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In this paper, we propose a fast online closed-loop identification method combined with an output-feedback controller of the generalized proportional integral (GPI) type for the control of an uncertain flexible robotic arm with unknown mass at the tip, including a Coulomb friction term in the motor dynamics. A fast nonasymptotic algebraic identification method developed in continuous time is used to identify the unknown system parameter and update the designed certainty equivalence GPI controller. In order to verify this method, several informative simulations and experiments are shown. Index Terms--Adaptive control, algebraic estimation, flexible robots, generalized proportional integral (GPI) control.

This paper addresses the robust trajectory tracking problem for a redundantly actuated omnidirectional mobile manipulator in the presence of uncertainties and disturbances. The development of control algorithms is based on sliding mode control (SMC) technique. First, a dynamic model is derived based on the practical omnidirectional mobile manipulator system. Then, a SMC scheme, based on the fixed large upper boundedness of the system dynamics (FLUBSMC), is designed to ensure trajectory tracking of the closed-loop system. However, the FLUBSMC scheme has inherent deficiency, which needs computing the upper boundedness of the system dynamics, and may cause high noise amplification and high control cost, particularly for the complex dynamics of the omnidirectional mobile manipulator system. Therefore, a robust neural network (NN)-based sliding mode controller (NNSMC), which uses an NN to identify the unstructured system dynamics directly, is further proposed to overcome the disadvantages of FLUBSMC and reduce the online computing burden of conventional NN adaptive controllers. Using learning ability of NN, NNSMC can coordinately control the omnidirectional mobile platform and the mounted manipulator with different dynamics effectively. The stability of the closed-loop system, the convergence of the NN weight-updating process, and the boundedness of the NN weight estimation errors are all strictly guaranteed. Then, in order to accelerate the NN learning efficiency, a partitioned NN structure is applied. Finally, simulation examples are given to demonstrate the proposed NNSMC approach can guarantee the whole system's convergence to the desired manifold with prescribed performance. Index Terms--Omnidirectional mobile manipulators, robust neural network (NN), sliding mode control (SMC), trajectory tracking control, uncertainties.

This paper presents a unified treatment of the motion control of underactuated two-link manipulators, including acrobots and pendubots. The motion space is divided into two areas: swing-up and attractive; and control laws are designed for each. First, a control law based on a weak-control Lyapunov function (WCLF) is employed to increase the energy of and control the posture of the actuated link in the swing-up area. Next, one parameter of the WCLF is chosen to be a nonlinear function of the state to avoid singularities. Then, another parameter of the control law is adjusted based on the state to improve the control performance. Finally, an optimal control law is designed for the attractive area. Stability is guaranteed in the swing-up area by the use of a WCLF based on LaSalle's invariance principle. Moreover, the global stability of the control system is guaranteed by integrating the WCLF and a nonsmooth Lyapunov function. Index Terms--Acrobot, LaSalle's invariance principle, nonsmooth Lyapunov function (NSLF), singularity, stabilization, underactuated manipulator, weak-control Lyapunov function (WCLF).

This paper presents an optimal design of a parallel manipulator aiming to perform pick-and-place operations at high speed and high acceleration. After reviewing existing architectures of high-speed and high-acceleration parallel manipulators, a new design of a 4-DOF parallel manipulator is presented, with an articulated traveling plate, which is free of internal singularities and is able to achieve high performances. The kinematic and simplified, but realistic, dynamic models are derived and validated on a manipulator prototype. Experimental tests show that this design is able to perform beyond the high targets, i.e., it reaches a speed of 5.5 m/s and an acceleration of 165 m/[s.sup.2]. The experimental prototype was further optimized on the basis of kinematic and dynamic criteria. Once the motors, gear ratio, and several link lengths are determined, a modified design of the articulated traveling plate is proposed in order to reach a better dynamic equilibrium among the four legs of the manipulator. The obtained design is the basis of a commercial product offering the shortest cycle times among all robots available in today's market. Index Terms--Articulated traveling plate, dynamic model, parallel robot, pick and place, Schoenflies motion.

The importance of energy efficiency of a robotic manipulator is clearly evident when the manipulator has to use on-board power. With miniature machines, this issue is even more important since the size and the weight guides the performance of a design. In this paper, a design methodology is proposed which may allow a robot to follow desired trajectories approximately without actuator inputs. Actuator inputs are used to further modify the trajectories. The design philosophy has the following key elements: (i) the inertia matrix of the device is suitably altered using mass distribution; (ii) compliant elements are introduced to take away the gravity terms; and (iii) additional springs are used to create certain periodic gait motion. This design philosophy is applied on a two dof leg executing a swing motion. It is found that the passive motion of the designed leg is close to the desired trajectories but is not exact. Actuators are added to get the desired response fully. Power input for two legs with and without this design philosophy, are then compared. [DOI: 10.1115/1.2712218]

The precise control of a manipulator depends on its velocity as well as on its configuration and dynamic properties. This paper presents some observations that can serve as a useful tool for identifying nonlinear ear effects in a manipulator. The tool is based on equations of motion being expressed in terms of inertial quasi-velocities (IQVs). They are rates containing both kinematic and mechanical parameters of the system. The presented approach gives a further insight into the manipulator motion. An analytical example shows the proposed strategy. [DOI: 10.1115/1.2363203] Keywords: manipulators, inertia matrix, dynamics, matrix equations

This paper presents a practical method for automatic tip-over prevention and path following control of a redundant nonholonomic mobile modular manipulator. According to modular robot concept, the mobile platform is treated as a special module attached to the base of the modular manipulator, then an integrated structure is constructed and its dynamic modeling is performed. A new tip-over stability criterion based on the supporting forces is proposed in consideration of inertia, gravity, and acceleration. An online fuzzy logic (FL) self-motion planner and an adaptive neural-fuzzy controller (ANFC) are presented: The former is used to generate desired self-motions in a real-time manner, and the latter is used to prevent the robot from tipping over and to control the end-effector to follow a desired spacial trajectory at the same time. The proposed algorithm does not need any a priori knowledge of dynamic parameters and can suppress bounded external disturbances effectively. Simulation results for a real robot validate the dynamic modeling method and the controller design algorithm. [DOI: 10.1115/1.2229253]

The application of joint-torque sensory feedback (JTF) in robot control has been proposed in the past that, unlike the model-based controllers, does not require the dynamic model of the robot links. JTF, however, assumes precise measurement of joint torque and accurate friction model of the joints. This paper presents an adaptive JTF control algorithm that does not rely on these assumptions. First, the robot dynamics with JTF is presented in a standard form with a minimum number of parameters, where the inertia matrix appears symmetric and positive definite. Second, an adaptive JTF control law is developed that requires only incorporation of uncalibrated joint-torque signals, i.e., the gains and offsets of multiple sensors are unknown. Also, all physical parameters of the joints including inertia of the rotors, link twist angles, and friction parameters are assumed to be unknown to the controller. The stability analysis of the control system is presented. Experimental results demonstrating the tracking performance of the proposed adaptive JTF controller are presented. Index Terms--Adaptive control of manipulators, friction compensation, joint-torque feedback, joint-torque sensory feedback (JTF), motion control.

Visual servoing of eye-in-hand flexible manipulators is addressed in this paper. Dynamic effects of both the rigid and the flexible motion of the manipulator are fully taken into account in a control solution where the two-time scale nature of the problem is exploited. The visual information is used in the "slow" subsystem for a task-space-oriented control law, where computationally expensive operations, such as inverse and time derivative of the Jacobian, are avoided. A constructive proof of stability of this control scheme, based on Lyapunov theory, is also presented. The effectiveness of the proposed controller is shown by means of a numerical simulation concerning a trajectory tracking problem. Some experimental results finally demonstrate the precision enhancement achieved by the proposed algorithm on a single-link flexible manipulator. Index Terms--Flexible manipulators, Lyapunov stability, two-time scale control, visual servoing.

This paper presents a new adaptive controller for image-based dynamic control of a robot manipulator using a fixed camera whose intrinsic and extrinsic parameters are not known. To map the visual signals onto the joints of the robot manipulator, this paper proposes a depth-independent interaction matrix, which differs from the traditional interaction matrix in that it does not depend on the depths of the feature points. Using the depth-independent interaction matrix makes the unknown camera parameters appear linearly in the closed-loop dynamics so that a new algorithm is developed to estimate their values on-line. This adaptive algorithm combines the Slotine-Li method with on-line minimization of the errors between the real and estimated projections of the feature points on the image plane. Based on the nonlinear robot dynamics, we prove asymptotic convergence of the image errors to zero by the Lyapunov theory. Experiments have been conducted to verify the performance of the proposed controller. The results demonstrated good convergence of the image errors. Index Terms--Adaptive control, robot manipulator, uncalibrated camera parameters, visual servoing.

We present a new approach to path planning for deformable linear (one-dimensional) objects such as flexible wires. We introduce a method for efficiently computing stable configurations of a wire subject to manipulation constraints. These configurations correspond to minimal-energy curves. By restricting the planner to minimal-energy curves, the execution of a path becomes easier. Our curve representation is adaptive in the sense that the number of parameters automatically varies with the complexity of the underlying curve. We introduce a planner that computes paths from one minimal-energy curve to another such that all intermediate curves are also minimal-energy curves. This planner can be used as a powerful local planner in a sampling-based roadmap method. This makes it possible to compute a roadmap of the entire "shape space," which is not possible with previous approaches. Using a simplified model for obstacles, we can find minimal-energy curves of fixed length that pass through specified tangents at given control points. Our work has applications in cable routing, and motion planning for surgical suturing and snake-like robots. Index Terms--Deformation, differential geometry, flexible manipulation, flexible object representation, minimal-energy curves, modeling, motion planning, path planning.

This paper presents a novel fuzzy genetic algorithm (GA) approach to tackling the problem of trajectory planning of two collaborative robot manipulators sharing a common workspace, where the manipulators have to consider each other as a moving obstacle whose trajectory or behaviour is unknown and unpredictable, as each manipulator has individual goals and where both have the same priority. The goals are not restricted to a given set of joint values, but are specified in the workspace as coordinates at which it is desired to place the end-effector of the manipulator. By not constraining the goal to the joint space, the number of possible solutions that satisfies the goal increases according to the number of degrees of freedom of the manipulators. A simple GA planner is used to produce an initial estimation of the movements of the robots' articulations and collision free motion is obtained by the corrective action of the collision-avoidance fuzzy units. Index Terms--Collision avoidance, fuzzy logic, genetic algorithms (GAs), multiple manipulators, trajectory planning.

Error propagation on the Euclidean motion group arises in a number of areas such as errors that accumulate from the base to the distal end of manipulators. We address error propagation in rigid-body poses in a coordinate-free way, and explain how this differs from other approaches proposed in the literature. In this paper, we show that errors propagate by convolution on the Euclidean motion group, S E(3). When local errors are small, they can be described well as distributions on the Lie algebra se(3). We show how the concept of a highly concentrated Gaussian distribution on S E(3) is equivalent to one on se (3). We also develop closure relations for these distributions under convolution on S E(3). Numerical examples illustrate how convolution is a valuable tool for computing the propagation of both small and large errors. Index Terms--Euclidean group, error propagation, manipulator kinematics, spatial uncertainty.

The paper presents an algorithm for the real-time evaluation of the actual end-effector orientation of general parallel spherical wrists. Conceptually, the method relies on evidence that the pose of a rigid body is defined once the location of at least two linearly independent vectors attached to the body is known. The location of these vectors of the wrist end-effector is determined by the solution of the direct position analysis of some properly chosen kinematic chains (legs) of the manipulator. In order to accomplish this analysis, extra sensors, which measure suitable non-actuated variables of the chosen legs, need to be placed in addition to the ones normally embedded in the servomotors, i.e., the sensors which measure the actuated variables. From a mathematical point of view, the algorithm is built on the polar decomposition of a matrix and has inherent least square features. Thus, together with measurement redundancy, i.e., more sensors (extra sensors) than the mechanism degrees of freedom, the method also makes it possible to minimize the influence of both round-off and measurement errors on the estimation of the location of the wrist end-effector. The method is general but, in order to prove its effectiveness, without loss of generality it has been customized to the solution of the 3(UPS)-S fully parallel wrist architecture (where U, P and S are for universal prismatic and spherical joint, respectively). Comparison of the proposed method, in both its general and specialized form, with others from the literature is provided. [DOI: 10.1115/1.2114888]

This paper presents a method for characterizing the performance limitations imposed by the yielding of the cables in systems with cable-driven transmissions. The method involves developing a rigid-body model of the system, where the cable tensions are considered as reaction forces. The kinematic coupling between links in the mechanism due to the use of cables is also considered. Here, the limitations on dynamic performance caused by cable yielding are added to the limitations caused by the bounds on actuator torque capacity, in order to give a more comprehensive description of the system's capabilities. A two degrees-of-freedom planar mechanism is analyzed in order to illustrate the methodology. [DOI: 10.111511.2121748]

The stiffness of cable-based robots is studied in this paper. Since antagonistic forces are essential for the operation of cable-based manipulators, their effects on the stiffness should be considered in the design, control and trajectory planning of these manipulators. This paper studies this issue and derives the conditions under which a cable-based manipulator may become unstable because of the antagonistic forces. For this purpose, a new approach is introduced to calculate the total stiffness matrix. This approach shows that, for a cable-based manipulator with all cables in tension, the root of instability is a rotational stiffness caused by the internal cable forces. A set of sufficient conditions are derived to ensure the manipulator is stabilizable meaning that it never becomes unstable upon increasing the antagonistic forces. Stabilizability of a planar cable-based manipulator is studied as an example to illustrate this approach. [DOI: 10.1115/1.2114890]

In this paper an algebraic formulation is presented for the boundary workspace of 3-R manipulators in Cartesian Space. It is shown that the cross-section boundary curve can be described by a 16th order polynomial as function of radial and axial reaches. The cross-section boundary curve and workspace boundary surface are fully cyclic. Geometric singularities of the curve are identified and characterized. Numerical examples are presented to show the usefulness of the proposed investigation and to classify the design characteristics. Keywords: kinematics, serial manipulators, workspace, geometric singularities, void

The design of a robotic manipulator begins with the dimensioning of its various links to meet performance specifications. However, a methodology for the determination of the manipulator architecture, i.e., the fundamental geometry of the links, regardless of their shapes, is still lacking. Attempts have been made to apply the classical paradigms of linkage synthesis for motion generation, as in the Burmester Theory. The problem with this approach is that it relies on a specific task, described in the form of a discrete set of end-effector poses, which kills the very purpose of using robots, namely, their adaptability to a family of tasks. Another approach relies on the minimization of a condition number of the Jacobian matrix over the architectural parameters and the posture variables of the manipulator. This approach is not trouble-free either, for the matrices involved can have entries that bear different units, the matrix singular values thus being of disparate dimensions, which prevents the evaluation of any version of the condition number. As a means to cope with dimensional inhomogeneity, the concept of characteristic length was put forth. However, this concept has been slow in finding acceptance within the robotics community, probably because it lacks a direct geometric interpretation. In this paper the concept is revisited and put forward from a different point of view. In this vein, the concept of homogeneous space is introduced in order to relieve the designer from the concept of characteristic length. Within this space the link lengths are obtained as ratios, their optimum values as well as those of all angles involved being obtained by minimizing a condition number of the dimensionally homogeneous Jacobian. Further, a comparison between the condition number based on the two-norm and that based on the Frobenius norm is provided, where it is shown that the use of the Frobenius norm is more suitable for design purposes. Formulation of the inverse problem--obtaining link lengths--and the direct problem--obtaining the characteristic length of a given manipulator--are described. Finally a geometric interpretation of the characteristic length is provided. The application of the concept to the design and kinetostatic performance evaluation of serial robots is illustrated with examples. [DOI: 10.1115/1.2120808]

This contribution presents a more general mobility criterion applicable to parallel platforms, unlike previously employed mobility criteria based on the well-known Kutzbach-Grubler criterion that often fails to provide the correct number of degrees of freedom of parallel manipulators, the mobility criterion introduced in this contribution provides the correct number of degrees of freedom for a wider class of parallel manipulators. Furthermore, the analysis provides insight into why the criteria based on the Kutzbach-Grubler criterion often fails. Moreover, the recently developed criterion computes the passive degrees of freedom in parallel platforms and the mobility of some classes of kinematically defficient parallel platforms. Finally, it is important to note that this criterion is based on an analysis of the subalgebras of the Lie algebra, se(3), also known as screw algebra, of the Euclidean group, SE(3). Moreover, it should be emphasized that, unlike other attempts to develop a criterion, the criterion developed in this contribution does not require any consideration of reciprocal screws. As is common in many areas of kinematics, the criterion presented here can be also obtained by an analysis of the subgroups of the Euclidean group.

The paper presents the position analysis of a spatial structure composed of two platforms mutually connected by one RRP and three SS serial kinematic chains, where R, P, and S stand for revolute, prismatic, and spherical kinematic pair, respectively. A set of three compatibility equations is laid down that, following algebraic elimination, results in a 28th-order univariate algebraic equation, which in turn provides the addressed problem with 28 solutions in the complex domain. Among the applications of the results presented in this paper is the solution to the forward kinematics of the Tricept, a well-known in-parallel-actuated spatial manipulator. Numerical examples show adoption of the proposed method in dealing with two case studies. [DOI: 10.1115/1.1992507]

A wide family of parallel manipulators (PMs) is the one that groups all PMs with three legs where the legs become kinematic chains constituted of a passive spherical pair (S) in series with either a passive prismatic pair (P) or a passive revolute pair (R) when the actuators are locked. The topologies of the structures generated by these manipulators, when the actuators are locked, are ten. Two out of these topologies are the SR-2PS topology (one SR leg and two PS legs) and the SP-2RS topology (one SP leg and two RS legs). This paper presents two algorithms. The first one determines all the assembly modes of the SR-2PS structures. The second one determines all the assembly modes of the SP-2RS structures. The presented algorithms can be applied without changes to solve, in analytical form, the direct position analysis (DPA) of all the parallel manipulators that generate a SR-2PS structure or a SP-2RS structure when the actuators are locked. In particular, the closure equations of two generic structures, one of type SR-2PS and the other of type SP-2RS, are written. The eliminants of the two systems of equations are determined and the solution procedures are presented. Finally, the proposed procedures are applied to real cases. This work demonstrates that (i) the DPA solutions of any PM that becomes a SR-2PS structure are at most eight, and (ii) the DPA solutions of any PM that becomes a SP-2RS structure are at most sixteen. Keywords: Kinematics, Position Analysis, Parallel Mechanisms, Parallel Structure

In this paper, the geometric design problem of serial-link robot manipulators with three revolute (R) joints when three precision points are specified is solved using an algebraic elimination method for the first time. Three spatial positions and orientations are defined and the dimensions of the geometric parameters of the 3R manipulator are computed so that the manipulator will be able to place its end-effector at these three prespecified locations. In this problem, six of the design parameters are set as free choices and their values are selected arbitrarily. For the specific case studied in this paper, a 12 deg single variable polynomial is calculated that has eight roots that are the design solutions and the other four roots are extraneous solutions. [DOI: 10.1115/1.2125970]

This paper is a study of the duality between the statics of a variety of structures and the kinematics of mechanisms. To provide insight into this duality, two new graph representations are introduced; namely, the flow line graph representation and the potential line graph representation. The paper also discusses the duality that exists between these two representations. Then the duality between a static pillar system and a planar linkage is investigated by using the flow line graph representation for the pillar system and the potential line graph representation for the linkage. A compound planetary gear train is shown to be dual to the special case of a statically determinate beam and the duality between a serial robot and a platform-type robot, such as the Stewart platform, is explained. To show that the approach presented here can also be applied to more general robotic manipulators, the paper includes a two-platform robot and the dual spatial linkage. The dual transformation is then used to check the stability of a static system and the stationary, or locked, positions of a linkage. The paper shows that two novel platform systems, comprised of concentric spherical platforms inter-connected by rigid rods, are dual to a spherical six-bar linkage. The dual transformation, as presented in this paper, does not require the formulation and solution of the governing equations of the system under investigation. This is an original contribution to the literature and provides an alternative technique to the synthesis of structures and mechanisms. To simplify the design process, the synthesis problem can be transformed from the given system to the dual system in a straightforward manner. Keywords: statics, kinematics, duality, graph representations, static pillar systems, beams, planetary gear trains, serial robots, platform-type robots, unstable truss, deadcenter positions, synthesis

This paper develops analytical techniques to delineate the workspace boundaries for parallel mechanisms with cables. In such mechanisms, it is not only necessary to solve the closure equations but it is also essential to verify that equilibrium can be achieved with non-negative actuator (cable) forces. We use tools from convex analysis and linear algebra to derive closed-form expressions for the workspace boundaries and illustrate the applications using planar and spatial examples. [DOI: 10.1115/1.2121741]

A full-pose, position and orientation, trajectory-tracking control of kinematically redundant flexible-macro-rigid-micro manipulators is proposed. Redundancy is resolved such that the forces exciting the lowest-frequency 'modal coordinates' of the system are minimized, while imposing a proportional damping on the flexural dynamics, rendering it stable under certain conditions. The simulation results show that the initial posture of the manipulator plays an important role in satisfying the foregoing stability conditions. [DOI: 10.1115/1.1870039]

Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel manipulator may track a path through singular poses if its velocity and acceleration are properly constrained. Techniques for path verification and tracking are presented, and an inverse dynamics algorithm that takes actuator bounds into account is examined. Simulation results for a planar parallel manipulator are given to demonstrate the details of this approach. [DOI: 10.1115/1.2098893]

We focus on the development of modular and recursive formulations for the inverse dynamics of parallel architecture manipulators in this paper. The modular formulation of mathematical models is attractive especially when existing sub-models may be assembled to create different topologies, e.g., cooperative robotic systems. Recursive algorithms are desirable from the viewpoint of simplicity and uniformity of computation. However, the prominent features of parallel architecture manipulators-the multiple closed kinematic loops, varying locations of actuation together with mixtures of active and passive joints-have traditionally hindered the formulation of modular and recursive algorithms. In this paper, the concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular. The various formulation stages in this process are highlighted using the illustrative example of a 3R Planar Parallel Manipulator. [DOI: 10.1115/1.2098890]

PPR-equivalent parallel manipulators (PMs) are a class of 3-DOF PMs with great application potential. They are indeed the parallel counterparts of the 3-DOF PPR serial robots, in which the moving platform can rotate arbitrarily about an axis undergoing a planar translation. This paper deals with the type synthesis of 3-DOF PPR-equivalent PMs. At first, virtual chains are introduced to represent the motion patterns of 3-DOF motions and relevant results from screw theory are recalled. A method is then proposed for the type synthesis of 3-DOF PPR-equivalent PMs. Using the proposed approach, the type synthesis of 3-DOF PPR-equivalent PMs is performed in three steps. In addition to all the 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs proposed in the literature, a number of new 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs are identified. It is also found that there are no PPR-equivalent PMs with identical type of legs. The type synthesis of PPR-equivalent PMs is well solved using the proposed approach. The characteristic of the proposed approach is that the type synthesis of PPR-equivalent parallel kinematic chains is reduced to the type synthesis of 3-DOF single-loop kinematic chains and thus easy to perform.

The minimum torque norm control scheme for redundant manipulators has long been known to exhibit instabilities. In this paper, an analysis is made of a class of acceleration-level redundancy resolution schemes that includes the minimum torque, minimum acceleration, and other well known schemes. It is proved that divergence of joint velocity norm to infinity in finite time is possible, and in fact does occur for self motions of mechanisms with one degree of redundancy under almost all such schemes in the class. The schemes that do not diverge in finite time are associated with conserved quantities and include minimum acceleration norm and dynamically consistent redundancy resolution schemes. Besides the divergence, all these schemes can exhibit local instabilities in the form of abrupt increases in joint velocities and torques. Simulations are presented that illustrate the types of divergence and instability. The details of the analysis should be useful to designers seeking to modify these resolution schemes. For example, it is proved that linear dissipation of nullspace velocity cannot stabilize the algorithms. Index Terms--Dynamically consistent control, instability, minimum torque control, optimization, redundancy resolution.

Continuum manipulators, inspired by the natural capabilities of elephant trunks and octopus tentacles, may find niche applications in areas like human--robot interaction, multiarm manipulation, and unknown environment exploration. However, their true capabilities will remain largely inaccessible without proper analytical tools to evaluate their unique properties. Ellipsoids have long served as one of the foremost analytical tools available to the robotics researcher, and the purpose of this paper is to first formulate, and then to examine, three types of ellipsoids for continuum robots: manipulability, force, and compliance. Index Terms--Compliance, continuum robot, ellipsoid, hyperredundant, manipulability.

This letter presents an adaptive fuzzy neural controller suitable for multilink manipulators motion control. The proposed controller has the following salient features: 1) self-organizing fuzzy neural structure; 2) online learning of the robot dynamics; 3) fast convergence of tracking error; and 4) adaptive control. Computer simulation results of a two-link manipulator demonstrate that excellent tracking performance can be achieved under external disturbances. Index Terms--Adaptive control, fuzzy neural networks, multilink manipulators.

This paper presents a genetic algorithm approach for the synthesis of planar three degree-of-freedom parallel manipulators. A genetic algorithm is an optimization method inspired by natural evolution. As in nature, the fittest members of a population are given better chances of reproducing and transmitting part of their genetic heritage to the next generation. This leads to stronger and stronger generations which evolve towards the solution of the problem. For the applications studied here, the individuals in the population consist of the architectural parameters of the manipulators. The algorithm optimizes these parameters to obtain a workspace as close as possible to a prescribed working area. For each individual of the population, the geometric description of the workspace can be obtained. The algorithm then determines the intersection between the prescribed workspace and the actual workspace, and minimizes the area of the regions that do not intersect. The method is applied to two planar three-degree-of-freedom parallel manipulators, one with prismatic joints and one with revolute joints.

The singularities of manipulators with offset wrists are difficult to enumerate. This article presents a numerical study to illuminate singularity problems when using an offset wrist with an articulated regional arm. Ironically, the regional manipulator singularity problem is worsened when using a singularity-free offset wrist. No wrist singularities exist (they are forced by design to lie outside of joint limits). However, the existing regional arm singularities become skewed from the well-known singular configurations of common manipulators. The wrist offset also skews the well-known wrist singularities (though they hopefully still lie outside of joint limits, their locations are no longer easily determined). Thus, a zero-offset singularity-free wrist is preferable with regard to overall manipulator singularities.

This letter presents a neural-network-based computational scheme for redundancy resolution of manipulators. The Tank-Hopfield (TH) network is adopted for pseudoinverse and inverse kinematics calculations and it can provide joint velocity and joint acceleration solutions within a time frame of the order of hundreds of nanoseconds. Incorporating the TH network into the redundancy resolution scheme allows planning algorithms to be implemented in real time. Simulation results for a three-link planar manipulator are presented to demonstrate that the proposed approach is efficient and practical. Index Terms - Neural networks, redundancy resolution, robot manipulators.

The control problem for a truly cooperative manipulator system cannot be regarded as a simple extension of single manipulator control since additional complexity arises from the need for ensuring coordinated motion of the system. Recently, we have proposed a control strategy based on two stages, namely, kinematic inversion of a set of cooperative task variables and a joint space control law with kinetostatic filtering of cooperative task space errors; this strategy avoids some of the drawbacks of other approaches. In this paper, the stability analysis for the joint space control law is provided and asymptotic stability of a set of equilibrium points is demonstrated. The case of imperfect compensation of the gravity terms has been analyzed. The addition of a force loop to achieve internal force regulation is also discussed. Index Terms - Cooperative manipulators, robotics, stability.

In a recent work of [16], a hybrid adaptive controller for rigid-link electrically-driven robot manipulators was proposed. Semi-global asymptotic stability of the controller was established in the Lyapunov sense. However, there are two limitations in it. One is that the controller requires the joint velocity measurements, that with the required accuracy can be difficult to realize in practical applications. The other one assumes the boundedness of estimated inertia parameters of the manipulator in order ta reduce the computation complexity. In this paper, we propose a modification of the hybrid adaptive controller, which eliminate the above-mentioned limitations. Hence the range of applicability of the method in [16] can be greatly broadened. The capabilities of the proposed control strategies are illustrated through computer simulation. Index Terms - Actuators, robust control, adaptive control, robotic manipulators.

In this article, two results concerning the control of force-reflecting teleoperation systems with time-delays are presented. The first result consists of a general framework for stability analysis of such systems. This analysis is performed on the basis of methods developed for linear time-delay systems, here extended and applied to the case of teleoperation schemes. The analysis shows whether the overall system is asymptotically stable independently of time-delay, or determines the maximum time-delay which guarantees asymptotic stability. The second issue discussed in this paper is the design of a control law able, under proper conditions, to stabilize the time-delay teleoperator. Examples of application of the stability criteria are discussed and experimental results of the control law are given. Index Terms - Force reflection, stability, telemanipulation, time-delay systems.

Fault tolerance is an important design criterion for robotic systems operating in hazardous or remote environments. This article addresses the issue of tolerating a free-swinging joint failure by focusing on how to best configure a slow-moving manipulator before a failure. Three scalar measures of fault susceptibility are defined using joint torques/forces, accelerations, and swing angles. Minimizing these measures is an approach to achieving fault tolerance, and for this, algorithms to calculate their gradients are also given. The formulas are valid for general n-link manipulators. Index Terms - Fault/failure tolerance, free-swinging failure, kinematics, kinematically redundant, manipulators, redundant robots/manipulators, robots.

This paper deals with the position control of robot manipulators. Proposed is a simple class of robot regulators consisting of a linear proportional-derivative (PD) feedback plus an integral action of a nonlinear function of position errors. By using Lyapunov's direct method and LaSalle's invariance principle, the authors characterize a class of such nonlinear functions, and they provide explicit conditions on the regulator gains to ensure global asymptotic stability. These regulators offer an attractive alternative to global regulation compared with the well-known partially model-based PD control with gravity compensation and PD control with desired gravity compensation. Index Terms - Manipulators, position control, stability.

The singularity problem of a 7-degrees-of-freedom (DOF) redundant manipulator is analyzed, and a new resolution method is proposed. In this paper, the singularities are decoupled into the position singularities and the orientation singularity by the technique of workspace decomposition, then ali sigularity conditions for both cases are derived, and the new singularity avoidance (NSA) method is proposed. The NSA method resolves the escapable singularities which can be reconfigured into a nonsingular posture via self motion. Unlike some existing methods, the NSA method considers the position singularities and the orientation singularity separately. This method only needs to optimize two order-3 minors, one for the 3 x 4 Jacobian translational submatrix and the other for the 3 x 7 Jacobian rotational submatrix. Therefore, the computation for the optimization is greatly reduced. Three examples are presented to demonstrate the generality and efficiency of this new method. Index Terms - Redundant manipulator, singularity, workspace decomposition.

Learning control is a concept for controlling dynamic systems in an iterative manner. It arises from the recognition that robotic manipulators are usually used to perform repetitive tasks. Most researches on the iterative learning control of robots have been focused on the problem of free motion control and hybrid position/force control where the learning controllers are designed to track the desired motion and force trajectories. The iterative learning impedance control of robotic manipulators, however, has been studied recently. In this paper, an iterative learning impedance control problem for robotic manipulators is formulated and solved. A target impedance is specified and a learning controller is designed such that the system follows the desired response specified by the target model as the actions are repeated. A design method for analyzing the convergence of the learning impedance system is developed. A sufficient condition for guaranteeing the convergence of the system is also derived. The proposed learning impedance control scheme is implemented on an industrial selective compliance assembly robot arm (SCARA) robot, SEIKO TT3000. Experimental results verify the theory and confirm the effectiveness of the learning impedance controller. Index Terms - Convergence analysis, impedance control, iterative learning algorithm, robot force control.

The reported study investigates the stochastic dynamics of a mobile manipulator. The manipulator is mounted atop a vehicle supported on multiple wheels. Stochastic excitations and deterministic excitation of the manipulator are induced by the acceleration of the vehicle on a traction surface. The stochastic excitations are related by time delays due to the longitudinal alignment of the vehicle wheels. Expressions for the deterministic and covariance matrices of the manipulator stochastic motions are developed. Sensitivity of the system responses to the surface roughness, the dynamics and the kinematics parameters of the manipulator is investigated. Suggestions for mobile manipulator design to minimize the influence of the stochastic base excitations are presented.

Interactive control schemes, such as stiffness control and impedance control, are widely accepted as a means to actively accommodate environmental forces, but have not been widely applied. This is in part because well-known controllers are parametrized in a mathematically convenient, but nonintuitive way. 'Spatial compliance control' is a Euclidean-geometrical version of compliance control that is parametrized in an intuitive way. A family of compliances is introduced with spatial transformation properties that simplify spatial reasoning aspects of compliance parameter selection. A control law is derived assuming that the robot consists of a serial linkage of rigid links actuated by variable-effort actuators.

Although most of the literature on manipulation systems deals with systems with as many degrees of freedom as the dimension of their task space, or even with more (redundant manipulators), kinematically defective manipulation systems are often encountered in robotics, in particular when dealing with simple industry-oriented grippers, or when the whole surface of the manipulator limbs is exploited to constrain the manipulated object, as in 'whole-arm' manipulation. Kinematically defective systems differ from nondefective and redundant manipulation systems in many ways, some of which have been addressed in the literature. In this paper, we focus on one of the central problems of manipulation, i.e., controlling the manipulator in order to track a desired object trajectory, while guaranteeing that contact forces are controlled so as to comply with contact constraints (friction bounds, etc.) at every instant. We attack this problem by an unified approach that is appropriate for manipulation systems with general kinematics. When dealing with kinematically defective systems, it is not possible to assign arbitrary trajectories of object motions and contact forces. To understand what restrictions position and force reference trajectories should exhibit in order to be feasible by a given system, is the central issue of this work.

This work introduces a new robust motion control algorithm using partial state feedback for a class of nonlinear systems in the presence of modelling uncertainties and external disturbances. The effects of these uncertainties are combined into a single quantity called perturbation. The major contribution of this work comes as the development and design of a robust observer for the state and the perturbation which is integrated into a Variable Structure Controller (VSC) structure. The proposed observer combines the procedures of Sliding Observers (Slotine et al., 1987) with the idea of Perturbation Estimation (Elmali and Olgac, 1992). The result is what is called Sliding Perturbation Observer (SPO). The VSC follows the philosophy of Sliding Mode Control (SMC) (Slotine and Sastry, 1983). This combination of controller/observer gives rise to the new routine called Sliding Mode Control with Sliding Perturbation Observer (SMCSPO). The stability analysis shows how the algorithm parameters are scheduled in order to assure the sliding modes of both controller and observer. A simplified form of the general design procedure is also presented in order to ease the practical applications of SMCSPO. Simulations are presented for a two-link manipulator to verify the proposed approach. Experimental validation of the methodology is also performed on a PUMA 560 robot. A superior control performance is obtained over some full state feedback techniques such as SMC and Computed Torque Method.