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.     

Impact reduction for redundant manipulators using augmented impedance control

In this article, the problem of controlling redundant manipulators to reduce collision impact effects is considered, and an augmented kinematics and impedance control scheme is proposed for its solution. The proposed scheme achieves satisfactory performance by minimizing the magnitudes of impulsive forces as well as reducing rebound effects of the end-effector. In the proposed control scheme, kinematic redundancy is resolved using an augmented kinematics approach where the augmentation of the Jacobian matrix is based on an impact model derived using the Cartesian-space dynamic model of the manipulator. The proposed impact controller uses a simplified impedance control scheme aimed at reducing impulsive forces as well as rebound effects. The performance of the proposed controller is illustrated by computer simulations. © 2995 John Wiley & Sons, Inc.     

Robot manipulator control for hazardous waste-handling applications

The U.S. Department of Energy has identified robotics as a major technology to be utilized in its program of environmental restoration and waste management, and in particular has targeted robotic handling of hazardous waste to be an essential element in this program. Successful performance of waste-handling operations will require a robot to perform complex tasks involving both accurate positioning of its end effector and compliant contact between the end effector and the environment, and will demand that these tasks be completed in uncertain surroundings. This article focuses on the development of a robot control system capable of meeting the requirements of hazardous-waste-handling applications and presents as a solution an adaptive scheme for controlling the mechanical impedance of kinematically redundant manipulators. The proposed controller is capable of accurate end effector impedance control and effective redundancy utilization, does not require knowledge of the complex robot dynamic model or parameter values for the robot or the environment, and is implemented without calculation of the robot inverse kinematic transformation. Computer simulation results are given for a 4 degree of freedom redundant robot under adaptive impedance control. These results indicate that the proposed controller is capable of successfully performing tasks of importance in robotic waste-handling applications.     

A recurrent neural network for minimum infinity-norm kinematiccontrol of redundant manipulators with an improved problem formulationand reduced architecture complexity

This paper presents an improved neural computation where scheme for kinematic control of redundant manipulators based on infinity-norm joint velocity minimization. Compared with a previous neural network approach to minimum infinity-non kinematic control, the present approach is less complex in terms of cost of architecture. The recurrent neural network explicitly minimizes the maximum component of the joint velocity vector while tracking a desired end-effector trajectory. The end-effector velocity vector for a given task is fed into the neural network from its input and the minimum infinity-norm joint velocity vector is generated at its output instantaneously. Analytical results are given to substantiate the asymptotic stability of the recurrent neural network. The simulation results of a four-degree-of-freedom planar robot arm and a seven-degree-of-freedom industrial robot are presented to show the proposed neural network can effectively compute the minimum infinity-norm solution to redundant manipulators.     

Adaptive hybrid force-position control for redundant manipulators

An adaptive control scheme for manipulators with redundant degrees of freedom is presented. The control purpose is to achieve a desired interaction force between the end-effector and the environment as well as to regulate the robot tip position in the Cartesian space. This control approach does not require measurement of the joint acceleration or the force derivative     

A Neural Network Adaptive Controller for End-effector Tracking of Redundant Robot Manipulators

In this paper we propose a neural network adaptive controller to achieve end-effector tracking of redundant robot manipulators. The controller is designed in Cartesian space to overcome the problem of motion planning which is closely related to the inverse kinematics problem. The unknown model of the system is approximated by a decomposed structure neural network. Each neural network approximates a separate element of the dynamical model. These approximations are used to derive an adaptive stable control law. The parameter adaptation algorithm is derived from the stability study of the closed loop system using Lyapunov approach with intrinsic properties of robot manipulators. Two control strategies are considered. First, the aim of the controller is to achieve good tracking of the end-effector regardless the robot configurations. Second, the controller is improved using augmented space strategy to ensure minimum displacements of the joint positions of the robot. Simulation examples are also presented to verify the effectiveness of the proposed approach.     

Data-Driven Human-Robot Interaction Without Velocity Measurement Using Off-Policy Reinforcement Learning

In this paper, we present a novel data-driven design method for the human-robot interaction (HRI) system, where a given task is achieved by cooperation between the human and the robot. The presented HRI controller design is a two-level control design approach consisting of a task-oriented performance optimization design and a plant-oriented impedance controller design. The task-oriented design minimizes the human effort and guarantees the perfect task tracking in the outer-loop, while the plant-oriented achieves the desired impedance from the human to the robot manipulator end-effector in the inner-loop. Data-driven reinforcement learning techniques are used for performance optimization in the outer-loop to assign the optimal impedance parameters. In the inner-loop, a velocity-free filter is designed to avoid the requirement of end-effector velocity measurement. On this basis, an adaptive controller is designed to achieve the desired impedance of the robot manipulator in the task space. The simulation and experiment of a robot manipulator are conducted to verify the efficacy of the presented HRI design framework.      

Velocity field control of a class of electrically-driven manipulators

This article addresses the control of robotic manipulators under the assumption that the desired motion in the operational space is encoded through a velocity field. In other words, a vectorial function assigns a velocity vector to each point in the robot workspace. Thus, the control objective is to design a control input such that the actual operational space velocity of the robot end-effector asymptotically tracks the desired velocity from the velocity field. This control formulation is known in the literature as velocity field control. A new velocity field controller together with a rigorous stability analysis is introduced in this article. The controller is developed for a class of electrically-driven manipulators. In this class of manipulators, the passivity property from the servo-amplifier voltage input to the joint velocity is not satisfied. However, global exponential stability of the state space origin of the closed-loop system is proven. Furthermore, the closed-loop system is proven to be and output strictly passive map from an auxiliary input to a filtered error signal. To confirm the theoretical conclusions, a detailed experimental study in a two degrees-of-freedom direct-drive manipulator is provided. Particularly, experiments consist of comparing the performance of a simple PI controller and a high-gain PI controller with respect to the new control scheme.     

Adaptive control of free-floating space robots in Cartesian coordinates

An adaptive control scheme is proposed for the end-effector trajectory tracking control of free-floating space robots. In order to cope with the nonlinear parameterization problem of the dynamic model of the free-floating space robot system, the system is modeled as an extended robot which is composed of a pseudo-arm representing the base motions and a real robot arm. An on-line estimation of the unknown parameters along with a computed-torque controller is used to track the desired trajectory. The proposed control scheme does not require measurement of the accelerations of the base and the real robot arm. A two-link planar space robot system is simulated to illustrate the validity and effectiveness of the proposed control scheme.     

Multi-point impedance control for redundant manipulators

This paper proposes an impedance control method called the multi-point impedance control (MPIC) for redundant manipulators. The method can not only control end-effector impedance, but also regulate impedances of several points on the links of the manipulator, which are called virtual end-point impedances, utilizing arm redundancy. Two approaches for realizing the MPIC are presented. In the first approach, controlling the end-effector impedance and the virtual end-point impedances are considered as the tasks with the same level, and the joint control law developed in this approach can realize the closest impedances of the multiple points, including the end-effector and the virtual end-points to the desired ones in the least squared sense. On the other hand, in the second approach, controlling the end-effector impedance is considered the most important task, and regulating the impedances of the virtual end-points is considered as a sub-task. Under the second approach, the desired end-effector impedance can be always realized since the joint control torque for the regulation of the virtual end-point impedances is designed in such a way that it has no effect on the end-effector motion of the manipulator. Simulation experiments are performed to confirm the validity and to show the advantages of the proposed method.     

Hierarchical control of end-point impedance and joint impedance forredundant manipulators

This paper proposes an impedance control method for redundant manipulators, which can control not only the end-point impedance using one of the conventional impedance control methods, but the joint impedance which has no effects on the end-point impedance. First, a sufficient condition for the joint impedance controller is derived. Then, the optimal controller for a given desired joint impedance is designed using the least squares method. Finally, computer simulations and experiments using a planar direct-drive robot are performed in order to confirm the validity of the proposed method     

Adaptive Task-Space Control of Flexible-Joint Manipulators

This paper considers the motion control and compliance control problemsfor uncertain rigid-link, flexible-joint manipulators, and presents newadaptive task-space controllers as solutions to these problems. The motioncontrol strategy is simple and computationally efficient, requires littleinformation concerning either the manipulator or actuator/transmissionmodels, and ensures uniform boundedness of all signals and arbitrarilyaccurate task-space trajectory tracking. The proposed compliant motioncontrollers include an adaptive impedance control scheme, which isappropriate for tasks in which the dynamic character of theend-effector/environment interaction must be controlled, and an adaptiveposition/force controller, which is useful for those applications thatrequire independent control of end-effector position and contact force. Thecompliance control strategies retain the simplicity and model independenceof the trajectory tracking scheme upon which they are based, and are shownto ensure uniform boundedness of all signals and arbitrarily accuraterealization of the given compliance control objectives. The capabilities ofthe proposed control strategies are illustrated through computer simulationswith a robot manipulator possessing very flexible joints.     

Extended impedance control of redundant manipulators based on weighted decomposition of joint space

In this work, impedance control approach based on an extended task space formulation is addressed to control the kinematically redundant manipulators. By defining a weighted inner product in joint space, a minimal parameterization of the null space is achieved, and we can visualize the null space motion explicitly. Moreover, it is shown that careful choice of the weighting matrix gives physically consistent and inertially decoupled dynamics. By augmenting this minimal null motion parameter with a forward kinematic relation, a new extended task space formulation can be obtained. Based on this formulation, we propose two control methods, a kinematically decomposed impedance controller and an inertially decoupled impedance controller, to control the motion of the end-effector as well as the internal motion expanding the conventional impedance control. We also show the relationship with the previous dynamic controllers of a redundant manipulator. Some numerical simulations are given to demonstrate the performance of the proposed control methods. © 1998 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 position/force control of robot manipulators withoutvelocity measurements: theory and experimentation

In this paper, we design an adaptive position/force controller for robot manipulators during constrained motion. The proposed controller can compensate for parametric uncertainty while only requiring measurements of link position and end-effector force. A filtering technique is utilized to produce a pseudo-velocity error signal and thus, eliminate the need for link velocity measurements. The control strategy provides semiglobal asymptotic tracking performance for the end-effector position and the interaction force between the constraint and the end-effector. An experimental implementation of the proposed controller on a two-link planar robot is also presented.     

Model reference adaptive impedance control in Cartesian coordinates for physical human–robot interaction

In this paper, a nonlinear model reference adaptive impedance controller is proposed and tested. The controller provides asymptotic tracking of a reference impedance model for the robot end-effector in Cartesian coordinates applicable to rehabilitation robotics or any other human–robot interactions such as haptic systems. The controller uses the parameters of a desired stable reference model which is the target impedance for the robot’s end-effector. It also considers uncertainties in the model parameters of the robot. The asymptotic tracking is proven using Lyapunov stability theorem. Moreover, the adaptation law is proposed in joint space for reducing the complexity of its calculations; however, the controller and the stability proof are all presented in Cartesian coordinates. Using simulations and experiments on a two DOFs robot, the effectiveness of the proposed controller is investigated.     

一种基于操作空间的操作器分散自适应控制方法

本文提出了一种操作器分散自适应阻力控制方法．这种方法不要求知道操作器动态模型的结构和参数，采用分散控制的形式，可以对各自由度单独进行控制，因此计算简单有效，具有一定的容错能力，控制系统有较好的暂态性能，由于控制律以操作空间坐标形式描述，适合于具有冗余自由度的操作器的控制．计算机仿真表明了该方法的良好的控制效果     

Adaptive control of redundant multiple robots in cooperative motion

A redundant robot has more degrees of freedom than what is needed to uniquely position the robot end-effector. In practical applications the extra degrees of freedom increase the orientation and reach of the robot. Also the load carrying capacity of a single robot can be increased by cooperative manipulation of the load by two or more robots. In this paper, we develop an adaptive control scheme for kinematically redundant multiple robots in cooperative motion.In a usual robotic task, only the end-effector position trajectory is specified. The joint position trajectory will therefore be unknown for a redundant multi-robot system and it must be selected from a self-motion manifold for a specified end-effector or load motion. In this paper, it is shown that the adaptive control of cooperative multiple redundant robots can be addressed as a reference velocity tracking problem in the joint space. A stable adaptive velocity control law is derived. This controller ensures the bounded estimation of the unknown dynamic parameters of the robots and the load, the exponential convergence to zero of the velocity tracking errors, and the boundedness of the internal forces. The individual robot joint motions are shown to be stable by decomposing the joint coordinates into two variables, one which is homeomorphic to the load coordinates, the other to the coordinates of the self-motion manifold. The dynamics on the self-motion manifold are directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected to optimize a certain type of objective functions, then stable dynamics on the self-motion manifold result. The overall stability of the joint positions is established from the stability of two cascaded dynamic systems involving the two decomposed coordinates.     

Force Control of Robotic Manipulators Using a Fuzzy Predictive Approach

This paper proposes a force control strategy for robotic manipulators considering a non-rigid environment described by a nonlinear model. This approach uses a fuzzy predictive algorithm to generate, in an optimal way, the reference or virtual position to the classical impedance controller in order to apply a desired force profile on the environment. The main advantage of this control strategy is the possibility of including a nonlinear model of the environment in the controller design in a straightforward way, improving the global force control performance, especially in non-rigid environments. Moreover, in order to reduce the oscillations on the optimized reference position a fuzzy scaling machine is included on the force control strategy. The performance of the force control scheme is illustrated for a two degree-of-freedom PUMA 560 robot, which end-effector is forced to move along a flat surface located on the vertical plane. The simulation results obtained with the fuzzy control scheme reveal significant improvement in the force tracking performance, when compared to the impedance control with force tracking in non-rigid environments.     

An Adaptive Controller Dominant-Type Hybrid Adaptive and Learning Controller for Trajectory Tracking of Robot Manipulators

This paper proposes a new hybrid adaptive and learning control method based on combining model-based adaptive control, repetitive learning control (RLC) and proportional–derivative control to consider the periodic trajectory tracking problem of robot manipulators. The aim of this study is to obtain a high-accuracy trajectory tracking controller by developing a simpler adaptive dominant-type hybrid controller by using only one vector for estimation of the unknown dynamical parameters in the control law. The RLC input is adopted using the original learning control law, adding a forgetting factor to achieve the convergence of the learning control input to zero. We will improve and prove that the adaptive dominant-type controller could be applied for tracking a periodic desired trajectory in which adaptive control input increases and becomes dominant of the control input, whereas the other control inputs decrease close to zero. The domination of the adaptive control input gives the advantage that the proposed controller could adjust the feed-forward control input immediately and it does not spend much time relearning the learning control input when the periodic desired trajectory is switched over from the first trajectory to another trajectory. We utilize the Lyapunovlike method to prove the stability of the proposed controller and computer simulation results to validate the effectiveness of the proposed controller in achieving the accurate tracking to the periodic desired trajectory.