Canonical parameterization of excess motor degrees of freedom withself-organizing maps

The problem of sensorimotor control is underdetermined due to excess (or "redundant") degrees of freedom when there are more joint variables than the minimum needed for positioning an end-effector. A method is presented for solving the nonlinear inverse kinematics problem for a redundant manipulator by learning a natural parameterization of the inverse solution manifolds with self-organizing maps. The parameterization approximates the topological structure of the joint space, which is that of a fiber bundle. The fibers represent the "self-motion manifolds" along which the manipulator can change configuration while keeping the end-effector at a fixed location. The method is demonstrated for the case of the redundant planar manipulator. Data samples along the self-motion manifolds are selected from a large set of measured input-output data. This is done by taking points in the joint space corresponding to end-effector locations near "query points", which define small neighborhoods in the end-effector work space. Self-organizing maps are used to construct an approximate parameterization of each manifold which is consistent for all of the query points. The resulting parameterization is used to augment the overall kinematics map so that it is locally invertible. Joint-angle and end-effector position data, along with the learned parameterizations, are used to train neural networks to approximate direct inverse functions.     

Task space control of a welding robot using a fuzzy coordinator

This paper introduces a fuzzy coordinator as a novel application of fuzzy controller. A control transformation from the task space to the joint space is required to control a robot manipulator in the task space. Because the actuators operate in the joint space while the manipulator is controlled in the task space. A conflict between two spaces is produced due to using an imprecise transformation. Fuzzy coordinator coordinates two spaces by modifying the control transformation affected by uncertainties. The fuzzy coordinator is designed simply and operates as a robust controller. The role of fuzzy coordinator is analyzed and illustrated in the robust control of a welding robot in the task space. A circular trajectory is planned for a welding task performed by a SCARA robot. The fuzzy coordinator is then used to improve the performance of control system affected by imprecise transformations including the imprecise path transformation and the approximated feedback linearization.     

Selection of near-minimum time geometric paths for robotic manipulators

A number of trajectory planning algorithms exist for calculating the joint positions, velocities, and torques which will drive a robotic manipulator along a given geometric path in minimum time. However, the time depends upon the geometric path, so the traversal time of the path should be considered again for geometric planning. There are algorithms available for finding minimum distance paths, but even when obstacle avoidance is not an issue, minimum (Cartesian) distance is not necessarily equivalent to minimum time. In this paper, we have derived a lower bound on the time required to move a manipulator from one point to another, and determined the form of the path which minimizes this lower bound. As numerical examples, we have applied the path solution to the first three joints of the Bendix PACS arm and the Stanford arm. These examples do indeed demonstrate that the derived approximate solutions usually require less time than Cartesian straight-line (minimum-distance) paths and joint-interpolated paths.     

Path-constrained control of a redundant manipulator in a task space

This study addresses the problem of controlling a redundant manipulator with both state and control dependent constraints. The task of the robot is to follow by the end-effector a prescribed geometric path given in the task space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results, carried out for a planar manipulator whose end-effector follows a prescribed geometric path given in a task space, illustrate the trajectory performance of the proposed control scheme.     

The power manipulability – A new homogeneous performance index of robot manipulators

Jacobian-based performance indices such as the manipulability ellipsoid, the condition number and the minimum singular value, have been very helpful tools both for mechanical manipulator design and for determining suitable manipulator postures to execute a given task. For a manipulator having complex degrees of freedom (translations and rotations), Jacobian matrix becomes non-homogeneous, i.e. it contains elements with different physical units; therefore, the evaluation of its determinant, eigenvalues or singular values needs the combination of quantities of different nature, which is physically inconsistent and moreover it corresponds to a noncommensurable system. In this paper, a new performance index of robot manipulators is proposed. It is fully homogeneous and it constitutes a physically consistent system whether the manipulator contains joints of different natures, or the task space combines both translation and rotation motion. The development is concerned with the study of power within the mechanism. Given that the power has the same physical units in translation and rotation, it can be used as a homogeneous or natural performance index of manipulators by examining the behaviour of its basic components namely, force and speed, at different kinematics configurations. Furthermore, the new concept of vectorial power is introduced, followed by to the quadrivector of apparent power, and leading to the final homogeneous performance index of the power manipulability (PM). This new approach matches perfectly with mechanisms having joints of different natures, as well as with a task space combining both translation and rotation.     

Optimal location of a general position and orientation end-effector's path relative to manipulator's base,considering velocity performance

The objective of the present paper is to introduce an offline algorithm searching for the optimal or suboptimal placement of a robot's base during workcell design, so that its end-effector can perform a position and orientation path following task of a given 3D curved path and orientation, maximizing the manipulator's velocity performance. The global index employed for this velocity performance optimization is the approximation of the minimum manipulator velocity ratio (AMMVR).     

Planning of collision-free paths for a reconfigurable dual manipulator equipped mobile robot

In this paper, we study the problem of finding a collision-free path for a mobile robot which possesses manipulators. The task of the robot is to carry a polygonal object from a starting point to a destination point in a possibly culttered environment. In most of the existing research on robot path planning, a mobile robot is approximated by a fixed shape, i.e., a circle or a polygon. In our task planner, the robot is allowed to change configurations for avoiding collision. This path planner operates using two algorithms: the collision-free feasible configuration finding algorithm and the collision-free path finding algorithm. The collision-free feasible configuration finding algorithm finds all collision-free feasible configurations for the robot when the position of the carried object is given. The collision-free path finding algorithm generates some candidate paths first and then uses a graph search method to find a collision-free path from all the collision-free feasible configurations along the candidate paths. The proposed algorithms can deal with a cluttered environment and is guaranteed to find a solution if one exists.     

Data-Driven Human-Robot Interaction Without Velocity Measurement Using Off-Policy Reinforcement Learning

In this paper, we present a novel data-driven design method for the human-robot interaction (HRI) system, where a given task is achieved by cooperation between the human and the robot. The presented HRI controller design is a two-level control design approach consisting of a task-oriented performance optimization design and a plant-oriented impedance controller design. The task-oriented design minimizes the human effort and guarantees the perfect task tracking in the outer-loop, while the plant-oriented achieves the desired impedance from the human to the robot manipulator end-effector in the inner-loop. Data-driven reinforcement learning techniques are used for performance optimization in the outer-loop to assign the optimal impedance parameters. In the inner-loop, a velocity-free filter is designed to avoid the requirement of end-effector velocity measurement. On this basis, an adaptive controller is designed to achieve the desired impedance of the robot manipulator in the task space. The simulation and experiment of a robot manipulator are conducted to verify the efficacy of the presented HRI design framework.      

Calculation of repeatable control strategies for kinematically redundant manipulators

A kinematically redundant manipulator is a robotic system that has more than the minimum number of degrees of freedom that are required for a specified task. Due to this additional freedom, control strategies may yield solutions which are not repeatable in the sense that the manipulator may not return to its initial joint configuration for closed end-effector paths. This paper compares two methods for choosing repeatable control strategies which minimize their distance from a nonrepeatable inverse with desirable properties. The first method minimizes the integral norm of the difference of the desired inverse and a repeatable inverse while the second method minimizes the distance of the null vectors associated with the desired and the repeatable inverses. It is then shown how the two techniques can be combined in order to obtain the advantages of both methods. As an illustrative example the pseudoinverse is approximated in a region of the joint space for a seven-degree-of-freedom manipulator.     

Visual Motor Control of a 7 DOF Robot Manipulator Using Function Decomposition and Sub-Clustering in Configuration Space

This paper deals with real-time implementation of visual-motor control of a 7 degree of freedom (DOF) robot manipulator using self-organized map (SOM) based learning approach. The robot manipulator considered here is a 7 DOF PowerCube manipulator from Amtec Robotics. The primary objective is to reach a target point in the task space using only a single step movement from any arbitrary initial configuration of the robot manipulator. A new clustering algorithm using Kohonen SOM lattice has been proposed that maintains the fidelity of training data. Two different approaches have been proposed to find an inverse kinematic solution without using any orientation feedback. In the first approach, the inverse Jacobian matrices are learnt from the training data using function decomposition. It is shown that function decomposition leads to significant improvement in accuracy of inverse kinematic solution. In the second approach, a concept called sub-clustering in configuration space is suggested to provide multiple solutions for the inverse kinematic problem. Redundancy is resolved at position level using several criteria. A redundant manipulator is dexterous owing to the availability of multiple configurations for a given end-effector position. However, existing visual motor coordination schemes provide only one inverse kinematic solution for every target position even when the manipulator is kinematically redundant. Thus, the second approach provides a learning architecture that can capture redundancy from the training data. The training data are generated using explicit kinematic model of the combined robot manipulator and camera configuration. The training is carried out off-line and the trained network is used on-line to compute the joint angle vector to reach a target position in a single step only. The accuracy attained is better than the current state of art.     

Task-Space Modular Dynamics for Dual-Arms Expressed through a Relative Jacobian

This paper presents modular dynamics for dual-arms, expressed in terms of the kinematics and dynamics of each of the stand-alone manipulators. The two arms are controlled as a single manipulator in the task space that is relative to the two end-effectors of the dual-arm robot. A modular relative Jacobian, derived from a previous work, is used which is expressed in terms of the stand-alone manipulator Jacobians. The task space inertia is expressed in terms of the Jacobians and dynamics of each of the stand-alone manipulators. When manipulators are combined and controlled as a single manipulator, as in the case of dual-arms, our proposed approach will not require an entirely new dynamics model for the resulting combined manipulator. But one will use the existing Jacobians and dynamics model for each of the stand-alone manipulators to come up with the dynamics model of the combined manipulator. A dual-arm KUKA is used in the experimental implementation.     

Mobile manipulator path planning by a genetic algorithm

This article addresses the path-planning problem for a mobile manipulator system that is used to perform a sequence of tasks specified by locations and minimum oriented force capabilities. The problem is to find an optimal sequence of base positions and manipulator configurations for performing a sequence of tasks given a series of task specifications. The formulation of the problem is nonlinear. The feasible regions for the problem are nonconvex and unconnected. Genetic algorithms applied to such problems appear to be very promising while traditional optimization methods cause difficulties. Computer simulations are carried out on a three-degrees-of-freedom manipulator mounted on a two-degrees-of-freedom mobile base to search for the near optimal path-planning solution for performing the sequence of tasks. © 1994 John Wiley & Sons, Inc.     

Motion planning and contact control for a tele-assisted hydraulic underwater robot

Implementing tele-assistance or supervisory control for autonomous subsea robots requires atomic actions that can be called from high level task planners or mission managers. This paper reports on the design and implementation of a particular atomic action for the case of a subsea robot carrying out tasks in contact with the surrounding environment.Subsea vehicles equipped with manipulators can have upward of 11 degrees of freedom (DOF), with degenerate and redundant inverse kinematics. Distributed local motion planning is presented as a means to specify the motion of each robot DOF given a goal point or trajectory. Results are presented to show the effectiveness of the distributed versus non-distributed approach, a means to deal with local minima difficulties, and the performance for trajectory following with and without saturated joint angles on a robot arm.Consideration is also given to the modelling of hydraulic underwater robots and to the resulting design of hybrid position/force control strategies. A model for a hydraulically actuated robot is developed, taking into account the electrohydraulic servovalve, the bulk modulus of oil, piston area, friction, hose compliance and other arm parameters. Open and closed-loop control results are reported for simulated and real systems.Finally, the use of distributed motion planning and sequential position/force control of a Slingsby TA-9 hydraulic underwater manipulator is described, to implement an atomic action for tele-assistance. The specific task of automatically positioning and inserting a Tronic subsea mateable connector is illustrated, with results showing the contact conditions during insertion.     

Period sensitivity analysis and D-P domain feasibility region in dynamic priority systems

In the design of a real-time application it is fundamental to know how a change in the task parameters would affect the feasibility of the system. Relaxing the classical assumptions on static task sets with fixed periods and deadlines can give higher resource utilisation and better performance. But the changes on task parameters have to be done always maintaining feasibility. In practice, period and deadline modifications are only necessary on single tasks. Our work focuses on finding the feasibility region of deadlines and periods (called D-P feasibility region) for a single task in the context of dynamic, uniprocessor scheduling of hard real-time systems. This way, designers can choose the optimal deadline and period pairs that best fit application requirements. We provide an exact and an approximated algorithm to calculate this region. We will show that the approximated solution is very close to the exact one and it takes considerably less time.     

Visual servoing tracking control of uncalibrated manipulators with a moving feature point

The paper is concerned with the problem of uncalibrated visual servoing robots tracking a dynamic feature point along with the desired trajectory. A nonlinear observer and a nonlinear controller are proposed, which allow the considered uncalibrated visual servoing robotic system to fulfil the desired tracking task. Based on this novel control method, a dynamic feature point with unknown motion parameters can be tracked effectively along with the desired trajectory, even with multiple uncertainties existing in the camera, the kinematics and the manipulator dynamics. By the Lyapunov theory, asymptotic convergence of the image errors to zero with the proposed control scheme is rigorously proven. Simulations have been conducted to verify the performance of the proposed control scheme. The results demonstrated good convergence of the image errors.     

Robotic date fruit harvesting using machine vision and a 5-DOF manipulator

Date fruits can be found at the highest point of the palm tree, so harvesting can be a dangerous task for humans. In this study, a robotic arm is presented to harvest date fruits. A manipulator, traveling on a U-shaped rail with four prismatic joints and one revolute joint, was designed and constructed to approach the fruits efficiently. The end-effector of the manipulator was an electric chainsaw capable of cutting the date bunch. Two cameras were located on the manipulator in perpendicular directions to capture images, which were then transmitted to a decision-making unit to control the speed of the manipulator links. The decision-making unit included three fuzzy inference systems that used the location data of the fruit bunch stems and the area of tree leaves in the images to determine the speed of electromotors of the trolley, horizontal link, and vertical link. An artificial palm tree with dimensions similar to a real palm tree was constructed to evaluate the performance of the robot. The performance of the robot was evaluated in various lighting conditions. The results showed that the introduced image processing algorithm could adequately detect the stems of the date bunches with accuracy, precision, and recall of 0.88, 0.92, and 0.96, respectively, in suitable lighting, that is, when there was sufficient natural lighting. Moreover, the experimental results revealed that the accuracy of the control system in cutting the stems was 87%, with a production loss of 5%. The proposed robot makes it possible to improve the capacity of using mechanized harvesting in date palm fields.     

Dynamic analysis and control of a stewart platform manipulator

The Stewart platform is a six-axis parallel robot manipulator with a force-to-weight ratio and positioning accuracy far exceeding that of a conventional serial-link arm. Its stiffness and accuracy approach that of a machine tool yet its workspace dexterity approaches that of a conventional manipulator. In this article, we study the dynamic equations of the Stewart platform manipulator. Our derivation is closed to that of Nguyen and Pooran because the dynamics are not explicitly given but are in a step-by-step algorithm. However, we give some insight into the structure and properties of these equations: We obtain compact expressions of some coefficients. These expressions should be interesting from a control point of view. A stiffness control scheme is designed for milling application. Some path-planning notions are discussed that take into account singularity positions and the required task. The objective is to make the milling station into a semiautonomous robotic tool needing some operator interaction but having some intelligence of its own. It should interface naturally with part delivery and other higher-level tasks.     

On the use of free-floating space robots in the presence of angular momentum

Free-floating space manipulator systems include at least one manipulator mounted on an unactuated spacecraft. It is known that such systems exhibit nonholonomic behavior due to angular momentum conservation. In this paper, the initial angular momentum of the system is not assumed to be zero and its influence on system behavior is studied. In contrast to the case of zero initial momentum, in the presence of momentum, the manipulator end effector in general cannot remain at a given location for indefinite time. The paper studies the conditions under which this is possible, rendering the end-effector immune to angular momentum accumulation. The relevant kinematics and dynamics are studied in 2D and 3D systems, and workspace subsets, where the end effector can remain fixed, are identified. Examples illustrate the validity of the results.     

Path following by the end-effector of a redundant manipulator operating in a dynamic environment

This paper addresses the problem of generating at the control-loop level a collision-free trajectory for a redundant manipulator operating in dynamic environments which include moving obstacles. The task of the robot is to follow, by the end-effector, a prescribed geometric path given in the work space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results for a planar manipulator whose end-effector follows a prescribed geometric path, given in both an obstacle-free work space and a work space including the moving obstacles, illustrate the trajectory performance of the proposed control scheme.     

Screening of factors influencing the performance of manipulator using combined array design of experiment approach

A robot must manipulate objects with high accuracy and repeatability to perform precise tasks. However, deviation in performance is attributed to uncertainties and improper selection of control, noise, and process factors. The information regarding the effect of these factors on performance is almost non-existent. A probabilistic approach has been used to model and simulate the performance of manipulator. The combined array fractional factorial design of experiment approach has been employed to identify the significant factors and their interactions. This approach helps in screening of the manipulator factors and focus on those that are important. To explore further, two indices, viz. link length ratio and link mass ratio, have been proposed and impact of these indices on manipulator performance is investigated. A two degree of freedom (2-DOF) RR planar manipulator performing a task with cubic and quintic trajectory has been used to illustrate the approach. It has been observed that the statistically significant factors are different for different tasks in workspace. It has also been observed that for the same task, factors responsible for performance variations are different for cubic and quintic trajectories. Finally, it has been demonstrated that the link length ratio change has significant influence on performance compared to link mass ratio.