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Design and optimal control of a dual-stage Stewart robot is performed in this paper using sequential optimal feedback linearization method considering the dynamics of the jacks. Considering the limited length of the jacks, the possible dynamic workspace of this robot is extremely limited. Dual-stage platform version of this robot is designed and proposed in this paper to improve this limitation. As a result, the dynamic workspace of the robot is increased by increasing the degrees of freedom (DOFs) of the system. Modeling and dynamics of the new proposed system are developed considering the dynamics of the jacks. Besides, the robot is controlled with the highest accuracy and the lowest energy using an optimal control strategy based on Feedback-Linearized Quadratic Regulator (FLQR). Two sequential controlling loops are employed for simultaneous control of the joint space and work space of the robot. The efficiency of the proposed manipulator toward increasing the workspace of the robot and also the...

In this paper, a geometrical expression to delineate the sum of tensions (i.e. minimum 1-norm tensions) of 2-DoF planar cable-driven parallel manipulators (CDPMs) is proposed and proofed, which can be used to reduce calculation time of workspace determination. Furthermore, this paper also presents a systematic analysis on the relation between cable tension and workspace by means of convex analysis. In order to obtain wrench-feasible workspace, a unified and feasible algorithm is adopted in simulation examples of spatial CDPMs with different configurations, which demonstrate that the proposed method is valid and straightforward to calculate workspace.

In this paper, we present a method, based on interval analysis, to solve the problem of designing cable-driven parallel manipulators (CDPMs) for a desired workspace. The constraint of having positive cable tensions ensuring the equilibrium of the platform has to be satisfied within the given workspace. The proposed algorithm is based on interval analysis, which covers the entire workspace and hence guarantees a singularity-free workspace. Furthermore, the algorithm is capable of finding all possible solutions for this problem and an optimal one is selected according to the user-defined criterion. Two examples are selected to show the efficiency of the developed algorithm in solving this complex problem. The first one deals with the design of a planar CDPM and the second one considers a spatial CDPM. In both cases, the algorithm succeeded to find all possible designs from which the designer can select a solution that fits best his application.

This paper discusses the tracking trajectory in the workspace of rigid manipulators using distributed adaptive control strategy. This control strategy consists of two steps; first, the classical MIMO dynamical system is decomposed into a set of nonlinear interconnected subsystems. Each subsystem has one joint. Second, the distributed adaptive control strategy is introduced. This control strategy consists of controlling the last subsystem while assuming that the remaining subsystems are stable. Then, going backward to the second last subsystem, the same strategy is applied and so on until the first one. The system parameters are assumed to be unknown. An adaptive control is used to estimate these parameters. Indeed, the unknown parameters existing in the equation of motion of the last subsystem are first estimated and the control law is developed based on these estimated parameters. Then, going backward to the before last joint, the control law is developed using its own estimated parameters and th...

We proposed a design method for pediatric surgical robots that evaluates the workspace and view information in computer simulator before the actual robot is developed. In this study, we investigated a suturing task in a virtual environment using forceps manipulators with different mechanical parameters. We reproduced the surgical workspace for congenital esophageal atresia and measured the working volume and invisible area to obtain suitable parameters for the suturing task. We also calculated the suitable mechanical parameters using Pareto optimal solution method and verified the mechanical parameters in Pareto optimal solution. We verified from the experimental results that there is a trade-off between the working volume and invisible area during the suturing task. Moreover, we determined from the calculation results that the mechanical design of the forceps manipulator is influenced by the invisible area during the suturing task. Finally, we confirmed that it is possible to obtain suitable para...

Maximizing the singularity-free workspace of parallel manipulators is highly desirable in a context of robot design. So far, no work has been found to address the maximal singularity-free orientation workspace over a position region. In practice, this type of workspace is interesting because a mechanism often works in a range of positions. This work focuses on the Gough–Stewart platform. An optimal position at which the mechanism holds the maximal singularity-free orientation workspace is determined. This optimal position lies on the line which is perpendicular to the base and passes the centroid of the base. Considering the symmetry, a parallelepiped with centre at the determined optimal position could be an interesting working position region for the Gough–Stewart platform. Two algorithms are presented to compute the maximal singularity-free orientation workspace over such an interesting position region. An example is provided for demonstration.

In this paper, an imitation learning framework that includes an evolutionary process based on principal component analysis (PCA) is presented. The framework comprises offline and online processes. In the offline process, human demonstrations are used to develop a motion database. The database covers the workspace and includes robot properties. The evolved database has a clustered structure for efficiency. In the online process, a robot can generate desired motions using a real-time motion reconstruction method based on PCA. The performance of this method is verified through two case studies. The proposed framework is applied to the generation of reaching motions to an object on a table and a shelf.

This research aims to solve online collision avoidance problem of two manipulators with independent controller. Since industrial robot controller is a closed commercial system, trajectory generation part of robot controlling is always proprietary or unknown. Thus, this paper proposes a collision avoidance system of two manipulators which are controlled by point-to-point (PTP) commands, in condition that the internal of robot controller is unknown and unchangeable. Based on this condition, collision avoidance is supposed to be realized by online scheduling of these PTP controlling commands. This paper proposes the collision avoidance method that assumes the three-dimensional common workspace between two manipulators can be partitioned into many subregion elements. And with managing these subregion elements, which are occupied by robot motion, PTP commands are scheduled to adjust execution timing for collision avoidance. A deadlock problem caused by the partition of the workspace is also taken into consideration in the method. And the effectiveness and efficiency of the method have been verified by simulations and experiments.

This paper is dealt with dynamic analysis of the wheeled mobile manipulators in the presence of moving obstacles considering optimal payload criterion. General dynamic formulation of the system was derived, and the moving obstacle avoidance strategy was proposed in terms of dynamic potential functions. The problem of dynamic motion planning and payload maximization was formulated using open-loop optimal control theory. Then, the indirect solution based on Pontryagin’s minimum principle was employed to solve the problem. Using the proposed method, complete nonlinear states and control constraints were treated without any simplifications such as linearizing the dynamics equations, discretizing the robot’s workspace, or parameterizing the solution. The proposed method will be useful for the system design and in the situation where the trajectories of obstacles are predefined. Finally, capability and applicability of the proposed method were investigated by the number of simulations on a two-link mobile manip...

Cable-driven parallel manipulators (CDPMs) provide an easy way to achieve large workspace since flexible cables can be readily stored on reels. Generally, cables are treated as massless and inextensible that can only be tensioned. But for large workspace applications, cable curve due to their self-weight must be considered. In this paper, a curved cable is modeled as the series of an inextensible parabolic cable and a flat elastic cable to accurately account for its curve effect. The stiffness and Jacobian matrices of CDPMs are derived, which provide quantitative representations of stiffness and dexterity of manipulators. An optimization model is presented to simultaneously improve the stiffness and dexterity by selecting proper sectional area of cables and other structural parameters. Numerical examples demonstrate the curve effect on the stiffness of manipulators and a remarkable improvement of the performances can be obtained by properly determining structural parameters.

This article focuses on the relation between workspace path geometry and the timing along the path, obtained via simple timing generators yielding constant end-link speed motion, natural motion, and two types of globally optimized joint velocity motions. The generators are designed within the Singularity-Consistent framework developed originally to tackle motion control in the vicinity of kinematic singularities. A comparative study highlights how performance expressed in terms of various kinematic and dynamic criteria of local (peak joint velocity and torque) and global (joint velocity/torque uniformity and total mechanical power) nature is influenced by the curvature of the path image in configuration space and by the vicinity of singular configurations. Results from simulations with a simple planar 2R limb and a spatial 3R positioning limb following linear and circular paths are presented.

A novel method is proposed for real-time solution of direct kinematics problem of Stewart platform (SP) using six measurements on three legs’ joints consisting of the rotations of three legs in two directions. After the application of the method on a laboratory sample SP, it is observed that the method is preferable to the conventional method that uses the length measurements of all six legs, in the grounds of industrial applicability. It is due to simpler implementation, less expense, easier maintenance, and stress-free assembly. The algorithms of both forward and inverse kinematics are fully derived based on geometric relationships between the platform states and the measurement data. The sensitivity to the measurement errors is analyzed theoretically and is applied through a computer simulation to several configurations of the sample SP which are uniformly distributed in the workspace. The variances of measurement errors for those configurations are compared between the conventional and proposed method...

There are many applications for which reliable and safe robots are desired. For example, assistant robots for disabled or elderly people and surgical robots are required to be safe and reliable to prevent human injury and task failure. However, different levels of safety and reliability are required for different tasks so that understanding the reliability of robots is paramount. Currently, it is possible to guarantee the completion of a task when the robot is fault tolerant and the task remains in the fault-tolerant workspace (FTW). The traditional definition of FTW does not consider different reliabilities for the robotic manipulator's different joints. The aim of this paper is to extend the concept of a FTW to address the reliability of different joints. Such an extension can offer a wider FTW while maintaining the required level of reliability. This is achieved by associating a probability with every part of the workspace to extend the FTW. As a result, reliable fault-tolerant workspaces (RFT...

International audience; The optimal design of parallel kinematic machines goes through two fundamental stages. The first one concerns the structural synthesis. It enables, a priori, to determine the choice of families of the most adapted architectures according to the desired applications such as flight simulators, machine-tools, medical applications, etc. This can be done by applying several techniques such as: screw theory, Lie groups, graph theory, finite element method, etc. The second one concerns the dimensional synthesis and aims to determine the dimensions of the architecture that has been selected during the structural synthesis. This stage remains a major task because the criteria of performance of a given architecture are strongly dependent on its sizing. In this paper, we present a dimensioning methodology of the architectural parameters of the 6-dof UPS (U: universal joint, P: prismatic joint, and S: ball-and-socket joint) parallel manipulators (the positions of the attachment points of the actuators on the base and mobile plate as well as the radius of the base and the mobile plate). The problem will be formulated as a multiobjective optimization problem (MOOP) by taking into account simultaneously several criteria of performance such as the workspace, kinetostatic performances, stiffness, and dynamic dexterity. The SPEA-II genetic algorithm is adopted to solve this type of MOOP.

High-speed visual servoing of manipulators including flexibilities is considered. In the proposed methodology, a model taking into account all the dynamics of the system is identified from the measurements usually available in visual servoing. This model is valid around the working position of the arm and can be easily recomputed after camera displacement. Two multivariable strategies are proposed for controlling the position of the end-effector: generalized predictive control and control. Comparative simulation and experimental results on a 2-degrees of freedom planar manipulator are given. A robustness evaluation step shows that the available working space is quite large.

When performing femur fracture reduction surgery, both the patient and surgeon are exposed to a great amount of radiation, which is harmful to their health. In order to reduce such radiation from the usage of an image intensifier, various robots have been proposed for femur fracture reduction surgery. Most of these robots are based on serial architecture. The low transportable load and poor accuracy are both inherent in serial robots, which makes them inappropriate for femur fracture reduction. Some parallel robots based on the 'Stewart platform' have also been developed for femur fracture reduction, but their restricted workspace limits their applicability and accessibility. To balance the accuracy, payload and workspace, a new robot system is reported in this paper. The proposed robot system consists of a 2-d.o.f. device and a 6-d.o.f. hybrid robot. The 2-d.o.f. device is used for distraction, which requires a very large force. The hybrid robot is used to manipulate a bone fragment for alignment and fix...

The growing interest in the use of parallel manipulators in machining applications requires clear determination of the workspace and dexterity. In this paper, the workspace optimization of a Tricept parallel manipulator under joint constraints is performed. This parallel manipulator has complex degrees of freedom and, therefore, leads to dimensionally inhomogeneous Jacobian matrices. Here, we divide the Jacobian entries by units of length, thereby producing a new Jacobian that is dimensionally homogeneous. By multiplying the associated entries of the twist array to the same length, we made this array homogeneous as well. The workspace of the manipulator is parameterized using several design parameters and is optimized using a genetic algorithm. For the workspace of the manipulator, local conditioning indices and minimum singular values are calculated. For the optimal design, it is shown that by introducing the local conditioning indices and minimum singular values, the quality of the parallel manipulator ...

In this paper, we propose a novel numerical approach and algorithm to compute and visualize the workspace of a multifingered hand manipulating an object. Based on feasibility analysis of grasps, the proposed approach uses an optimization technique to first compute discretely the position boundary of the grasped object and then calculate the rotation ranges of the object at specified positions within the boundary. In other words, workspace generation with the approach is fulfilled by obtaining reachable boundaries of the grasped object in the sense of both position and orientation, and the discrete boundary points are computed by a series of optimization models. Unlike in workspace generation of other robotic systems where only geometric and kinematic parameters of the robots are considered, all factors including geometric, kinematic and force-related factors that affect the workspace of a hand–object system can be taken into account in our approach to generate the workspace of multifingered manipulation. ...

Various products and patents have been established with regard to telescopic mechanisms over a long period of time. However, to the best of our knowledge, with reference to motional characteristics, few studies have been reported on a telescopic mechanism that is capable of bidirectional extension. Moreover, as we wish to point out here, such a kind of mechanism has received little attention due to the absence of practical applications. However, in the case of blast-cleaning and painting in double-hulled structures in shipbuilding, the bidirectional-extension mechanism seems to be a worthwhile subject for investigation since it will be of great help in the execution of suggested tasks for the entire transverse web floor with a range of 2–3 m. Since the self-traveling robotic platform is located on longitudinal stiffeners whose heights range from 400 to 800 mm, the manipulator to be installed on the robotic platform should have a bidirectional stroke to continuously approach the upper and lower sections of...

For a robotic system, the complete description of the end-effector motion requires six independent parameters, while the desired end-effector motion for a task often needs less than 6 d.o.f. Therefore, the end-effector motion can be divided into desired motion and undesired motion. The end-effector motion is transformed from the joint motions. In this paper, the efficiency of the joint motions to implement the desired motion is investigated and a new concept called motion purity is proposed to measure this efficiency. The new concept is more comprehensive and direct than other existing performance measures, such as the volume of workspace and manipulability. It is appropriate as a design objective at various phases in designing a robotic mechanism. The tripod machine tool is studied and its structure is optimized from the viewpoint of the motion purity.

This paper addresses the orientation-singularity analysis and the nonsingular orientation-workspace computation of the semi-regular Stewart–Gough platform manipulator (SRSGPM). Based on the half-an...

Using the common serial robot or parallel robot it is difficult to implement computed tomography (CT) guided surgery in a limited workspace. A novel hybrid robot with 9 d.o.f. is presented, the det...

Identification of a workspace and its boundary is an important issue in the design and performance evaluation for manipulators, especially for the exoskeleton rehabilitation robot. This paper estimates roughly the volume covering the workspace of a manipulator and then meshes the volume into a lot of small cubes. A distance-weight and a three-dimensional (3-D) distance-weight matrix are defined. The distance-weight describes the point distribution around the corners of 3-D cubes and the 3-D distance-weight matrix characterizes the degree of point distribution in the workspace. The smoothing procedure and boundary curve extraction of grey-scale images available in mathematic morphology are employed to process the 3-D distance-weight matrix. A general algorithm of the workspace boundary extraction is proposed. The set of boundaries of all slices of the workspace forms the manipulator's workspace boundary. Two examples are given to verify the workspace boundary extracting algorithm. The workspace boundary of...

Accurate robot dynamic models require the estimation and validation of the dynamic parameters through experiments. To this end, when performing the experiments, the system has to be properly excited so that the unknown parameters can be accurately estimated. The experiment design basically consists of optimizing the trajectory executed by the robot during the experiment. Due to the restricted workspace with parallel robots this task is more challenging than for serial robots; thus, this paper is focused on the experiment design aimed at dynamic parameter identification of parallel robots. Moreover, a multicriteria algorithm is proposed in order to reduce the deficiencies derived from the single-criterion optimization. The results of the identification using trajectories based on a single criterion and the multicriteria approaches are compared, showing that the proposed optimization can be considered as a suitable procedure for designing exciting trajectories for parameter identification.

The classical mapping methods were developed based on anthropomorphic robot hands. Normally, they are not applicable or cannot provide satisfactory performance if the robot hand is non-anthropomorphic. This paper presents a virtual circle mapping method dealing with the three-fingered non-anthropomorphic robot hand. The basic idea is to express the operator's motion by a virtual circle determined by the three fingertips. Four sets of parameters are used to describe the circle: circle radius, central angles, circle center and circle orientation. By transforming the four sets of parameters from the human frame to the robot frame, the information of relative positions between the fingertips is delivered. The robot fingertip positions are then computed according to the transformed parameters. The concept is introduced and implemented on a specific three-fingered non-anthropomorphic robot hand. The simulation results and the experiments have shown that the proposed method is able to obtain better workspace mat...

Given a planar workpiece R, the objective of region coverage is to find an ordered list of waypoints and the geometry of paths between consecutive waypoints along which the centroid of a sensor footprint can be moved to efficiently trace a minimal superset of R. We consider the problem of maximally parallelizing the coverage of a contiguous rectilinear region represented by P ∈ R by dividing P amongst η unmanned aerial vehicles (UAVs). The rates at which the UAVs can perform region coverage may differ. The optimum solution to this problem comprises a decomposition of P into η parts such that the cost C i of covering a part using UAV i is proportional to the relative rate at which the UAV can coverage. This problem, however, is NP-hard and we instead give a polynomial time algorithm for solving a closely related problem: divide P into η parts that are each rectilinear, contiguous and whose areas are in the ratio of relative capabilities of the UAVs. Following the division of P, each part is covered by the ...

This paper presents stiffness analysis of hexaslides, a class of parallel manipulators with six constant length legs, the base joints of which move along six distinct rail-axes. In the design of hexaslides for machine tool applications, stiffness as well as its variation within the workspace is important. The stiffness of any parallel kinematic machine and, thus, the accuracy depends on the pose of the tool platform. A stiffness model of a generic hexaslide is developed here considering the flexibilities in both the actuator and the legs of the hexaslide. The methodology adopted is based on the concept of the determination of stiffness of a group of serially connected linear springs. Based on the proposed model, the average stiffness and its variation along and about the Cartesian coordinate axes offered by three typical hexaslides, having the same foot print size, are estimated and compared. Other typical performance indices, i.e. workspace volume, workspace volume index (ratio of workspace volume to mac...

This paper proposes a self-reconfigurable planar parallel robot which is capable of reconfiguring itself to various types of planar parallel robots in the horizontal plane. The robot can change its workspaces by coupling and decoupling of a platform and two or more 2R open kinematic chains with second joints unactuated (limb). The platform should be light and therefore no additional actuators are used for reconfigurations. We have already shown that uncertainty singular configurations are appropriate for coupling of two limbs. This paper describes positive and negative aspects of the uncertainty singularity for coupling and decoupling. In addtion, decoupling needs to be carried out with more care than coupling. It must be considered to assure the safety of a decoupled limb and to prevent unexpected decoupling of other limbs. We propose feasible coupling and decoupling configurations for the proposed self-reconfigurable planar parallel robot. We also introduce our real robot and show its coupling mechanism...

Fault tolerance is an important aspect in the development of control systems for multi-legged robots since a failure in a leg may lead to a severe loss of static stability of a gait. In this paper, an algorithm for tolerating a locked joint failure is described in gait planning for a quadruped robot with crab walking. A locked joint failure is one for which a joint cannot move and is locked in place. If a failed joint is locked, the workspace of the resulting leg is constrained, but legged robots have fault tolerance capability to continue walking maintaining static stability. A strategy for fault-tolerant gaits is described and, especially, a periodic gait is presented for crab walking of a quadruped. The leg sequence and the formula of the stride length are analytically driven based on gait study and robot kinematics. The adjustment procedure from a normal gait to the proposed fault-tolerant crab gait is shown to demonstrate the applicability of the proposed scheme.

A new adaptive linear robot control system for a robot work cell that can visually track and intercept stationary and moving objects undergoing arbitrary motion anywhere along its predicted trajectory within the robot's workspace is presented in this paper. The proposed system was designed by integrating a stationary monocular CCD camera with off-the-shelf frame grabber and an industrial robot operation into a single application on the MATLAB platform. A combination of the model based object recognition technique and a learning vector quantization network is used for classifying stationary objects without overlapping. The optical flow technique and the MADALINE network are used for determining the target trajectory and generating the predicted robot trajectory based on visual servoing, respectively. The necessity of determining a model of the robot, camera, all the stationary and moving objects, and environment is eliminated. The location and image features of these objects need not be preprogrammed, mark...

In this paper we present a new, and extremely fast, algorithm for the inverse kinematics of discretely actuated manipulator arms with many degrees of freedom. Our only assumption is that the arm is macroscopically serial in structure, meaning that the overall structure is a serial cascade of units with each unit having either a serial or parallel kinematic structure. Our algorithm builds on previous works in which the authors and coworkers have used the workspace density function in a breadth- e rst search for solving the inverse kinematics problem. The novelty of the method presented here is that only the ' mean' of this workspace density function is used. Hence the requirement of storing a sampled version of the workspace density function (which is a function on a six-dimensional space in the case of a spatial manipulator) is circumvented. We illustrate the technique with both planar revolute and variable-geometry-truss manipulators, and briee y describe a new manipulator design for which this algorithm is applicable.

A new controller design framework for cooperating manipulators is considered in this paper based on a reliable controller design concept. The objective of this paper is to derive a set of controllers for cooperating manipulators, particularly those that can hand over an object. The key idea is to reformulate the original problem of coordinated control as a reliable stabilization problem, i.e. to design a set of controllers which can stabilize a plant both jointly and alone. By introducing a kind of strict force control scheme in the workspace, the reliably stabilizing controller design technique is applied to derive the controllers. Two contributions exist: (i) clarifying a class of the object which can be handed over by using the proposed control scheme and (ii) presenting a constructive design method of the controllers. Experimental results on the hand-over control of a spherical inverted pendulum with two 6 d.o.f. manipulators are included.

Mobile robots for advanced applications have to act in environments which contain moving obstacles (humans). Even though the motions of such obstacles are not precisely predictable, usually they are not completely random; long-term observation of obstacle behavior may thus yield valuable knowledge about prevailing motion patterns. By incorporating such knowledge as statistical data, a new approach called statistical motion planning yields robot motions which are better adapted to the dynamic environment. To put these ideas into practice, an experimental system has been developed. Cameras observe the workspace in order to detect obstacle motion. Statistical data is derived and represented as a set of stochastic trajectories. This data can be directly employed in order to calculate collision probability, i.e. the probability of encountering an obstacle during the robot's motion. Further aspects of motion planning are addressed: path planning which minimizes collision probability, estimation of expected time...

—This paper proposes a control algorithm for the scrollic (synchronously closing with rolling constraints) gripper in order to control the trajectory of an object grasped outside the workspace toward the center of the gripper. The gripper has fingers composed of two cylinders in parallel, the translation and rotation of which are independently driven by direct-drive motors. The algorithm is based on sensory information about angular displacements of the cylindrical fingers, i.e. rollers. In fact, the object has direct affects on the rollers and the displacements are actively collected by rotary encoders. That is, contact sense not by tactile sensors but by intrinsic angular sensors is utilized. The algorithm yields the gripper to reduce a dynamic decoupled behavior and makes it compliant not only to close but also to open during a close motion. The algorithm presents a high level of tolerance concerning uncertainties about the object's position, orientation, size, shape and weight. The kinematics, the des...

This paper proposes a third generation teleoperation system based on a status driven slave symbolically instructed by the master control panel. Furthering the first-generation joint-angle control techniques and second-generation coordinate transformation techniques, this system recognizes the target status specified by the operator by extracting the task status from visual sensors. The task environment is initially described via sensing points in the work environment and on the manipulated object. The relationships between the sensing points and the change of those relationships describes the task at hand. Operation can proceed in automatic mode where the system completely directs the slave or in shared mode where the system assists the operator by constraining the slave motion while the operator directs via a visual communication interface. Although status driven techniques offer several improvements in teleoperated control, this work explores the robustness and reliability provided in dynamic workspace ...

In multifingered grippers and multiarm manipulation systems it is possible to manipulate a grasped object by rolling the object along the contacting links. This affords greater versatility, a potentially larger workspace and the ability to adapt to external loads without regrasping. The reachable workspace, or the set of points that can be reached by a reference point on the object, is an important measure of performance. The functional workspace, a subspace of the reachable workspace in which the object can be held in a force-closed grasp, is also an important design consideration. In this paper, the reachable and functional workspaces and methods to determine their boundaries are studied. The basic idea is to determine extreme configurations using screw system theory and obtain the locus of the reference point as the system is moved through these configurations. Although this procedure has been used in an earlier paper, the modeling of rolling contacts and consideration of joint limits require a differe...

Tasks consisting of manipulating an object with two cooperating robots are studied from the standpoints of statics and kinematics; coordinates to describe these tasks are derived theoretically, on which forces, velocities, and positions are defined consistently. Based on those results, a hybrid position/force control scheme which distinguishes neither a master robot nor a slave robot is presented for the coordination of the two robots. In the static and kinematic analyses, the concept of a 'virtual stick' is introduced, which is used to make the motions of the two robots be considered at the centre of the object. Thus, use of the matrix pseudo-inverse technique decouples the motions into absolute and relative motions. Generalized forces, velocities, and positions are derived theoretically in those decoupled subspaces. These forces, velocities, and positions are symmetric functions of the jointspace forces, velocities, and positions. Therefore, the hybrid position/force control scheme using the workspace c...

The collision avoidance problem of a robot manipulator whose workspace includes moving objects is considered in this paper. It is shown that the proposed computer simulation system can be used in a dialogue mode with a designer to check whether or not collision with obstacles is avoided and to determine the appropriate movement.