The assessment and training of respiratory muscles are two essential tasks for indirect screening of status and improvement of lung function, respectively, especially in times of COVID-19. To perform both tasks, we have designed an innovative handheld mouth pressure biofeedback system for assessment and personalized game-based training of respiratory muscle strength. Thirty recovered COVID-19 patients were involved in an across-ages pilot study to evaluate their respiratory muscle strength and the system’s usability, and eight of the thirty patients were involved in a home inspiratory training program of 3 weeks to assess its effectiveness. Results revealed that participants rated the system’s overall usability as excellent (91.3 ± 6.4) and consistently performed respiratory cycles along with the game-based training program in terms of mouth pressure. Furthermore, patients involved in the home training program showed a 40% increase in their Maximal Inspiratory Pressure (Pimax). These results indicate that the proposed system stands for a proper healthcare solution for the initial diagnosis of respiratory muscle dysfunction or disease and for guiding the correct performance of tailored and consecutive threshold load breathing cycles playfully and engagingly. Furthermore, it stands for an attractive and personalized biofeedback solution to promote adherence to at-home therapy. Finally, it can be used to investigate new and effective training protocols that improve respiratory muscle performance.

Force exertion, object manipulation, and interaction are novel trending research topics of autonomous flying robots that can yield hoovering. Moreover, specifically with quadrotors, the vibration caused by the high natural frequency of rotating propellers exacerbates the problem of maintaining contact and exerting force against a rigidly fixed object. This contact vibration transfers back kinetic energy to the quadrotor that, in worst-case scenarios, surpasses its flying capabilities, which may lead to a crash. This paper studies the problem of aerial contact stabilization of a quadrotor equipped with a hemispherical deformable tip, which accommodates contact forces at a lower frequency. Thus two phenomena not studied in the literature arise: the rolling motion, and the deformation at contact. The contact force stabilization restores the effects of deformation while simultaneously endowing rolling by controlling a tangent constrained force. A model-free continuous attitude fractional controller to guarantee finite-time attitude stabilization is proposed. The residual coupled nonlinear dynamics yields the desired attitude corresponding to a given contact force; thus, force stabilization is achieved. Finally, experimental results are presented to assess the performance of the proposed approach.

An omnidirectional mobile manipulator (OMM) provides extended capabilities to a robotic system since it enlarges its workspace at the expense of an omnidirectional mobile base, which is nowadays a reality. When various OMM transport an object, the resultant constrained OMM dynamics is quite complex that demands effective control schemes without neglecting dominant nonlinear effects nor interaction forces. In this paper, it is proposed a decentralized cooperative control for a set of k OMMs (k-OMM) subject to homogeneous holonomic constraints imposed by the object being manipulated. A chatterless integral sliding mode force-position control guarantees exponential tracking whose implementation does not require any knowledge of dynamics. This controller is decentralized in a sense that neither dynamics nor interaction forces of the i-OMM are required for the j-controller, and it is cooperative by correcting collectively the velocity deviation due to the pushing of the other j-OMM. Each omnidirectional base provides object mobility along passive smooth velocity fields to avoid obstacles on the floor, which is synthesized as the secondary task when resolving redundancy, and the force control stabilizes internal forces to ensure object grasp, which are declared together with end-effector position, as the primary task. Simulations are discussed for two 8-DoF Kuka youBot OMM system navigating in a cluttered environment.

Dexterous object manipulation with robotic hands (subject to holonomic constraints) usually requires the capacity of fingertips to roll onto the object, which is very difficult to achieve with frictionless point contact model . As an alternative, deformable contact model has been considered based on hemispherical shape end-effector to yield rolling. However, it entails dexterity at the expense of dealing with normal and tangential forces, as well as more elaborated dynamic models. In this paper, a passivity-based controller is proposed for redundant robotic fingers with hemi-spherical deformable fingertips to manipulate dexterously a circular dynamic object. Redundancy and rolling are exploited to control normal and tangent contact forces to yield an optimal grasping. The optimal grasping is based on to align dynamically the normal forces applied to the object that allow its manipulation with minimum tangent forces. Stability conditions are presented to guarantee local asymptotic convergence. Finally, numerical simulations show the performance of the forces toward desired pose. This approach can be extended to objects with arbitrary shape that admit a local decomposition by a circular curvature.

The success in real applications of PID regulator has thought us that it is desirable a simple controller with clear and intuitive policy for tuning of feedback gains, as well as minimum or null dependency on the dynamics of the system. In this paper, theoretical and experimental results of PD-like structures for tracking of robots subject to friction and disturbances is presented. The salient feature of our proposal is a neuro-fuzzy schemes used to a single gain that multiplies the regressor-free PID structure. This bounded time-varying gain plays the role of enforcing a dissipative mapping to obtain exponential stability. Stability is obtained in the sense of Lyapunov and experimental study is presented and discussed, which highlights the viability and feasibility for real applications.

This paper proposes a general scheme based on terminal attractors to parametrize operational tasks with respect to time in continuous kinematic controllers. Commonly, a pseudo-inverse operator is applied to solve operational tasks. However, it is known that discontinuities in the control signals appear as a by-product of task transitions during motion execution. In particular, these transitions involve the insertion, removal and swapping of tasks. Recently, some methods have been reported that overcome such discontinuities in the control signals. In this work, we provide time parametrization capabilities to these continuous kinematic controllers in order to handle the time axis of operational tasks at will. Then, we show that the proposed scheme can be naturally extended for the case of prioritized kinematic tasks while preserving continuity under task transitions. Our scheme is validated in a real experiment with a NAO humanoid robot.

A simple, fast and robust Passive Velocity Field Control (PVFC) scheme for contour tracking in 2D and 3D is presented. A model-free and chattering-free second order sliding mode controller is proposed, which enforces an invariant manifold for all time such that the generalized velocity tracks the spatial velocity field. A constructive simple and intuitive method to design this velocity field is built upon a fuzzy aggregation of orthogonal vectors to guide the end-effector subject to a dissipative map. Stability properties in the sense of Lyapunov establish the fast and yet smooth tracking with typical robustness of sliding modes. In this way, the closed-loop system exhibits the mildness of PVFC but it evades the subtle complexities of the original approach PVFC. A simulation study is discussed, and experimental results highlight the characteristics of the proposed approach.

Force-position control through one or multiple robots, or fingers, typically assumes a rigid endpoint without rolling nor slipping. However, there are some interesting tasks where rolling is involved, such as turning a knob (object is pivoting at a fixed rotational axis) or rolling a wheel (object rotational axis is moving). In such a case, rigid endpoint force control becomes very difficult if not impossible, even for us humans. This stems from two facts, firstly, infinitesimally small rigid point does not yield a tangent force, therefore it is very difficult to control it indirectly; and secondly, the pair robot-object stands for a highly non-linear constrained underactuated dynamical systems. In this paper, we aim at exploring rolling of a rigid dynamic circular object with hemispherical deformable fingertip, then with area, not point, contact. The dynamic model and a control scheme are presented inspired in previous works, but regulation of normal and tangential forces, as well as position and orientation of the object are synthesized. In particular, tangential force control proves instrumental to regulate posture, and displacement of the object with a simple transpose Jacobian Cartesian PDF+g control. Regulation of rolling angle and displacement with stable normal and tangential forces are obtained without force sensing, neither any model of the deformation nor any dynamic parameter of the object. To entertain these control objectives, a redundant configuration is required so as to yield local regulation, based on the stability-in-the-manifold criteria, whose dimension is greater than the operational space. Illustrative simulations are discussed that provide insight into the closed-loop numerical performance, and finally, remarks on the structure and potential applications are addressed.

A passivity-based model-free control scheme for an underwater fully actuated vehicle-manipulator system (UVMS) in contact tasks is proposed. Orthogonalized motion and force second-order sliding modes are enforced for all time for the redundant noninertial robotic UVMS, including when it is subject to a class of fluid disturbances. To this end, we first determine the constrained dynamics using the quasi-Lagrangian formulation to explicitly characterize hydrodynamic fluid perturbations. Our scheme aims at exploiting the structural properties of Lagrangian systems, then we derive a mapping between the quasi-Lagrangian UVMS to its equivalent Lagrangian form, and study the conditions for open-loop passivity preservation during the interaction of postures and contact constraints between the end effector of the UVMS and the rigid contact surface of bulky objects in cluttered submarine environments. Internal motions are simultaneously computed by solving, in the tangent subspace of the contact manifold, a hierarchy of secondary tasks to satisfy the posture constraints. More importantly, the solution shapes the extended errors that are used to preserve passivity and to enforce dissipativity so as to guarantee local exponential stability without any knowledge of the complex UVMS dynamics, and the energetic performance of the UVMS in closed-loop. Illustrative simulations are discussed to show the feasibility of the proposed scheme.

Manipulation with soft-fingertips is proposed as a tool for interacting with rigid objects, based on an online bilateral teleoperation fuzzy controller, without time delay. The fuzzy inference engine tunes continuously the force feedback gain to increase awareness of physical interaction so as to grasping is achieved. In contrast to the case of rigid fingertip, wherein infinitely small contact point is assumed, it is argued that our scheme allows safe and intuitive interaction, which has proved effective in an experimental study with 19 subjects. Results indicate success due to feedback of slave contact force to the human user. Subjects consistently judge comfort and easiness of manipulation, with an experimental two-hand prototype.

In this paper, we are interested in a scheme that proves effective use of soft fingertips for human-in-the-loop telemanipulation. Motion planning is carried out by the human-in-the-loop to grasp and manipulate an object using viscoelastic soft fingertips. In addition, to grasp an object firmly, an estimated torque is synthesized based on fuzzy inference. Experimental results show that the user confidence presents small variations using soft fingertips. Then, the soft fingertips in pHRI induce a more user dexterity than rigid fingertips.

Classical prioritized inverse kinematics (PIK) allows to generate admissible trajectories for redundant robotic systems according to a prioritized finite set of kinematic tasks to simultaneously handle multiple posture constraints. In this paper, we propose a novel regulation scheme that permits to define terminal attractors (TA) at each priority level for satisfying an additional constraint which is the final time. TA were first introduced in the context of movement neuroscience for studying the targeting problem in reaching movements. Based on the underlying properties of TA, we extend PIK methods for achieving desired time convergence of each task while guaranteeing smooth transitions between active and inactive tasks during execution. The proposed scheme is illustrated in simulation with branched robotic manipulators and verified with a real redundant robotic arm.

Based on recent studies which establishes that skill acquisition requires not just specification of motor skills, learning and skill application but also intervention of human expert only in certain phases, we present an approach which encode the human expert demonstration into a teacher class based on Fuzzy ArtMap network. Then, the human novice trainee produces the approximate knowledge, which is in turn coded into student class. The evaluation function introduces a class metric which simultaneously allows the student to refine motor commands to increase the trainee pace while modifies accordingly the desired trajectory of the robot. Preliminary experiments indicates a high success rate in contact robotic tasks, in a deterministic setting.

We propose a scheme to deal simultaneously with local motion planning and dynamic control of redundant cooperative robots subject to holonomic, posture and loop-closure constraints. In contrast to previous contributions, an iterative method, that glue together the problem of kinematic motion planning with dynamic control, generates the sequence of feasible collision-free motions by combining in a single strategy the task-priority redundancy formalism with a joint model-free smooth force-motion control scheme based on a well-posed projection, which allows motions of the system only in the tangent subspace of the contact constrained manifold. Overall the new algorithm is able to compute fast and accurately local solutions involving severely constrained robotic motions. We have successfully verified in simulations the effectiveness of the proposed iterative method in the context of cooperative manipulation tasks.

A novel haptic teleoperated scheme for an efficient obstacle avoidance under human guidance is introduced. A remote robot immersed in an environment with obstacles is guided by a user using the end-effector of a haptic device. The system provides force feedback to the user when he approaches a potential field surrounding an obstacle. The user assigns the potential fields to the obstacles based on subjective judgments, i.e. a loose fitting potential field whether the obstacle is fragile or tough, to avoid a close approach to it. Obstacle avoidance experiments under visual and force feedback were performance and the results confirm the effectiveness of this scheme.

In this paper, a new hybrid active mechanical technique is proposed, which nullifies the torque coming from gravitational acceleration by means of controlled displacements of the center of mass of each link. Modeling, design and control issues are presented as well as some preliminary experimental results illustrate this principle.

A neural network training method for identification in bounded time of nonlinear systems is presented in this paper. A sliding mode surface drives the adalines, perceptrons and multilayer perceptrons so as to a new second order sliding mode is enforced for all time. This neural network-based sliding mode enforces an invariant differential manifold, with a time-varying feedback gain to give rise to finite-time convergence, consequently, the chattering free sliding mode allows identification of the underlying system in finite-time, with zero error. Convergence characteristics of the algorithm are proven with Lyapunov stability theory and concepts drawn from variable structure systems. Numerical simulations for a full nonlinear nonlinear robot arm, subject to noise, show the validity of the proposed approach.

The required tasks in fixed-base exoskeletons demand a fast position/force controller; yet robust against unknown disturbances due to the application itself is tightly coupled with a human in a wide range of operational conditions, which give rise to human-exoskeleton interaction dynamics, high nonlinear uncertain exoskeleton dynamics, noisy sensors and other parametric uncertainties, such as environmental contacts. These factors do not allow to account on a precise dynamical model, thus model-based (regressor-based) controllers are difficult to implement. This paper deals with a regressor-free smooth PID-like fast force/position controller which guarantees finite-time convergence within second order sliding modes, thus ensuring inherent robustness. Experimental platform allows assessing its performance for rehabilitation tasks, which validates its functionality in practical implementation.

This paper presents a new haptic training method for motor skill acquisition working in a teleoperated system. The method promotes a visuo-motor learning process base on the active attention and participation of the apprentice during training. Using a robot end-effector, the master describes a desired path which is followed by the apprentice using a haptic device. The master aids the apprentice by restricting his motion within upper and lower boundaries parallel to the path being created in real time. The boundaries are located at a given distance established by the master base on the apprentice learning improvement. Using this method, the master does not disturb or control the position and velocity of the apprentice directly which avoids apprentice dependence on the master. A training handdrawing scheme was designed and implemented to evaluate the visuo-haptic method; experimental results show faster and better apprentice's motor performance than using only visual information. These results suggest a possible implementation of the method in complex motors tasks such as calligraphy or surgery, to name a few.

Fixed-Base Exoskeleton applications have increased rapidly in the last few years, evidently as part of promising rehabilitation robotic programs of the robotics worldwide community, where in particular Human-Robot-Interaction (HRI) plays an important role in its design and control because they are tightly coupled to human-limbs. Exoskeletons embrace HRI as well as technological and theoretical challenges towards real and effective rehabilitation. In this realm, some questions arise, to name a few, what is the relationship between the exchanged energy between human and exoskeleton? How can we assess rehabilitation factors under HRI philosophy? This paper attempts to establish answers to these questions, which can be embodied into rehabilitation HRI using a Light-Exoskeleton. A compliant haptic guidance scheme for human arm subject to minimum-jerk-trajectories criterion is proposed. Preliminary experimental results provide further insight of a haptic guidance scheme taking into account decisive factors into the HRI such as human pose, haptic guidance control, reaching and tracking tasks, the complexity of the virtual environment, and muscles activity.

The adaptive controller for a class of nonlinear discrete-time systems based on Multi-Input Fuzzy Rules Emulated Network (MIFREN) is introduced in this article. MIFREN is assigned to identify the unknown plant under control, then a novel control law is introduced based the previously identified plant with another MIFREN. All control parameters, including the learning rates are selected to guarantee bounded close-loop signals, via Lyapunov stability criteria. The performance of the proposed control algorithm is demonstrated by computer simulation results.

This paper studies the open problem of uncalibrated visual servoing for constrained robots with parametric uncertainties, interacting with unknown environments. A new theoretical framework and its experimental validation are given. This approach produces global exponential convergence of the constrained visual position and the contact force between the end-effector and the unknown constrain surface. This approach is based on the formulation of the visual orthogonalization principle (VOP), which, under the framework of passivity, yields a closed-loop system that fuses camera, encoder and force sensor signals. An experimental system running on Linux-RTAI OS is implemented to visually drive a constrained direct-drive robot manipulator, equipped with six axis JR3 force sensor and a FireWire CCD digital camera posed in fixed configuration. This experimental system proves the effectiveness of the proposed approach even when the robot, camera and restriction surface parameters are assumed as unknown

Sliding mode control has been used extensively in robotics to cope with parametric uncertainty and hard nonlinearities, in particular for time-delay teleoperators, which have gained gradual acceptance due to technological advancements. However, since the slave teleoperator is in contact to a rigid environment, the slave controller requires a free of chattering control strategy, thus making first order sliding mode teleoperation control unsuitable. As an alternative, chattering free, higher-order sliding mode teleoperator control is proposed in this paper to guarantee robust tracking under unknown constant time delay. Moreover, complete order observers are proposed to avoid measurement of velocity and acceleration, along with a formal closed-loop stability proof of the observer-based controller. Experimental results are presented and discussed, which reveals the effectiveness of the proposed teleoperation scheme

Visual servoing of constrained dynamical robots has not yet met a formal treatment. Also, notices that due technological constraints, this task is done slowly at velocity reversals, thus dynamic friction arises, which complicates even more the problem. In this paper, a new adaptive scheme for visual servoing of constrained robots subject to dynamic friction is proposed. An image-based control is introduced to produce simultaneous convergence of the constrained visual position and the contact force between the end-effector and the constraint surface. Camera and robot parameters are considered uncertain. This new approach is based on a new formulation of the orthogonalization principle used in force control, coined here visual orthogonalization principle. This allows, under the framework of passivity, to yield a synergetic scheme that fuses camera, encoder and force sensor signals. Simulation results are presented and show that image errors and force errors converge despite uncertainties of friction model.

Cooperative robots have attracted the attention because they allow carrying out of tasks which cannot be done with a single robot. Though cooperative robot dynamics are quite complex to handle, regularly it is necessary to implement a nonlinear dynamics-based controller which guarantees fast tracking. A method for very fast constrained object maneuvering for non redundant rigid cooperative robot manipulators is proposed in this paper. The novelty of our approach lies in the fact that very fast decentralized Cartesian cooperative tracking is obtained without using the model of the robot nor exact knowledge of inverse Jacobian. The model-free sliding PD force controller, driven by second order position/force commuting sliding surfaces, is presented, such that approximate compensation of nonlinear dynamics of each robot arises, and the residual error dynamics is finally cancelled by a chattering-free Cartesian sliding mode to guarantee convergence of position and force tracking errors. Notice that inverse kinematics are avoided by synthesized Cartesian, rather than joint, error sliding surfaces, thus the commuting manifold does not depend on the Jacobian, therefore, the system is robust against Jacobian uncertainty, A simulation study of two cooperative robots manipulating a constrained object shows the expected performance.

A globally convergent visual feedback control scheme is proposed for the dynamic model of uncertain planar robot manipulators with uncalibrated camera. Additionally, a time-varying feedback gain induces a terminal attractor in the visual error manifold to guarantee finite-time convergence of image-based tracking errors. Simulations results of a two degrees-of-freedom manipulator with uncalibrated CCD camera are presented to illustrate the dynamic closed-loop performance.

A decentralized state visual feedback control scheme is presented using an uncalibrated camera. Full nonlinear robot dynamics is considered only in the stability analysis. The closed loop equation renders local exponential tracking by means of the existence of a chattering-free second order sliding mode regime for all time. Additionally, a time-varying feedback gain induces a well-posed terminal attractor of visual tracking errors to prove finite-time tracking of image-based desired trajectories. The system is computationally very inexpensive in comparison to the few dynamic visual servoing controllers available in the literature since the regressor is not computed. Simulations results presented, which confirms the expected dynamic closed-loop performance.

Haptic interaction with a virtual object establishes a kinesthetic sensation to the user. It is well accepted that to better perceive a given virtual object, it is relevant to yield some surface properties of the object, for instance the shape through the normal contact force, the roughness by the sliding friction, and the texture as a combination of both of them. On this problem, force control is the key issue. This problem has been highlighted three decades ago, when there was not available any good haptic display. Since then, a number of methods on force feedback have been proposed to convey these features, wherein the main scheme is based on the penalty method. However, when the object is deformable, the penalty method cannot compute properly the shape and roughness since the contact force ignores the inherent deformation of the object. In contrast, if the contact force is computed using the constrained Lagrangian, this force depends on the dynamic deformation of the object. In this paper, a constrained Lagrangian-based oriented framework is proposed to compute the contact force dynamically, in such a way that it can easily realize these effects over implicit dynamical objects. This powerful scheme can produce these effects seamlessly. Experimental results using PHANTOM on deformable and undeformable virtual objects are presented and discussed.

For a class of robot arms, a proportional-derivative (PD) controller plus gravity compensation yields the global asymptotic stability for regulation tasks, and some proportional-integral-derivative (PID) controllers guarantee local regulation without gravity cancellation. However, these controllers cannot render asymptotic stability for tracking tasks. In this paper, a simple decentralized continuous sliding PID controller for tracking tasks that yields semiglobal stability of all closed-loop signals with exponential convergence of tracking errors is proposed. A dynamic sliding mode without reaching phase is enforced, and terminal attractors, as well as saturated ones, are considered. A comparative experimental study versus PD control, PID control, and adaptive control for a rigid robot arm validates our design.

A continuous control system is proposed which guarantees robust tracking in finite time for uncertain robot arms subject to unknown dynamic friction. To achieve this result, several algorithms were combined: a dynamic adaptive sliding mode control; a time base generator (TBG) to yield a time-varying gain, which allows us to obtain finite time convergence; continuous parametrization to compensate for unknown dynamic friction, which in turn yields a continuous friction compensator; and a moving sliding surface, without knowledge of initial conditions, to obtain sliding mode all the time, and hence robustness. Two controllers are derived, the adaptive and the sliding mode version, both with similar closed-loop stability properties. Simulation data of a rigid robot arm is discussed.

In this paper it is shown that smooth object maneuvering can be achieved via an adaptive control scheme for cooperative control of multiple manipulators subject to holonomic constraints. Smooth object maneuvering is obtained via a dynamic impedance relationship, Optimal internal forces that ensure a stable grasp are obtained dynamically by linearly constrained gradient flows. Asymptotic stability is proved via a Lyapunov function and smooth performance and convergence are shown via simulations.

This paper deals with the decentralized control of multiple manipulators in a class of cooperative tasks called holonomic cooperation and presents two joint-space controllers. The controllers decouple the position and force control by the joint-space orthogonalization method. The first controller implicitly realizes the force control through a feedforward of the desired force, but the second one includes a loop of the force feedback. Their global and exponential stability is guaranteed by Lyapunov functions. Unlike centralized controllers, our decentralized controllers are designed in the joint spaces of individual robots so that the implementation does not need to manipulate high dimensional matrices.

Based on a novel error coordinate system which induces a sliding mode, two passivity-based adaptive controllers are proposed. The control strategies, similar to the one proposed by Slotine-Li (1987) for free motion and by Arimoto et al. (1993, 1994) for constrained motion, give rise to the exponential convergence of tracking errors. Computer simulation data for free and constrained motions show a high performance.

This paper presents a general approach for adaptively and distributively controlling multiple cooperative manipulators. The proposed approach does not adopt a centralized architecture but assigns a controller to each robot. Any communication requirement is determined by motion constraints existing in the cooperative system. All physical parameters of the manipulators or the load of the system are online estimated by a model-based adaptive algorithm. A Lyapunov function guarantees asymptotic convergence of trading errors of the trajectory and the interactive force among the robots. Performance of this controller is further shown by simulations on six DOF manipulators.

We propose a robot controller for stably executing all phases of contact tasks involving discontinuities due to the introduction or removal of contact forces. Systems executing such tasks are characterized by ambiguous right hand sides in the differential equations of motion. Consequently, our approach develops upon ideas from generalized dynamical systems (GDSs), an orthogonalization principle, the Hertz contact model, and model-based adaptive control. The result is an asymptotically stable controller that discontinuously switches among three possible configurations based on the contact situation. The method is used to tune the controller independently for both position and constrained motion as also for reducing contact forces during the process of making contact with the environment. The underlying theory is first described. Then the controller synthesis and proof of its asymptotic stability, based on Lyapunov's method, are presented. The idea is illustrated with a simulation of a simple task.>

This paper has a twofold objective: 1) to show that, when an adaptive law designed with a Lyapunov function and dependant also of the parametric error is introduced into a variable structure controller the existence of a sliding mode is no longer guaranteed for all t; and 2) a time varying boundary layer modulated by the tracking errors to propose a variable structure robot control with asymptotic stability. It is shown that the high activity on the actuators, typical of variable structure controllers, can be arbitrarily reduced in both adaptive and nonadaptive cases. These controllers give rise to the asymptotic stability and at the same time the sliding mode is guaranteed with very small chattering. A trade off arises in terms of chattering and robustness but the convergence of tracking errors is always assured. Computer simulations show the performance of the proposed controllers with comparison of two other algorithms.>

When multiple manipulators are going to manipulate one target object coordinately, it is necessary to control both the motion of the object and the forces exerted at the endpoints of manipulators. It is important particularly to control the so-called internal force which does not affect the motion of the object. In this paper, a model-based adaptive control method for such coordinated control of multiple manipulators is proposed. The proposed method is a natural extension of the adaptive control scheme for geometrically endpoint constrained manipulators. It is proved theoretically that both the desired position trajectory of the object and the internal force converge to the desired ones respectively. The effectiveness of the proposed method is demonstrated by computer simulation using two planar 3-DOF manipulators.>