Conventional soft pneumatic actuators (SPAs) are made of soft materials that facilitate safe interaction and adaptability. In positioning and loading tasks, however, SPAs demonstrate limited performance. In this article, we extend the current designs of SPAs upon integrating a tendon-driven parallel mechanism into a pneumatic origami chamber, inspired by the performances and structures of vertebrates. The inner rigid/outer soft actuator exploits the advantages of both, parallel mechanisms to achieve precise, versatile motion, and SPAs, to form a compliant, modular structure. With the antagonistic actuation of tendons-pulling and air-pushing, the actuator can exhibit multimode motion, tunable stiffness, and load-carrying maneuvers. Kinematic and quasi-static models are developed to predict the behavior and to control the actuator. Using readily accessible materials and fabrication methods, a prototype was built, on which validation experiments were conducted. The results prove the effectiveness of the model, and demonstrate the motion and stiffness characteristics of the actuator. The design strategy and comprehensive guidelines should expand the capabilities of soft robots for wider applications, and facilitate the development of robots with rigid-soft hybrid structures.

We propose a novel integrator for implementing bilateral constraints in multibody simulation using variational integrator methods. We first construct a variational penalty method, which is used to enforce a constraint. The penalty term is simulated using an asynchronous variational integrator, allowing the penalty part of the system to be simulated using a smaller time step. We compute the Discrete Euler-Lagrange (DEL) equations for an equivalent penalty term with a larger time step and then use this rescaled system in the aforementioned variational penalty method, thereby enforcing the constraints. This enables us to incorporate some of the behavior of a very stiff system, which would only be stable on the small time scale, into the system on the large time scale. The effect is better adherence to the constraints, at a larger time step. We demonstrate the method with a simulation of a chain of rigid bodies. We then discuss the potential applications of the integrator and highlight how the work can be used to better interpret the tuned values of the coefficients used in penalty formulations.

A number of applications of wheeled robots, including planetary exploration rovers and rescue missions, require that the vehicle operates in a non-structured environment. Optimizing the vehicle mobility is of key importance in such applications. Reduced mobility can limit the ability of the robot to achieve the mission goals, or even render it immobile in extreme cases. In this paper, the effect of normal contact forces on mobility is reported. A performance indicator based on the force distribution is defined and used to compare different vehicle configurations. The validity of this indicator was assessed using both simulation and experimental results obtained for a six-wheel rover prototype. Results suggest that modifying the robot configuration to alter the normal force distribution can lead to increased traction force available at the wheel-terrain interfaces, thus improving the mobility.

The quest for ever faster pick-and-place robots has led to ingenious parallel robots with reduced mobility, e.g., capable of producing motions proper of SCARA systems: three independent translations and one rotation about an axis of fixed direction. These robots are also known as Schönflies-motion generators (SMG). Some parallel versions are commercially available, as are serial-parallel designs. The former are provided with four limbs, the latter with three, the fourth degree of freedom being appended in series with a Delta robot. Parallel robots are more attractive than their hybrid counterparts, but the presence of four legs poses serious challenges to their designers, as limb-interference limits the rotatability of the moving plate. A solution to this problem includes a gear train for rotation-range amplification, but this increases the inertial load on the motors and complicates the design - too many parts - and the control - because of inherent gear backlash and Coulomb friction. Recently, a SMG system was proposed that is supplied with two limbs, arrayed in an isostatic structure, which provides high rotatability of its gripper. This robot is driven by one C (cylindrical)-joint at each limb. As this joint allows for two degrees of freedom, it calls for two motors, that might as well be fixed to the base, which poses interesting design challenges. Reported in this paper is a design solution for the drive of a C joint, which is termed the C (cylindrical)-drive, based on a cylindrical differential mechanism of the RHHR type, with R standing for revolute, H for helical (or screw) joint. The design, kinematics and dynamics of the drive are discussed, along with a realization, and preliminary tests.

A novel approach is proposed for the modeling of rigid-wheel and soft-soil interaction to efficiently compute normal and shear stress distributions in the contact area. The authors propose a velocity field in the vicinity of the contact area based on the physical nature of the problem. Thereupon, the incremental changes to the stress field are computed by resorting to elastoplasticity theory and an appropriate already existing constitutive relation for soil. The proposed approach leads to results that agree well with those obtained using well-established terramechanics models, while addressing some of their shortcomings. In addition, the proposed approach uses generalized velocities of the wheel as inputs, which makes it compatible with dynamic models of multibody systems. The dynamic slip-sinkage behavior of the wheel and the semielliptical shape of the normal stress distribution under the wheel are natural outcomes of the proposed model. Experimental investigation under various ranges of wheel slippage shows good agreement with the data available in the literature.

In this work, a multibody dynamics model of a wheeled mobile robot is developed to characterize the terrain reaction forces in terms of the physical and control parameters of the system. A common strategy for simulating the motion of mobile robots on soft soil is to compute the soil reaction forces using terramechanics models and to solve a forward dynamics problem by considering the soil reactions as a set of forces applied to the system. This intends to provide an accurate computation of the forces involved in the wheel-soil interaction; however, a series of factors such as the sensitivity of reaction forces to soil parameters limits the applicability of the existing terramechanics models in unstructured environments. We propose an alternative approach which does not rely on the soil properties, but at the same time does not intend to provide an exact computation of wheel-soil interaction forces. The main objective of this approach is to estimate the effect of changes in control and design parameters on the performance of the system, using the information provided by the dynamics model of the vehicle. To this end, the reaction forces for the wheel-terrain interaction in the ideal limit case of pure rolling and no penetration are obtained upon the specification of the motion at the contact points, via kinematic constraints. The validity of the analysis results obtained using the proposed paradigm is verified by simulation runs and experiments. The experimental results suggest that this approach is successful in predicting the variation of a set of important performance indicators in terms of the changes in the parameters of the system.

A fundamental problem with many solid freeform fabrication systems is the production of large dimensional errors, due to the freeform construction process. The subject of this paper is surface mapping feedback (SMF), a closed-loop technique for minimizing the dimensional errors produced by rapid prototyping systems. The main steps of the technique are presented, namely part measurement, control implementation, and deposition adjustment. A test platform, the Cobra 600 rapid freeze prototyping system, is used to validate SMF. A helical gear part is constructed first with open-loop control and then with SMF control; system performance and part quality are compared for the two cases.

A novel approach is proposed for the modeling of rigid-wheel and soft-soil interaction using infinitesimal plasticity theory. Our motivation is the need to have a model compatible with dynamic models of multibody systems. The idea is to use a prescribed velocity field in the vicinity of the contact area based on the physics of the problem, and find the changes in the stress field by resorting to plasticity theory and an appropriate constitutive relation for soil. In this paper the Drucker-Prager constitutive relation with cap hardening is employed. The proposed approach leads to results that tally with those obtained using well-established semi-empirical models. The calibration of the semi-empirical model parameters is done by performing simulation runs using detailed FEM models with the Abaqus/Explicit software package.

Ice has long been used by humankind for utilitarian purposes, and more recently for artistic and entertainment purposes. Nowadays, the field of ice construction is becoming more commercially relevant, with increased interest in ice modeling at the small scale, and in ice tourism, specifically ice hotels at the large scale. As a result, there is a market for automating ice construction, and building detailed structures that would otherwise require a significant amount of manual work. To address this demand, the authors are currently developing experimental robotic systems for building ice structures: the Fab@home, for building small-scale structures, and the Adept Cobra 600 robot, for building medium-scale structures. Further software and hardware development is needed for the Cobra, since it was not designed for rapid prototyping, and certainly not for rapid prototyping using ice as the working material. The authors have designed and built fluid delivery systems for each machine to permit the use of water as the building material. A signal-processing subsystem permits control of the water-delivery flow rate and synchronization with the robot motion. Additionally, we have developed a slicing algorithm to generate toolpaths for the Cobra using stereolithography (STL) files as the input. We also intend to develop a larger robotic system for producing ice sculptures and buildings at the architectural scale.

Several triaxial accelerometers are known. However, to the knowledge of the authors, no true, triaxial accelerometers are commercially available. By true we mean an accelerometer which would pick up the three components of point-accelerations using one single proof-mass. What we propose is novel architecture classes of parallel-kinematics-machine for multi-axial accelerometers, that is, accelerometers that can measure n components of point-accelerations, where n = 1, 2, 3. We call these architectures simplectic, as they use n + 1 legs oriented normally to the n + 1 faces of the regular simplex associated with the n-dimensional subspace of measured acceleration components. We show that the simplectic biaxial accelerometer can be fabricated using micromachining MEMS techniques, while the simplectic triaxial accelerometer lends itself to compliant-mechanism fabrication techniques. CAD models of the prototypes proposed are provided for all of the three novel mechanical architectures proposed. Finally, the direct kinematics problems associated with the simplectic biaxial and triaxial accelerometers are shown to be linear in both cases. This feature simplifies the estimation of the proof-mass displacement from piezoresistive or piezoelectric measurements taken at the flexible joints connecting the legs of the mechanism to the rigid body whose acceleration is under estimation.

Aspects of the mechatronic design and prototyping of a robot designed and realized with the quasiholonomy property are discussed here. After an overview of the motivation and applications of the project at hand, we show how we faced the challenges encountered in the mechatronic design and implementation of the prototype. The actuation system and power supply dimensioning are then described, along with the selection of the on-board control unit and programming of the real-time operating system. Advantages of quasiholonomic robotic systems are substantiated

The paper considers a specific class of wheeled mobile robots, namely, mobile wheeled pendulums (MWPs). Robots pertaining to this class are composed of two wheels rotating about a central body. The main feature of MWP pertains to the central body, which can rotate about the wheel axis. As such motion is undesirable, the problem of the stabilization of the central body in an MWP is crucial. The novelty of the work reported here resides in the construction of: 1) the system controllability Lie algebra for the purpose of a rigorous controllability analysis and the computation of the largest feedback-linearizable subsystem; 2) a controller by input-output linearization of the system for achieving the desired steering rate of the robot while stabilizing the central body; 3) a controller based on the internal properties of the system to achieve the desired heading velocity of the robot; and 4) a controller based on the sliding-mode approach for controlling both the position and the orientation of the robot. The entire control structure that permits full control of the robot posture comprises three imbricated loops. Simulations showing good performance of the controlled system are provided. Preliminary tests performed on an experimental platform confirm the validity of the controller.

This paper introduces a new family of two-wheeled mobile robots. The mathematical model of the proposed robots is formulated along with a controllability analysis, also taking into account the oscillations of the intermediate body. We prove that it is possible to completely control these robots using only the wheel motors, while tracking a desired path

Cam-roller mechanism can be used in transmissions and robotic devices as an alternative to their bevel-gear counterparts. Compared with gear transmissions, cam-roller mechanisms feature low friction, low backlash, and high strength. However, cam mechanisms may end up with a high pressure angle if negative action, a motion in which the cam is driven by rollers, occurs. This paper reports the design of transmissions with multi-lobe-cams (MLC), as a means to reduce the pressure angle. The kinematics problems associated to MLC, including profile generation and transmission errors, are studied. As an example, a pith-roll wrist designed with MLC is described

In this paper, the dynamics of planar parallel manipulators with joint-coupling is presented. In the manipulator with joint-coupling, the actuator torques are distributed among the coupled joints. Hence, the dynamic behavior of the manipulator and the trajectory planning will be different from those manipulators without joint-coupling. Furthermore, the coupling coefficients of the joint-coupling provide an additional way to adjust the dynamic performance of the manipulator. Because of joint-coupling, the total power consumption along the desired trajectory becomes a function of the coupling coefficients. With a maximum limit on the motor torque output, it is possible to find an appropriate set of coupling coefficients that minimize the total power consumption

We introduce a novel control scheme for an anti-tilting mobile robot moving on an inclined plane. The robot pertains to the family of mobile wheeled pendulums. The challenge faced here consists in designing a controller for the robot orientation and its forward velocity, while, concurrently, stabilizing the unstable zero-dynamics, due to the undamped oscillation of the central body. An internal feedback control structure is proposed, composed of two imbricated loops, and based on an intrinsic dynamical property of the system, that would be referred to as the natural behavior of the system. Simulations of the controlled motion, using MATLAB/Simulink, are provided

Current interest in the design of novel architectures for parallel robots with less than six degrees of freedom (dof) has called for a revisiting of the dof determination of a multiloop kinematic chain. The paper attempts to shed some light on the issue by resorting to the theory of groups, as first proposed by Hervé in 1978. The concepts, illustrated with various examples, should help robot designers produce novel architectures that would be difficult to devise otherwise.

Robotic wrists are commonly used in manipulators for applications that require a large dexterous workspace. Although bevel-gear wrists are widely used in industrial manipulators due to their simple kinematics and low manufacturing cost, their gear trains function under rolling and sliding, the latter bringing about noise and vibration. Sliding is inherent to the straight teeth of the bevel gears of these trains. To alleviate these drawbacks, a wrist with cam-roller pairs under pure rolling is proposed here. This paper reports the design of an innovative robotic pitch-roll wrist using multi-lobe cams. The wrist has two degrees of freedom and consists of two roller-carriers (RCs) driving a multi-lobe cam to produce roll and pitch motions. The pure rolling between cam and rollers helps reduce the friction. Moreover, the cam transmission works with low backlash and high stiffness. In view of the kinematic performance, the wrist exhibits favorable features, including a singularity-free unlimited workspace.

In this paper, a study of a wheeled mobile robot (WMR) with omni-directional mobility and rover-like climbing ability is presented. Various rovers with robust locomotion design had been developed. However, the rover locomotion design with omni-directional mobility has not been addressed commonly. Shrimp suspension system and parallel bogies were employed as robot locomotion. It adapts to the terrain profile passively and it has better climbing capability than other rovers. To achieve a singularityless motion, the kinematic model of a wheeled mobile robot (WMR), including a platform equipped with six omni-directional wheels (ODWs), is formulated. The contents of this study are the design principle, kinematics, and motion studies. Also, experimental results have been employed to verify the model developed.

The work reported here was motivated by the development of manipulator systems comprising one long-reach, flexible-link subsystem, termed the macromanipulator, and a short-reach, rigid-link subsystem, called the micromanipulator. The flexural states of the macromanipulator, needed for controlling such systems effectively, are not usually measurable directly. For this reason, a state-estimation algorithm is proposed which uses the velocity and angular-velocity data of the micromanipulator base to estimate the flexural states of the macromanipulator. The velocity data are inferred from the acceleration signals delivered by a kinematically redundant set of triaxial accelerometers. The accelerometer signals are also utilized to calculate the translational and angular accelerations of the micromanipulator base, which are, in turn, used along with the dynamics equations of the micromanipulator to obtain the reaction force and moment acting between the two subsystems. Treating the force and the moment as inputs, the dynamics equations of the macromanipulator alone are used in the observer, thus reducing the order of the dynamics model. The state-output relations, on the other hand, are linearized in closed form to lower the computational cost. The relations thus obtained are then used in an extended Kalman filter to estimate the flexural states of the system.

We report on the control of semi-autonomous two-wheeled mobile robots undergoing large variations of the payload. These robots being underactuated, their control poses some challenges when resorting to a simple controller. The latter being a linear controller, its robustness with respect to model uncertainty needs to be investigated. To do this, we conducted a time-domain analysis of robustness of the foregoing controller with respect to parametric and unmodeled dynamics uncertainty. The controller, which is designed by a dominant second-order pole technique, turns out to be fragile (as opposed to robust) with respect to unmodeled dynamics uncertainty. In order to cope with this problem, a linear-quadratic regulator is designed. By numerical simulation we show that the latter features robustness with respect to both types of uncertainty.

Joint-coupling is introduced in the design and control of parallel manipulators for purposes of singularity management. The idea behind joint-coupling is to drive several joints with one single actuator by mechanical or electronic means, while preserving the mobility of the manipulator. Such joint-coupling can affect the condition of direct singularities of parallel manipulators through its coupling coefficients. As drivability of the end-effector is affected by the direct singularities, a nonlinear optimization method is proposed to determine the appropriate coupling coefficients according to a given set of task postures. The coupling coefficients obtained in this manner can shape the direct singularity loci of the manipulator to ensure a given set of manipulator postures (tasks) free from direct singularities. Examples are included to illustrate the concept of joint-coupling and singularity management.

The subject of this paper is a state-estimation algorithm which uses the twist data, velocity and angular velocity, of the base of a micro-manipulator, placed on the end-effector of its macro counterpart, to estimate the flexural states of the flexible links of the macro-manipulator. The twist data are inferred from the acceleration signals delivered by an accelerometer array $a kinematically redundant array of tri-axial accelerometers. The array signals can also be utilized to calculate the translational and angular accelerations of the micro-manipulator base, which are in turn used to obtain a set of dynamics equations for the macro-manipulator, thus reducing the order of the dynamics model. Next, the dynamics equations of the macro-manipulator and the state-output relations are linearized, the latter in closed form so as to lower the computational cost in a control loop. The relations thus obtained are then used in an extended Kalman filter to estimate the flexural states of the system.

We report on the controllability of a novel mobile robot which comprises two driving wheels and an intermediate body carrying the payload. By virtue of quasiholonomy, a concept introduced elsewhere, the robot is underactuated by design. One challenge here is the control of the motion of the intermediate body, which will tend to rotate about the wheel axis as the wheels are actuated. We prove that it is possible to completely control the robot using only the wheel motors, while tracking a desired trajectory, with apparent advantages in terms of cost, weight and efficiency. To do this, we show that every linearization of the robot dynamics model around an equilibrium point verifies the Kalman rank condition for controllability. Moreover, using modern results from nonlinear control theory, we prove that the robot is locally accessible and small-time locally controllable.

This paper describes a new 2DOF planar manipulator (PM) using coupled kinematics to manage the singularities. It is designed in order to overcome the singularity configuration of planar manipulators. Manipulators are composed of five rigid links, five revolute joints and two actuators each actuating two of input links coordinated fashion, what we term coupled kinematics. Coupled kinematics is an actuating arrangement. It may be defined as a pair of axial rotations, which are distributed by an actuator at varieties of parameters, which depend transmission ratios of mechanism. Using the geometrical approach, the position of end-effector is obtained. Matching the velocity of end-effector from two branches, the input and output velocities relation can be derived. Considering the coupled kinematics effects, Jacobian matrix is determined. We show that, by mean of proper tuning of the parameters of coupled kinematics, the singularity manifold can be substantially simplified. Finally, note that kinematic coupling can be implemented using mechanical or electronic hardware.

An accelerometer-array attitude-calibration method is proposed. Being based on the compatibility of rigid-body point accelerations, this method can be applied to determine and account for the accelerometer installation errors with a high degree of accuracy. It is assumed that the number or three-axis accelerometers in the array is redundant in order to help reduce the effect of sensor noise, thereby obviating the Kalman-filtering of the signals. Procedures are developed to calculate the angular velocity and acceleration as well as the attitude of the body, all in the body frame. It is demonstrated that even large attitude errors can be dealt with via off-line iterative applications of the scheme.

We report the holonomy analysis of three wheeled mobile robots. Two of these, Vuton II and Nomad, have full mobility and are claimed by their inventors to be holonomic. We show that, in fact, they are nonholonomic. Nevertheless, conditions are given under which these robots can be designed for quasiholonomy, a concept introduced elsewhere and recalled here. The third robot, Quasimoro, has a mobility of two and is unconditionally quasiholonomic. It is shown that if the wheel mechanism of a robot with full mobility is designed in such a way that the platform is much heavier than the wheel mechanism, then the underlying mathematical models are free of the nonholonomy term.

An algorithm for estimating the pose and twist of a rigid body using measurements made by a redundant number of on-board accelerometers is formulated. Redundancy helps reduce the effect of the accelerometer noise. This algorithm is based only on rigid-body kinematics because it is intended to be used for rigid bodies acted upon by forces and moments elusive to modeling. Procedures are developed to calculate the angular velocity and acceleration as well as the attitude of the body along with the velocity and position of the centroid of the pickup points, all in the body frame. It is shown that a small installation error can cause the integration results to become unstable. This instability is compensated for by means of a pose-measurement sensor.

Focusing on the instantaneous velocities of passive joints, a formulation approach is proposed for the instantaneous kinematics and singularity analysis of a class of three-legged parallel robots. Since only four 3/spl times/3 matrices need to be analyzed, the complexity of singularity analysis is significantly, reduced. Using the product-of-exponentials (POE) formula, the kinematic equations possess well-defined algebraic structures so that the instantaneous kinematics and singularity analysis algorithms can be readily and systematically formulated. Three types of singularities, i.e. the forward, inverse, and combined singularities, have been identified. A unified condition for various singularities is proposed. Significant geometric conditions are also presented for identifying singularity configurations that require simple computations.

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace of the mobile platform. Singularity analysis become important in design, motion planning, and control of parallel robots. Focusing on the instantaneous velocities of passive joints, a new formulation approach is proposed for the instantaneous kinematics and singularity analysis of a class of three-legged parallel robots. Excluding the passive spherical joints at the leg ends, the number of 1-dof passive joints in a three-legged, 6-DOF, parallel robot is three, which is only half of the number of active joints (six). Consequently, the complexity of the singularity analysis is significantly reduced because only four 3/spl times/3 matrices need to be analyzed. Using the product-of-exponential formula, the kinematic equations possess well-defined algebraic structures so that the instantaneous kinematics and singularity analysis algorithms can be readily and systematically formulated. Three types singularities, i.e., the forward, inverse, and combined singularities, have been identified. A unified condition for various singularities is proposed. Significant geometric conditions are also presented for identifying singularity configurations that requires simple computations.

SCARA denotes a class of 4-DOF manipulators that exhibit a finite stiffness in four directions of their motion space, while being infinitely stiff in the remaining two directions. These four directions comprise translation along three axes and rotation about one single axis. Therefore, a SCARA is noncompliant in two directions of rotation. SCARA systems were originally developed for assembly tasks. We term here any motion with the foregoing features a SCARA motion. Current manipulators producing this class of motions are invariably designed with a common architecture, namely, three revolutes and one prismatic joint, the latter being indistinctly collocated either at the proximal to the base or at the distal joint. We introduce here a novel architecture producing SCARA motions that is based on what is known as a II-joint, as introduced elsewhere. The kinematics of this manipulator is fully discussed.

The workspace of REDIESTRO, a seven-axis manipulator with isotropic architecture, is evaluated numerically. Figures of merit such as volume, cross-section area, and dimensional ratio, are given. A parametric study of these figures is included.

The hand-eye problem consists in determining the relative pose between two coordinate frames fixed to the same rigid body from measurements of the poses attained by these two frames, as the body moves. In robotics this problem arises when two frames are attached to the end-effector (EE), one of these at the gripper, the other to a sensor such as a camera or a laser range-finder. Various procedures have been proposed to solve this problem when perfect pose measurements are available at a pair of EE poses, the treatment of noisy measurements being a current research topic. Solutions proposed for the case of perfect measurements require an iterative procedure based on the singular-value decomposition, which itself relies on iterative procedures. The treatment of noisy measurements has led to offline least-square solutions. It is shown in this paper that, based on an invariant formulation of the problem at hand, a solution is possible that relies on recursive linear least squares. Thus, the procedure lends itself to an online implementation, as demonstrated here with experimental results. A major difference between the proposed procedure and those reported in the literature is that the latter are iterative; ours is recursive.

We study, for each of the possible joint-sensor layouts, the subspaces into which the motion of the hip-attachment points of parallel manipulators are completely measured. The projection of the motion of these points onto their subspaces allows us to write the underlying direct kinematics as a linear algebraic system constrained by the proper orthogonality of the rotation matrix. Although the solution of this problem requires a nonlinear technique, we propose a linear procedure that provides what we term a polar least square estimate. The resulting procedure is fast, robust to measurement noise, and produces estimates with about the same accuracy as a nonlinear procedure.

In this paper we decouple the translational and rotational degrees of freedom of the end-effector of parallel manipulators, and hence, decompose the direct kinematics problem into two simpler subproblems. Most of the redundant joint-sensor layouts produce a linear decoupling equation expressing the least-square solution of position for a given orientation of the end-effector. The resulting orientation problem can be cast as a linear algebraic system constrained by the proper orthogonality of the rotation matrix. Although this problem is nonlinear, we propose a procedure that provides what we term a decoupled polar least-square estimate. The resulting procedure is fast, robust to measurement noise, and produces estimates with about the same accuracy as a procedure for nonlinear systems if sufficient redundancy is used.

The subject of this paper is a special class of closed chain manipulators. First, we analyze a family of two-degree-of-freedom (DOF) five-bar planar linkages. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. It is shown that the loci of points of the workspace where the condition number of the direct-kinematics matrix remains constant, i.e., the isoconditioning loci, are the coupler points of the four-bar linkage obtained upon locking the middle joint of the linkage. Furthermore, if the line of centers of the two activated revolutes is used as the axis of a third actuated revolute, then a 3-DOF hybrid manipulator is obtained. The isoconditioning loci of this manipulator are surfaces of revolution generated by the isoconditioning curves of the 2-DOF manipulator, whose axis of symmetry is that of the third actuated revolute.

Space manipulators mounted on an on-off thruster-controlled base are envisioned to assist in the assembly and maintenance of space structures. When handling large payloads, manipulator joint and link flexibility become important, for they can result in payload-attitude controller fuel-replenishing dynamic interactions. In this paper, the dynamics model of an N-flexible-joint space manipulator is developed. The model of a three-flexible-joint manipulator mounted on a six-degree-of-freedom spacecraft is used to compare three different on-off thruster attitude control systems. Two variations of a classical control scheme are suggested to minimize such undesirable dynamic interactions, as well as thruster fuel consumption.

The notions of manipulator layout, layout center, layout length, and layout conditioning for any serial-type robotic manipulators are discussed. The motivation behind these concepts is the devising of a kinetostatic performance index to serve in the optimum dimensioning of the geometric parameters of serial manipulators. Based on these definitions, a measure of manipulator conditioning is devised that is highly suited for the intended tasks of manipulator design. Moreover, this performance index is substantially less expensive to compute than other measures of kinematic conditioning.

The subject of this paper is the kinematic analysis of a hand controller at the displacement level. The device is a six degree-of-freedom hybrid mechanism comprising two modules, each with three degrees of freedom. Based on the proposed kinematic model of the mechanism, we derive the necessary relations between the Cartesian coordinates of the end-effector and the joint variables.

Using redundant sensors, the direct kinematics of general parallel manipulators is here decoupled and reduced to an orientation problem only. The accuracy of the decoupling depends on the condition number of a decoupling matrix. The conditions under which this matrix is isotropic are derived and illustrated with a numerical example.

With regard to planar parallel manipulators, a general classification of singularities into three groups is introduced. The classification scheme relies on the properties of the Jacobian matrices of the manipulator at hand. The Jacobian matrices of a general class of planar parallel manipulators are derived and the three types of singularities are identified for them. This class contains 20 manipulators constructed with three different combinations of legs of the PRR, PPR, RRR and RPR types, P and R representing prismatic and revolute pairs, respectively.

In this paper, the dynamics of a three-degree-of-freedom (3-dof) spatial parallel manipulator with flexible links is studied. Finite elements are used for discretization of the flexible links, while the Euler-Lagrange formulation is used to derive the equations of motion of the uncoupled links. The equations of motion of all the links are then assembled to obtain the governing equations of the manipulator. The method of the natural orthogonal complement is used to eliminate the constraint forces and to derive the minimum number of equations of motion. To highlight the link flexibility effect, the governing equations of motion are used in a simulation of the manipulator at hand for both rigid and flexible-link models.

Harmonic drive gears, of extensive use in robotics, exhibit a non-smooth torque transmission characteristic that significantly influences the dynamic behavior of the driving and driven elements. In this paper, the authors propose a mechanical model for the joint transmission unit that takes into account compliance, dynamic friction, static friction (startup torque) and hysteresis, the last two items also depend on the load history of the harmonic drive. Based on a series of quasistatic and stationary dynamic experiments, the authors describe a scheme to identify all necessary parameters. Finally, the quality of the model and parameters is verified experimentally with respect to its dynamic behavior by driving the actual system and the model with the same input and comparing the output signals.

This paper presents a spline-based solution method for the inverse kinematics of hyper-redundant manipulators. The reference or backbone curve, that describes the macroscopic geometric shape of the manipulator is modelled by cubic and quintic piecewise parametric spline segments. A procedure for the coordinate frame distribution is proposed that allows any desirable rotation to be deployed about the backbone curve. Moreover, control points are used to determine the optimum shape and to change the length of the manipulator. The proposed solution method is general and applicable to non-extensible as well as extensible planar or spatial hyper-redundant manipulators with different morphologies.

Space manipulators mounted on an on-off thruster-controlled base are envisioned to assist in the assembly and maintenance of space structures. When handling large payloads, manipulator joint and link flexibility become important for it can result in payload-attitude controller fuel-replenishing dynamic interactions. In this paper, the dynamic behavior of a flexible-joint manipulator on a free-flying base is approximated by a single-mode mechanical system, while its parameters are matched with available space-manipulator data. Describing functions are used to predict the dynamic performance of three alternative controller/estimator schemes, and to conduct a parametric study on the influence of key system parameters. Design guidelines and a particular state-estimator are suggested that can minimize such undesirable dynamic interactions as well as thruster fuel consumption.

The effect of redundant sensors in the solution of the direct kinematics of general parallel manipulators is studied here, for purposes of online implementation. We describe three measurement conditions under which the kinematic relations are linear and hence, a linear decoupling of the position and orientation of the direct kinematics is possible. For each condition, a decoupling equation is derived and used to reduce the direct kinematics to an orientation problem only. The latter is solved by resorting to the polar-decomposition theorem. The numerical accuracy and efficiency of the procedure are also investigated.>

In this paper we study the velocity and acceleration relations of a novel redundant parallel manipulator. Through this study, we derive the Jacobian matrices of the inverse and direct velocity problems. Moreover, we introduce two practical designs that are kinematically equivalent to the ideal manipulator. The proposed manipulator has potential to be used in a wide range of applications from space robotics to highly dexterous flight simulators.>

Presented in this paper is a new platform-type manipulator that is parallel and kinematically redundant. The use of redundancy not only increases the workspace, but also helps in coping with singularities and improves dexterity. A complete kinematic model of the structure is presented in this paper, that is used for its mobility, and its direct and inverse position analyses.>

The kinematic design of redundant seven-axis manipulators is addressed. It is shown that isotropic seven-axis manipulators are possible. Three different optimum solutions are presented: first, a nonlinear minimization problem is solved which, in effect, renders the Jacobian matrix fully isotropic. Next, it is argued that, despite the fully isotropic feature of the first solution, some of its structural features can be improved. This leads to pre-assigning some of the parameters defining the structure of the manipulator, resulting in a system of 21 nonlinear equations in 21 unknowns. As the second solution, the Hartenberg-Denavit parameters of an isotropic manipulator are then obtained by solving the said system of nonlinear equations. Further constraints to make the manipulator structure anthropomorphic yield a third solution. This last solution gave rise to a manipulator which is not fully isotropic but is very close to isotropy, and exhibits a greater resemblance to the structure of the human arm.>

Various methods of implementing forward and inverse kinematics of six-axis industrial robots are analyzed from the viewpoint of numerical conditioning and convergence speed both close to a solution and away from it. Computational complexities are derived in terms of the number of arithmetic operations and comparisons are made by observing the actual CPU time consumption. The formulations presented make use of different sets of invariants describing the orientation of the gripper. It is shown that, in inverse kinematics, there is a tradeoff between numerical stability and computational speed.>

The real-time control of cooperating manipulators, mechanical hands, and walking machines involves the optimization of an underdetermined force system subject to both equality and inequality constraints. The inequality constraints arise as a result of passive frictional contacts in systems that depend on these for force transmission or when taking into account the limited torque or force capability of the actuators. Since the results of the force optimization are used to provide force or torque setpoints for the actuators, they must be obtained in real time. A technique for solving a quadratic optimization problem with equality and inequality constraints is presented for this application. The technique is compared with linear programming schemes to show its superior performance in terms of the speed and quality of the solution. The technique is well suited to problems where the solution can change discontinuously in time, as is the case with the systems considered due to changes in their topology.>

The architecture singularity of platform manipulators is considered with reference to a class of six-DOF (degree-of-freedom) parallel manipulators. It is pointed out that an architecture singularity usually spans the whole workspace or a significant part thereof, which makes it very difficult to implement control or singularity-avoidance strategies. Several groups of singular architectures are reported, with comprehensive theoretical proofs. This work can serve as a guide for the optimum design of parallel manipulators in the sense of achieving optimum kinematic and force-transmission performances.>

Robotic systems whose kinematic structure varies during their task are discussed. When the system's kinematic structure changes large discontinuities may occur in the solution to its inverse dynamics problem. These discontinuities can be traced to discontinuous changes in the coefficients of the dynamics equations which describe the system's behavior. When this change occurs on the left-hand side of the equations, it corresponds to a change in the kinematic structure of the system. When the change occurs on the right-hand side, it corresponds to a collision between two constituent objects in the system. Since these systems are redundantly actuated, the solution to their inverse dynamics problem may be chosen according to an optimality criterion. Two methods are presented to specify the optimization problem to reduce the effect of the discontinuities-one introduces rate-dependent terms in the objective function while the other positively limits the rate of change of the solution.>

The real-time control of cooperating manipulators, mechanical hands, and walking machines involves the optimization of an underdetermined force system subject to both equality and inequality constraints. The inequality constraints arise as a result of passive frictional contacts in systems that depend on these for force transmission, or when taking into account the limited torque or force capability of the actuators. Since the results of the force optimization are used to provide force or torque setpoints to the actuators, they must be obtained in real time. A technique is presented for solving a quadratic optimization problem with equality and inequality constraints for this application. The technique is compared with linear programming to show its superior performance in terms of speed and the quality of the solution.>

An approach to parameter estimation of robot dynamic models, in particular inertial terms, using symbolic computations is presented. The approach makes use of a class of manipulator test motions whose definition is more general than in previous works. Methods for analyzing the symbolic structure of these test motions are presented and, in particular, an approach to motion determination providing good excitation of inertial parameters is introduced. An overall strategy for identifying all base inertial parameters of dynamic model is outlined.>

The concept of dynamic isotropy, a measure of the dynamic performance of manipulators, is presented. An associated index, the dynamic conditioning index, is defined to describe this concept quantitatively. This index measures the dynamical coupling and numerical stability of the generalized inertia matrix of a manipulator in its dynamics model. Reduction of this index weakens the dynamic coupling while increasing the numerical stability of the dynamics model, which leads in turn to an improvement of the robot performance for simulation and control under dynamical conditions. The concept can be used as a criterion for manipulator performance and design optimization. The application of this concept to inverse kinematics of redundant manipulators and to the optimum trajectory planning of nonredundant manipulators is illustrated with two examples.>

The different kinds of singularities encountered in closed-loop kinematics chains are analyzed. A general classification of these singularities in three main groups, which is based on the properties of the Jacobian matrices of the chain, is described. The identification of the singular configurations is particularly relevant for hard automation modules or robotic devices based on closed kinematic chains, such as linkages and parallel manipulators. Examples are given to illustrate the application of the method to these mechanical systems.>

Invariant concepts are applied in connection with the redundant sensing of physical quantities in robotics-related applications. It is shown that, by utilizing the properties of invariant quantities associated with physical scalar, vector, and tensor variables, it is possible to verify the compatibility of measurements and, in some cases, to determine the relative orientation of the coordinated frames attached to each of the various sensors. A numerical example was introduced to illustrate the benefits of invariant concepts that led to the determination of the relative orientation of two different coordinate frames attached to the same rigid body by sheer matrix multiplications, thereby eliminating the complexity of nonlinear-equation solving. Invariance is shown to be applicable to compatibility verification and instrument calibration.>

The authors establish why redundant actuation situations arise, the relationship of redundant actuation to time-varying topologies, and the desirability of redundant actuation. Various techniques are then outlined for solving the optimal force distribution problem, to obtain force setpoints for the controller in real time. Although direct substitutions is by far the fastest of these, its implementation requires a careful monitoring of numerical degeneracies. Solution of the problem using orthogonal decomposition is recommended as it provides the opportunity to introduce inequality constraints, which are important in many problems. An effective technique is introduced for smoothing the discontinuities in the optimal solution, which result from the discontinuous topology.>

A systematic method for the kinematic and dynamic modeling of a two-degree-of-freedom (DOF) automatic guided vehicle (AGV) is presented. This type of methodology can be used to analyze, design, simulate, and control any kind of rolling robots. The concept of orthogonal complement is used to develop the dynamical equations of motion. The vehicle is analyzed for simulation purposes. Simulation results are reported. It is shown that, using the natural orthogonal complement of the matrix of velocity constraint equations, it is possible to derive systematically the Euler-Lagrange equations of motion of nonholonomic robotic mechanical systems. Moreover, the introduction of the orthogonal complement leads naturally to an efficient computational algorithm.>

An adaptive control method for linearized models of robotic manipulators is presented. First, the highly coupled nonlinear dynamical equations of robotic manipulators are linearized. Based on the linearized equations, the controllers are designed so as to render the feedback model a prescribed second-order stationary system, under the assumption that the deviations of position, velocity, and acceleration from their nominal values are small. A recursive least-square identification scheme is used to perform the online parameter estimation for the feedback gains of the controllers, instead of estimating the inertial parameters of the robotic manipulator themselves. The arising algorithm is much simpler and the required computations are reduced, when compared with a similar scheme (see C.S.G. Lee and M.I. Chung, 1984). Simulation of a PUMA 600 robotic manipulator under errors in the inertial parameters between 5% and 15% shows that the position and velocity errors are within reasonable limits.>

The offline planning of Cartesian trajectories of three-degrees-of-freedom (3-DOF) spherical wrists is considered. Motions undergone by such wrists are regarded as points on the surface of the unit sphere centered at the origin of the four-dimensional space of the linear invariants of the rotations involved. The projection of the sphere onto the three-dimensional space of the linear vector invariant of the rotation sensor is shown to be a solid unit sphere centered at the origin of the three-dimensional space. Thus, a rigid-body rotation given as a smooth function of time appears as a smooth curve within the unit sphere of this space. A one-to-one relation between the time derivative of this 3-D vector and the angular-velocity vector yields the kinematic interpretation of the velocity of the point tracing that curve. This concept is applied to a problem of trajectory planning for robotics pick-and-place operations using a spline-based concept of curve synthesis introduced elsewhere.>

Trajectory planning of robot motions for continuous-path operations is formulated in configuration space, resorting to the intrinsic properties of the path traced by point of the end effector. It is shown that, by referring the orientation of the end effector to a unique orthogonal frame defined at every point of the aforementioned path, a systematic procedure for trajectory planning in configuration space is derived. The computations required to determine the angular velocity and angular acceleration of the path frame reduce to computing the Darboux vector of the path and its time derivative.>

A spline-based method of programming smooth trajectories for pick-and-place operations is introduced. Unlike continuous-path operations, which impose a unique Cartesian trajectory, an infinite number of smooth trajectories can be described between any given pick and its corresponding place configuration. The method begins with the mapping of the pick and the place configuration in Cartesian space into joint-coordinate space, using a general-purpose inverse kinematics package that handles singularities and redundancies. Next, a trajectory, composed of a C/sup 2/-continuous, periodic cubic spline segment, is defined between the pick and the place configurations in the joint-coordinate space. It is demonstrated that C/sup 2/-continuity will prevail in Cartesian space as well. The software implementing this method includes a graphics package as well as an interface to an offline programming system to realize the synthesis of the actual robot motion. Details of the procedure are illustrated with a numerical example applied to a commercial industrial robot.>