Two-time scale control and observer design for trajectory tracking of two cooperating robot manipulators moving a flexible beam

In this paper, we present two-time scale control design for trajectory tracking of two cooperating planar rigid robots moving a flexible beam, which does not require vibration measurement for the beam. First, the kinematics and dynamics of the robots and the object are derived. Then, using the relations between different forces acting on the object by the manipulators’ end-effectors, dynamics equations of the robots and the object are combined. The resulting equations show that the coupled dynamics including beam vibration and the rigid motion take place in two different time domains. By applying two-time scale control theory on the combined dynamics, a composite control scheme is elaborated which makes the beam orientation and its center of mass position track a desired trajectory while suppressing the beam vibration. For the controller algorithm, first a slow controller is utilized for the slow (rigid) subsystem and then a fast stabilizing controller is considered for the fast (flexible) subsystem. To avoid requiring measurement of beam vibration for the fast control law, a linear observer is also designed. The simulation results show the efficiency of the proposed control scheme.     

Symmetry position/force hybrid control for cooperative object transportation using multiple humanoid robots

A symmetry position/force hybrid control framework for cooperative object transportation tasks with multiple humanoid robots is proposed in this paper. In a leader-follower type cooperation, follower robots plan their biped gaits based on the forces generated at their hands after a leader robot moves. Therefore, if the leader robot moves fast (rapidly pulls or pushes the carried object), some of the follower humanoid robots may lose their balance and fall down. The symmetry type cooperation discussed in this paper solves this problem because it enables all humanoid robots to move synchronously. The proposed framework is verified by dynamic simulations.     

Vibration suppression control of 3D flexible robots using velocity inputs

Research on vibration suppression control of flexible robots has concentrated mainly on the one-link and two-link planar manipulators. Most of the techniques that have been presented cannot be easily extended to the case of a general 3D flexible robot. In this article we present a general control scheme based on hardware velocity servo cards. The velocity commands to move the robot are calculated by adding a vibration suppression term to the joint position feedback employed in “rigid” robots. Two different methods are proposed to calculate this term, one based on optimum quadratic control and the other based on pseudo-inverse nonlinear decoupling. These techniques are studied numerically in the case of a real two-link three-joint flexible robot, by computing the values of the closed-loop poles at different configurations. Experiments on position stabilization of the robot prove the validity of our methods.© 1997 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.     

Dynamic two arm hybrid position/force control

A useful two arm robot system will not only need to cooperatively manipulate the same object, but also need the ability for external force control. As an example, assume two robots are building a space station, which requires them to connect a structure to a partially built space station. This implies that they need to cooperatively move the object to the desired position, and then apply a force to connect it. Therefore, two arm hybrid position/force control is necessary. To accomplish this task quickly and accurately the dynamics of arm 1, arm 2, and the object must be taken into account. The external and internal forces must be clearly defined to be used in the servo control loop. There are several ways to choose the internal force: zero internal force, arbitrary force distribution, minimizing object strain energy, and minimizing the total torque. An example is shown to illustrate the trade-offs. A controller is presented which incorporates the dynamics of each arm, the dynamics of the object, and servos on the internal and external force. Experimental results show that servoing on the internal force will reduce the force error significantly.     

A Proposed Hybrid Recurrent Neural Control System for Two Co-operating Robots

This paper discusses a model refernce adaptive (MRAC) position/force controller using proposed neural networks for two co-operating planar robots. The proposed neural network is a recurrent hybrid network. The recurrent networks have feedback connections and thus an inherent memory for dynamics, which makes them suitable for representing dynamic systems. A feature of the networks adopted is their hybrid hidden layer, which includes both linear and nonlinear neurons. On the other hand, the results of the case of a single robot under position control alone are presented for comparison. The results presented show the superior ability of the proposed neural network based model reference adaptive control scheme at adapting to changes in the dynamics parameters of robots.     

Hybrid control of a two-arm robot for complex tasks

For many coordinated tasks, a two-arm robot cannot be properly controlled by using a simple position control scheme and therefore requires a certain form hybrid control. Uchiyama and Dauchez recently proposed a symmetric hybrid position/force scheme for the manipulation of rigid objects rigidly held. The main results of this theory are summarized in this paper, and the limitations are pointed out. Several examples in which the relative motion of the end effectors cannot be neglected are presented: manipulation of rigid objects non-rigidly held, deformation of a flexible object, and assemblies of two objects “in space”. These tasks are analyzed and attempted control schemes are given for each of them. The dynamic effects are always neglected in this preliminary theoretical approach. An experimental setup built around two six axis PUMA arms and a parallel processing controller has been installed in order to validate our theoretical results. The hardware and software of this setup are also briefly described in this paper.     

Dynamics and Noncollocated Model‐Free Position Control for a Space Robot with Multi‐Link Flexible Manipulators

In this paper, both the dynamics and noncollocated model‐free position control (NMPC) for a space robot with multi‐link flexible manipulators are developed. Using assumed modes approach to describe the flexible deformation, the dynamic model of the flexible space robotic system is derived with Lagrangian method to represent the system dynamic behaviors. Based on Lyapunov's direct method, the robust model‐free position control with noncollocated feedback is designed for position regulation of the space robot and vibration suppression of the flexible manipulators. The closed‐loop stability of the space robotic system can be guaranteed and the guideline of choosing noncollocated feedback is analyzed. The proposed control is easily implementable for flexible space robot with both uncertain complicated dynamic model and unknown system parameters, and all the control signals can be measured by sensors directly or obtained by a backward difference algorithm. Numerical simulations on a two‐link flexible space robot are provided to demonstrate the effectiveness of the proposed control.     

Sliding mode force,motion control,and stabilization of elastic manipulator in the presence of uncertainties

This article considers the question of position and force control of three-link elastic robotic systems on a constraint surface in the presence of robot parameter and environmental constraint geometry uncertainties. The approach of this article is applicable to any multi-link elastic robot. A sliding mode control law is derived for the position and force trajectory control of manipulator. Unlike the rigid robots, sliding mode control of an end point gives rise to unstable zero dynamics. Instability of the zero dynamics is avoided by Controlling a point that lies in the neighborhood of the actual end point position. The sliding mode controller accomplishes tracking of the end-effector and force trajectories on the constrained surface; however, the maneuver of the arm causes elastic mode excitation. For point-to-point control on the constraint surface, a stabilizer is designed for the final capture of the terminal state and vibration suppression. Numerical results are presented to show that in the closed-loop system position and force control is accomplished in spite of payload and constraint surface geometry uncertainty. © 1995 John Wiley & Sons, Inc.     

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.     

Joint-space orthogonalization and passivity for physical interpretations of dextrous robot motions under geometric constraints

A principle of ‘joint-space orthogonalization’ is proposed as an extended notion of hybrid (force and position) control for robot manipulators under geometric constraints. The principle realizes the hybrid control in a strict sense by letting position feedback signals be orthogonal in joint space to the contact force vector whose components exert at corresponding joints. This orthogonalization is executed via a projection matrix computed in real-time from a Jacobian matrix of the constraint equation in joint coordinates. To show the important role of the principle in control of robot manipulators, two basic set-point control problems are analysed. One is a hybrid PID control problem for robot manipulators under geometric endpoint constraint and another is a coordinated control problem of two arms. It is shown that passivity properties of residual dynamics of robots follow from the introduction of a quasi-natural potential and the joint-space orthogonalization. Various stability problems of PID-type feedback control schemes without compensating for the gravity force and with or without use of a force sensor are discussed from passivity properties of robot dynamics with the aid of the hyper-stability theory.     

A review on vision-based control of flexible manipulators

In this review, recent developments in the field of flexible robot arm control using visual servoing are reviewed. In comparison to rigid robots, the end-effector position of flexible links cannot be obtained precisely enough with respect to position control using kinematic information and joint variables. To solve the task here the use of a vision sensor (camera) system, visual servoing is proposed to realize the task of control flexible manipulators with improved quality requirements. The paper is organized as follows: the visual servoing architectures will be reviewed for rigid robots first. The advantages, disadvantages, and comparisons between different approaches of visual servoing are carried out. The using of visual servoing to control flexible robot is addressed next. Open problems such as state variables estimation as well as the combination of different sensor properties as well as some application-oriented points related to flexible robot are discussed in detail.     

Motion/force control scheme for electrically driven cooperative multiple mobile manipulators

This paper presents the motion and force control problem of rigid-link electrically driven cooperative mobile manipulators handling a rigid object. Although, the motion/force control problem of cooperative mobile manipulators has been enthusiastically studied. But there is little research on the motion/force control of electrically driven cooperative mobile manipulators. Due to the inclusion of the actuator dynamics with the manipulator’s dynamics, the controller exhibits some important characteristics. For the electromechanical system, we have designed a novel controller at the dynamic level as well as at the actuator level. In the proposed control scheme, at the dynamic level, uncertain non-linear mechanical dynamics is approximated with a hybrid controller containing model-based control scheme combined with model-free neural network based control scheme together with an adaptive bound. The adaptive bound is used to suppress the effects of external disturbances, friction terms, and reconstruction error of the neural network. At the actuator level, for the approximation of the unknown electrical dynamics, the model-free neural network is utilized. The developed control scheme provides that the position tracking errors, as well as the internal force, converge to the desired levels. Additionally, direct current motors are also controlled in such a way that the desired currents and torques can be attained. In order to make the overall system to be asymptotically stable, online learning of the weights and the parameter adaptation of the parameters is utilized in the Lyapunov function. The superiority of the developed control method is carried out with the numerical simulation results and its superior robustness is shown in a comparative manner.     

Fuzzy tuning control approach to perform cooperative object manipulation by a rigid–flexible multibody robot

We study cooperative object manipulation control of rigid–flexible multibody systems in space. During such tasks, flexible members like solar panels may get vibrated. Which in turn may lead to some oscillatory disturbing forces on other subsystems and consequently produce errors in the motion of the end-effectors of the cooperative manipulating arms. Therefore, to design and develop capable model-based controllers for such complicated systems, deriving a dynamics model is required. However, due to practical limitations and real-time implementation, the system dynamics model should require low computations. So, first, to obtain a precise compact dynamics model, the rigid–flexible interactive dynamics modeling (RFIM) approach is briefly introduced. Using this approach, the system is virtually partitioned into two rigid and flexible portions, and a convenient model for control purposes is developed. Next, a fuzzy tuning manipulation control (FTMC) algorithm is developed for a simple conceptual model for cooperative object manipulation. In fact, a suitable setup is designed for practical implementation of this controller. After that, a wheeled mobile robot (WMR) system with flexible appendages is considered as a practical case that necessitates delicate force exertion by several end-effectors to move an object along a desired path. The WMR system contains two cooperative manipulators, appended with two flexible solar panels. To reveal the merits of the developed model-based controller, the maneuver is deliberately planned such that flexible modes of solar panels get stimulated due to arms motion. The obtained results show an effective performance of the proposed approach as will be discussed.     

Telemanipulation of cooperative robots: a case of study

This article addresses the problem of dexterous robotic grasping by means of a telemanipulation system composed of a single master and two slave robot manipulators. The slave robots are analysed as a cooperative system where it is assumed that the robots can push but not pull the object. In order to achieve a stable rigid grasp, a centralised adaptive position-force control algorithm for the slave robots is proposed. On the other hand, a linear velocity observer for the master robot is developed to avoid numerical differentiation. A set of experiments with different human operators were carried out to show the good performance and capabilities of the proposed control-observer algorithm. In addition, the dynamic model and closed-loop dynamics of the telemanipulation is presented.     

Robust Hybrid Control of Constrained Robot Manipulators via Decomposed Equations

Basing on a constraint Jacobian induced orthogonal decomposition of the task space and by requiring the force controller to be orthogonal to the constraint manifold, the dynamics of the constrained robots under hybrid control is decomposed into a set of two equations. One describes the motion of robots moving on the constraint manifold, while the other relates the constraint force with the hybrid controller. This decomposition does not require the solution of the constraint equation in partition form. In this setting, the hybrid control of constrained robots can be essentially reduced to robust stabilization of uncertain nonlinear systems whose uncertainties do not satisfy the matching condition. A continuous version of the sliding-mode controller (from Khalil [12]) is employed to design a position controller. The force controller is designed as a proportional force error feedback of high gain type. The coordination of the position controller and the force controller is shown to achieve ultimately bounded position and force tracking with tunable accuracy. Moreover, an estimate of the domain of attraction is provided for the motion on the constraint manifold. Simulation for a planar two-link robot constraining on an ellipse is given to show the effectiveness of a hybrid controller. In addition, the friction effect, viewed as external disturbance to the system, is also examined through simulations.     

Adaptive hybrid control of manipulators on uncertain flexible objects

This paper presents an adaptive hybrid control approach for a robot manipulator to interact with its flexible object. Because of its flexibility, the object dynamics influence the robot's control system, and since it is usually a distributed parameter system, the object dynamics as seen from the robot change when the robot moves. The problem becomes further complicated such that it is difficult to decompose the robot's position and contact force control loops. In this paper, we approximate the object's distributed parameter model into a lumped 'position state-varying' model. Then, by using the well-known nonlinear feedback compensation, we decompose the robot's control space into a position control subspace and object torque control subspace. We design the optimal state feedback for the position control loop and control the robot's contact force through controlling the resultant torque of the object. We use the model-reference simple adaptive control strategy to control the torque control loop. We also study the problem on how to select a reasonable reference model for this control loop. Experiments of a PUMA robot interacting with an aluminum beam show the effectiveness of our approach.     

A Telepresence-Guaranteed Control Scheme for Teleoperation Applications of Transferring Weight-Unknown Objects

Currently, most teleoperation work is focusing on scenarios where slave robots interact with unknown environments. However, in some fields such as medical robots or rescue robots, the other typical teleoperation application is precise object transportation. Generally, the object’s weight is unknown yet essential for both accurate control of the slave robot and intuitive perception of the human operator. However, due to high cost and limited installation space, it is unreliable to employ a force sensor to directly measure the weight. Therefore, in this paper, a control scheme free of force sensor is proposed for teleoperation robots to transfer a weight-unknown object accurately. In this scheme, the workspace mapping between master and slave robot is firstly established, based on which, the operator can generate command trajectory on-line by operating the master robot. Then, a slave controller is designed to follow the master command closely and estimate the object’s weight rapidly, accurately and robust to unmodeled uncertainties. Finally, for the sake of telepresence, a master controller is designed to generate force feedback to reproduce the estimated weight of the object. In the end, comparative experiments show that the proposed scheme can achieve better control accuracy and telepresence, with accurate force feedback generated in only 500 ms.      

On cooperative manipulation of dynamic objects

This paper proposes a decentralized position/internal force hybrid control approach for multiple robot manipulators to cooperatively manipulate an unknown dynamic object. In this approach, each autonomous robot has its own controller and uses its own sensor information in performing the fast cooperation. This approach eliminates a lot of information communications between each robot and reduces numerous computations. The influences of the position and the internal force estimation errors to the overall control system is analyzed. A cooperative identification method for each autonomous robot to identify the object's complex dynamics, cooperatively, is presented. In addition, the trade-off between the unilateral force constraint and the robots' position response is studied. Experiments show the effectiveness of this control approach.