of kinematically redundant manipulators, conventional approaches to local torque minimization have induced physically unachievable joint torques that may exceed the torque limits in the tracing motion of a long end-effector trajectory. This article presents a new control method for redundant manipulators, named the “Null Torque-Based Dynamic Control” (NTDC), which can guarantee stability for joint torques. The proposed method resolves the redundancy at the torque level. The command torque induced by the proposed method is composed of two terms: (1) the minimum-norm torque, which locally minimizes torque loadings at the joints; and (2) the null torque, which is intermittently added to the minimum-norm torque according to a kinematic criterion to globally reduce excessively large torque requirements. In particular, the concept of null torque is based on the property of full row-rank minors for a Jacobian matrix—the aspect that is a function of a manipulator's configuration. The simulation results illustrate that the proposed method is effective for torque optimization when compared with conventional methods.     

The reachability and dexterity of elbow and dual-elbow robot manipulators

The objective of this article is to highlight the reachability and dexterity of dual-elbow manipulators and provide a comparative evaluation of their capabilities. By necessity, dual-elbow robots are compared to elbow manipulators, the de facto standard of industrial applications. Although it is well established that the ideal elbow and dual elbow geometries are comparable in terms of workspace optimization, it is shown that the corresponding realistic geometries exhibit distinct properties. Realistic dual-elbow and elbow manipulators are investigated and the effects of manufacturing distortions on the flexibility and workspace utilization of the two geometries are quantified and contrasted. Realistic dual-elbow geometries are shown to provide, in general, better reachability and dexterity, especially for manipulators with a large structural frame, and to be less sensitive to parallelism errors. © 1992 John Wiley & Sons, Inc.     

A framework for large‐force task planning of mobile and redundant manipulators

A framework tackling the problem of large wrench application using robotic systems with limited force or torque actuators is presented. It is shown that such systems can apply a wrench to a limited set of Cartesian locations called force workspace (FW), and its force capabilities are improved by employing base mobility and redundancy. An efficient numerical algorithm based on 2ⁿ‐tree decomposition of Cartesian space is designed to generate FW. Based on the FW generation algorithm, a planning method is presented resulting in proper base positioning relative to large‐force quasistatic tasks. Additionally, the case of tasks requiring application of a wrench along a given path is considered. Task workspace, the set of Cartesian space locations that are feasible starting positions for such tasks, is shown to be a subset of FW. This workspace is used for identifying proper base or task positions guaranteeing task execution along desired paths. Finally, to plan redundant manipulator postures during large‐force‐tasks, a new method based on a min–max optimization scheme is developed. Unlike norm‐based methods, this method guarantees no actuator capabilities are exceeded, and force or torque of the most loaded joint is minimized. Illustrative examples are given demonstrating validity and usefulness of the proposed framework. ©1999 John Wiley & Sons, Inc.     

Force Transmissibility Performance of Parallel Manipulators

In this paper, a new force transmission index called the mean force transmission index (MFTI) is proposed, and the force transmissibility analysis procedure is established for parallel manipulators. The MFTI is an extended definition of the force transmission index (FTI) introduced by the authors previously. It is shown that the FTI is a function of the input velocity ratio (IVR) for a multi‐DOF mechanism of the same configuration. To represent the force transmissibility by a definite value, the MFTI is defined as the mean value of the normalized FTIs function over the whole range of the IVR. The force transmissibility analysis of two planar parallel manipulators is illustrated using the MFTI method. The result is compared with that of the Jacobian matrix method and the joint force index (JFI) method. It shows that, especially for symmetric parallel manipulators, an approximate inverse‐proportionality relationship exists between the JFI and MFTI, and between the maximum input torque/force and MFTI. It is concluded that the MFTI can be used as a quantitative measure of the force transmissibility performance for parallel manipulators. In the end, a design optimization problem is studied by taking the global force transmission index as the objective function. © 2003 Wiley Periodicals, Inc.     

基于简单模糊逻辑的冗余度机器人动力学路径规划新方法

论文提出了基于模糊逻辑的冗余度机器人避障算法,算法中利用模糊规则自动调整避障控制参数,使机器人在最短的时间内做出快速回避反应,提高了系统的智能性;另一方面,算法中利用动力学控制代替了位置控制,减少了避障过程中,由于速度突变引起的关节冲击力,提高了系统使用寿命。最后通过一平面三连杆三自由度机器人进行仿真研究,结果证实了该算法的有效性。     

Adaptive compliant motion control of manipulators without velocity measurements

This article presents two adaptive schemes for compliant motion control of uncertain manipulators. The first strategy is developed using an adaptive impedance control approach and is appropriate for tasks in which the dynamic character of the end-effector/environment interaction must be controlled, while the second scheme is an adaptive position/force controller and is useful for those applications which require independent control of end-effector position and contact force. The proposed controllers are very general and computationally efficient, require virtually no information regarding the manipulator dynamic model or the environment, and are implementable without velocity measurements. It is shown that the schemes ensure semiglobal boundedness of all signals in the presence of bounded disturbances, and that the ultimate size of the system errors can be made arbitrarily small. The capabilities of the proposed control strategies are illustrated through both computer simulations and laboratory experiments with a 6 degree-of-freedom (DOF) IMI Zebra Zero manipulator. ©1997 John Wiley & Sons, Inc.     

Time-optimal control of kinematically redundant manipulators with limit heat characteristics of actuators

In this study, we present a time-optimal control scheme for kinematically redundant manipulators to track a predefined geometric path, subject to the limit heat characteristics of actuators (a DC motor was assumed to be the actuator used). Constraints due to the rated torque and the rated velocity of the motor would not be valid for continuous use of manipulators, since the required mechanical output of the actuator (DC motor) exceeds its maximum power capacity and far more exceeds its heat-converted power limit. The heat-converted power limit of the DC motor is thus considered as the actuation bound of the actuator and the time-optimal trajectories are generated by using the phase-plane analysis and the linear programming technique subject to this bound. Computer simulation was also executed on a three-link planar rotary manipulator to demonstrate the effectiveness of the proposed scheme.     

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.     

Method for kinematic calibration of stewart platforms

A Stewart platform is a six degrees of freedom parallel manipulator composed of six variable-length legs connecting a fixed base to a movable plate. Like all parallel manipulators, Stewart platforms offer high force/torque capability and high structural rigidity in exchange for small workspace and reduced dexterity. Because the solution for parallel manipulators' forward kinematics is in general much harder than their inverse kinematics, a typical control strategy for such manipulators is to specify the plate's pose in world coordinates and then solve the individual leg lengths. The accuracy of the robot critically depends on accurate knowledge of the device's kinematic parameters. This article focuses on the accuracy improvement of Stewart platforms by means of calibration. Calibration of Stewart platforms consists of construction of a kinematic model, measurement of the position and orientation of the platform in a reference coordinate frame, identification of the kinematic parameters, and accuracy compensation. A measurement procedure proposed in this article allows a great simplification of the kinematic identification. The idea is to keep the length of the particular leg, whose parameters are to be identified, fixed while the other legs change their lengths during the measurement phase. By that, redundant parameters can be eliminated systematically in the identification phase. The method also shows the estimation of each leg's parameters separately because the measurement equations are fully decoupled, which results in a drastical reduction of the computational effort in the parameter identification. Simulation results assess the performance of the proposed approach. © 1993 John Wiley & Sons, Inc.     

Design and analysis of kinematically redundant parallel manipulators with configurable platforms

Redundancy can, in general, improve the ability and performance of parallel manipulators by implementing the redundant degrees of freedom to optimize a secondary objective function. Almost all published researches in the area of parallel manipulators redundancy were focused on the design and analysis of redundant parallel manipulators with rigid (nonconfigurable) platforms and on grasping hands to be attached to the platforms. Conventional grippers usually are not appropriate to grasp irregular or large objects. Very few studies focused on the idea of using a configurable platform as a grasping device. This paper highlights the idea of using configurable platforms in both planar and spatial redundant parallel manipulators, and generalizes their analysis. The configurable platform is actually a closed kinematic chain of mobility equal to the degree of redundancy of the manipulator. The additional redundant degrees of freedom are used in reconfiguring the shape of the platform itself. Several designs of kinematically redundant planar and spatial parallel manipulators with configurable platform are presented. Such designs can be used as a grasping device especially for irregular or large objects or even as a micro-positioning device after grasping the object. Screw algebra is used to develop a general framework that can be adapted to analyze the kinematics of any general-geometry planar or spatial kinematically redundant parallel manipulator with configurable platform.     

Motion planning for mobile manipulators with a non-holonomic constraint using the FSP (full space parameterization) method

The efficient utilization of the motion capabilities of mobile manipulators, i.e., manipulators mounted on mobile platforms, requires the resolution of the kinematically redundant system formed by the addition of the degrees of freedom (DOF) of the platform to those of the manipulator. At the velocity level, the linearized Jacobian equation for such a redundant system represents an underspecified system of algebraic equations, which can be subject to a varying set of contraints such as a non-holonomic constraint on the platform motion, obstacles in the workspace, and various limits on the joint motions. A method, which we named the Full Space Parameterization (FSP), has recently been developed to resolve such underspecified systems with constraints that may vary in time and in number during a single trajectory. In this article, we first review the principles of the FSP and give analytical solutions for constrained motion cases with a general optimization criterion for resolving the redundancy. We then focus on the solutions to (1) the problem introduced by the combined use of prismatic and revolute joints (a common occurrence in practical mobile manipulators), which makes the dimensions of the joint displacement vector components non-homogeneous, and (2) the treatment of a non-holonomic constraint on the platform motion. Sample implementations on several large-payload mobile manipulators with up to 11 DOF are discussed. Comparative trajectories involving combined motions of the platform and manipulator for problems with obstacle and joint limit constraints, and with non-holonomic contraints on the platform motions, are presented to illustrate the use and efficiency of the FSP approach in complex motion planning problems. © 1996 John Wiley & Sons, Inc.     

Integrated adaptive robust control for multilateral teleoperation systems under arbitrary time delays

With the increasing industrial requirements such as bigger size object, stable operation, and complex task, multilateral teleoperation systems extended from traditional bilateral teleoperation are widely developed. In this paper, the integrated control design is developed for multilateral teleoperation systems, where n master manipulators are operated by human to remotely control n slave manipulators cooperatively handling a target object. For the first time, the control objectives of multilateral teleoperation including stability, synchronization, transparency, and internal force distribution are clarified systematically. A novel communication architecture is proposed to cope with communication delays, where the estimated environmental parameters are transmitted from the slave side to the master, to replace the traditional environmental force measurement in the communication channel. A kind of nonlinear adaptive robust control technique is used to deal with nonlinearities, unknown parameters, and modeling uncertainties existing in the master, slave, and environmental dynamics, so that the excellent tracking performance is achieved in both master and slave sides. The coordinated motion/force control is designed in the slave side by the optimal internal force distribution among n slave manipulators, and the impedance control is designed in the master side to realize the target transparency behavior. In summary, the proposed control algorithm can achieve the guaranteed robust stability, the excellent synchronization and transparency performance, and the optimal internal force distribution simultaneously for multilateral teleoperation systems under arbitrary time delays and various modeling uncertainties. The simulation is carried out on a 2‐master/2‐slave teleoperation system, and the results show the effectiveness of the proposed control design. Copyright © 2015 John Wiley & Sons, Ltd.     

Remedy scheme and theoretical analysis of joint-angle drift phenomenon for redundant robot manipulators

A quadratic programming (QP)-based method, as a remedy for joint angle drifts, is employed for redundant robot manipulators with physical constraints (e.g., joint-angle limits and joint-velocity limits) considered. By using the QP-based redundancy-resolution scheme, real-time repetitive motion planning (RMP) can be achieved in a drift-free manner. Theoretical analyses based on gradient-descent and neural-dynamic methods are also conducted. Based on analyses, the efficacy of the presented QP-based RMP scheme for redundant manipulators is successfully explained. To demonstrate the effectiveness of the RMP scheme, different kinds of redundant robot manipulators, such as PA10, PUMA560, and a six-link planar robot arm, are tested in order to perform circular and straight line end-effector trajectories by using computer simulations. Both theoretical analysis and computer simulation results have demonstrated the efficacy of the QP-based RMP scheme.     

Obstacle Avoidance for Redundant Manipulators Using Directional-Collidability/ Temporal-Collidability Measure

We present an efficient obstacle avoidance control algorithm for redundant manipulators using new measures called directional-collidability measure and temporal-collidability measure. Considering relative movements of manipulator links and obstacles, the directional-collidability/temporal-collidability measure is defined as the sum of inverse of predicted collision distances/times between manipulator links and obstacles. These measures are suitable for obstacle avoidance control since relative velocities between manipulator links and obstacles are as important as distances between them. Also, we present a velocity-bounded kinematic control law which allows reasonably large gain to improve the system performance. Simulation results are presented to illustrate the effectiveness of the proposed algorithm.     

Direct adaptive impedance control of robot manipulators

This article presents an adaptive scheme for controlling the end-effector impedance of robot manipulators. The proposed control system consists of three subsystems: a simple “filter” that characterizes the desired dynamic relationship between the end-effector position error and the end-effector/environment contact force, an adaptive controller that produces the Cartesian-space control input required to provide this desired dynamic relationship, and an algorithm for mapping the Cartesian-space control input to a physically realizable joint-space control torque. The controller does not require knowledge of either the structure or the parameter values of the robot dynamics and is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme represents a general and computationally efficient approach to controlling the impedance of both nonredundant and redundant manipulators. Furthermore, the method can be applied directly to trajectory tracking in free-space motion by removing the impedance filter. Computer simulation results are given for a planar four degree-of-freedom redundant robot under adaptive impedance control. These results demonstrate that accurate end-effector impedance control and effective redundancy utilization can be achieved simultaneously by using the proposed controller.     

Optimization of Actuator Forces in Cable-Based Parallel Manipulators Using Convex Analysis

In cable-driven parallel manipulators (CPMs), cables can perform only under tension, and therefore, redundant actuation, which can be provided by redundant limbs, is needed to maintain the cable tensions. By optimizing the distribution of the forces in the cables and the redundant limbs, the average size of actuators can be reduced resulting in lower cost. Optimizing the force distribution in CPMs requires consideration for the inequality constraints imposed on the cable forces as a result of the unilateral driving property of the cables. In this study, a projection method is presented to calculate optimum solutions for the actuators force distribution in CPMs. Two solutions are presented: 1) a minimum-norm solution that minimizes the 2-norm of all forces in the cables and redundant limbs and 2) a solution that minimizes the 2-norm of the forces in the cables only. The optimization problem is formulated as a projection on an intersection of convex sets and the Dykstra's projection method is used to obtain the solutions. This method is successfully applied to a 3-DOF CPM.