A global approach for the optimal path generation of redundant robot manipulators

In this article the optimal path generation of redundant robot manipulators is considered as an optimization problem, with given kinematics and subject to the robot requirements and a singularities avoidance constraint. This problem is formulated as a constrained continuous optimal control problem, which allows to consider joints and velocities constraints and/or manipulator dynamics. This approach is exemplified for a planar redundant manipulator and the resultant state constrained problem is solved by an efficient iterative numerical technique.     

Task decoupling in robot manipulators

Task decoupling in robotic manipulators implies that there is a subset of joints primarily responsible for the completion of a subset of the manipulator task. In this paper, we take a novel and general view of task decoupling in which we identify link subsystems primarily responsible for completion of a subset of the manipulator task components, which is not necessarily position or orientation. Our analysis leads to the discovery of other decoupled manipulator geometries never identified before, wherein the decoupled system is responsible for a subset of degress-of-freedom involving a hybrid combination of both position and orientation. Closed-form inverse kinematic solutions for these manipulator geometries are therefore guaranteed. Task decoupling also implied singularity decoupling wherein singularities of decoupled subsystems are equivalent to the manipulator singularities. The analysis leads to a novel and efficient method for identifying the singularities and solving the inverse kinematics problem of six-axes manipulators with decoupled geometries. The practicality of the concepts introduced is demonstrated through an industrial robot example involving a hybrid position and orientation decoupling.     

An efficient local approach for the path generation of robot manipulators

In this article an efficient local approach for the path generation of robot manipulators is presented. The approach is based on formulating a simple nonlinear programming problem. This problem is considered as a minimization of energy with given robot kinematics and subject to the robot requirements and a singularities avoidance constraint. From this formulation a closed form solution is derived which has the properties that allows to pursue both singularities and obstacle avoidance simultaneously; and that it can incorporate global information. These properties enable the accomplishment of the important task that while a specified trajectory in the operational space can be closely followed, also a desired joint configuration can be attained accurately at a given time. Although the proposed approach is primarily developed for redundant manipulators, its application to nonredundant manipulators is examplified by considering a particular commercial manipulator.     

Operating robot manipulators through kinematic singularities using a continuously sliding mode control

Planning the motion of end-effectors of robot manipulators can be carried out more directly in the Cartesian space compared to the joint space. Yet, Cartesian paths may include singular configurations where conventional control schemes suffer from excessive joint velocities and loss of tracking accuracy. The difficulties arise because the Jacobian matrix that is used to establish a linear relation between the velocities in the task and joint spaces loses rank at singularities. The problem can be resolved by using a local second-order approximation of robot kinematics for the joint velocities, which is called Resolved Motion Quadratic Rate Control. In this article, we present a control strategy based on this approach and a recently developed variable structure control scheme. The controller receives Cartesian inputs whenever the manipulator is outside the singular domain. Otherwise, it uses resolved motion quadratic rate control to compute the required joint inputs. Numerical simulation is performed to show that the proposed control scheme provides accurate tracking of the desired motion without inducing excessive control activity when operating robot manipulators through singular configurations. © 1994 John Wiley & Sons, Inc.     

On inverting singular kinematics and geodesic trajectory generation for robot manipulators

In this paper, a new method is proposed of solving the inverse kinematic problem for robot manipulators whose kinematics are allowed to possess singularities. The method is based upon the so-called generalized Newton algorithm, introduced by S. Smale, and can be adopted to both nonredundant and redundant kinematics. Moreover, given a pair of points in the external space of a manipulator, the method is capable of generating a minimum-length trajectory joining the points (a geodesic), in particular a straight-line trajectory. Results of representative computer experiments, including those with the PUMA 560 kinematics, are reported in order to illustrate the performance of the method.     

Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach

Kinematic analysis is one of the key issues in the research domain of parallel kinematic manipulators. It includes inverse kinematics and forward kinematics. Contrary to a serial manipulator, the inverse kinematics of a parallel manipulator is usually simple and straightforward. However, forward kinematic mapping of a parallel manipulator involves highly coupled nonlinear equations. Therefore, it is more difficult to solve the forward kinematics problem of parallel robots. In this paper, a novel three degrees-of-freedom (DOFs) actuation redundant parallel manipulator is introduced. Different intelligent approaches, which include the Multilayer Perceptron (MLP) neural network, Radial Basis Functions (RBF) neural network, and Support Vector Machine (SVM), are applied to investigate the forward kinematic problem of the robot. Simulation is conducted and the accuracy of the models set up by the different methods is compared in detail. The advantages and the disadvantages of each method are analyzed. It is concluded that ν-SVM with a linear kernel function has the best performance to estimate the forward kinematic mapping of a parallel manipulator.     

Inverse kinematics of planar redundant manipulators via virtual links with configuration index

This article presents a new method for generating inverse kinematic solutions for planar manipulators with large redundancy (hyper-redundant manipulators). The proposed method starts by decomposing a planar redundant manipulator into a series of local planar arms that are either 2-link or 3-link manipulator modules, and connecting the conjunction points between them with virtual links. The manipulator then can be handled by a simple virtual link system, which may be conveniently divided into non-singular and singular cases depending on its configuration. When the virtual link system is no longer effective due to a singular configuration, the displacement of the end-effector is then allocated to virtual links according to a displacement distribution criterion. A dexterity index called the “configuration index” distinguishes the non-singular and singular cases. The concept of virtual link is shown by computer simulations to be simple and effective for the inverse kinematics of a planar hyper-redundant manipulator with a discrete model. In particular, it can be applied to solving the inverse kinematics of a SCARA-type spatial redundant manipulator whose redundancy is included in its planar mechanism. © 1994 John Wiley & Sons, Inc.     

A fast approach for the robust trajectory planning of redunant robot manipulators

In this article, a fast approach for robust trajectory planning, in the task space, of redundant robot manipulators is presented. The approach is based on combining an original method for obstacle avoidance by the manipulator configuration with the traditional potential field approach for the motion planning of the end-effector. This novel method is based on formulating an inverse kinematics problem under an inexact context. This procedure permits dealing with the avoidance of obstacles with an appropriate and easy to compute null space vector; whereas the avoidance of singularities is attained by the proper pseudoinverse perturbation. Furthermore, it is also shown that this formulation allows one to deal effectively with the local minimum problem frequently associated with the potential field approaches. The computation of the inverse kinematics problem is accomplished by numerically solving a linear system, which includes the vector for obstacle avoidance and a scheme for the proper pseudoinverse perturbation to deal with the singularities and/or the potential function local minima. These properties make the proposed approach suitable for redundant robots operating in real time in a sensor-based environment. The developed algorithm is tested on the simulation of a planar redundant manipulator. From the results obtained it is observed that the proposed approach compares favorably with the other approaches that have recently been proposed. © 1995 John Wiley & Sons, Inc.     

Analysis of duality-based interconnected kinematics of planar serial and parallel manipulators using screw theory

In this paper, a method has been proposed to analyze the planar architectures of serial and parallel manipulators, based on the duality associated with their interconnected kinematics. The interconnected kinematics states that model of one architecture can be derived from the kinematic model of the other, using screw theory approach. The performance of the initial and the derived manipulators was evaluated with three criteria: isotropy, maximum force transmission ratio and local transmission index. Without loss of generality, the serial manipulator derived from parallel has better isotropy, while the parallel manipulator derived from serial can be designed to have better force and power transmission.

     

Estimation model for kinematic calibration of manipulators with a parallel structure

This article provides an estimation model for calibrating the kinematics of manipulators with a parallel geometrical structure. Parameter estimation for serial link manipulators is well developed, but fail for most structures with parallel actuators, because the forward kinematics is usually not analytically available for these. We extend parameter estimation to such parallel structures by developing an estimation method where errors in kinematical parameters are linearly related to errors in the tool pose, expressed through the inverse kinematics, which is usually well known. The method is based on the work done to calibrate the MultiCraft robot. This robot has five linear actuators built in parallel around a passive serial arm, thus making up a two-layered parallel-serial manipulator, and the unique MultiCraft construction is reviewed. Due to the passive serial arm, for this robot conventional serial calibration must be combined with estimation of the parameters in the parallel actuator structure. The developed kinematic calibration method is verified through simulations with realistic data and real robot kinematics, taking the MultiCraft manipulator as the case. © 1994 John Wiley & Sons, Inc.     

Computer generation of symbolic kinematics for robot manipulators

Computer generation of symbolic solutions for the direct and inverse robot kinematics is a desired capability not previously available to robotics engineers. In this article, we present a methodology for the design of a software system capable of solving the direct and inverse kinematics for n degree of freedom (dof) manipulators in symbolic form. The inputs to the system are the Denavit-Hartenberg parameters of the manipulator. The outputs of the system are the direct and inverse kinematics solutions in symbolic form. The system consists of a symbolic processor to perform matrix and algebraic manipulations and an expert system to solve the class of nonlinear equations involved in the solution of the inverse kinematics problem. The system can be used to study robot kinematics configurations whose inverse kinematics solutions are not known to exist a priori. Two examples are included to illustrate its capabilities. The first example provides explicit analytical solutions, previously believed nonexistent, for a 3 dof manipulator. A second example is included for a robot whose inverse kinematics solution requires intensive algebraic manipulations.     

Solving the forward kinematics of parallel manipulators with a genetic algorithm

A floating point genetic algorithm is proposed to solve the forward kinematic problem for parallel manipulators. This method, adapted from studies in the biological sciences, allows the use of inverse kinematic solutions to solve forward kinematics as an optimization problem. The method is applied to two 3-degree-of-freedom planar parallel manipulators and to a 3-degree-of-freedom spherical manipulator. The method converges to a solution within a broader search domain compared to a Newton-Raphson scheme. © 1996 John Wiley & Sons, Inc.     

Adaptive Regulation of Amplitude Limited Robot Manipulators With Uncertain Kinematics and Dynamics

Common assumptions in most of the previous robot controllers are that the robot kinematics and manipulator Jacobian are perfectly known and that the robot actuators are able to generate the necessary level of torque inputs. In this note, an amplitude-limited torque input controller is developed for revolute robot manipulators with uncertainty in the kinematic and dynamic models. The adaptive controller yields semiglobal asymptotic regulation of the task-space setpoint error. The advantages of the proposed controller include the ability to actively compensate for unknown parametric effects in the dynamic and kinematic model and the ability to ensure actuator constraints are not breached by calculating the maximum required torque a priori     

Extended Jacobian inverse kinematics algorithms for mobile manipulators

We consider the inverse kinematic problem for mobile manipulators consisting of a nonholonomic mobile platform and a holonomic manipulator on board the platform. The kinematics of a mobile manipulator are represented by a driftless control system with outputs together with the associated variational control system. The output reachability map of the driftless control system determines the instantaneous kinematics, while the output reachability map of the variational system plays the role of the analytic Jacobian of the mobile manipulator. Relying on a formal analogy between the kinematics of stationary and mobile manipulators we exploit the extended Jacobian construction in order to design a collection of extended Jacobian inverse kinematics algorithms for mobile manipulators. It has been proved mathematically and confirmed in computer simulations that these algorithms are capable of efficiently solving the inverse kinematic problem. Moreover, a choice of the Jacobian extension may lay down some guidelines for the platform‐manipulator motion coordination. © 2002 Wiley Periodicals, Inc.     

Inverse dynamics of redundant manipulators using a minimum number of control forces

The number of the control actuators used by the inverse kinematics and dynamics algorithms that have been developed in the literature for generating redundant robot joint trajectories is equal to the number of the degrees of freedom of the manipulator. In this article, an inverse dynamics algorithm that performs the tasks using only a minimum number of actuators is proposed. The number of actuators is equal to the dimension of the task space, and the control forces are solved simultaneously with the corresponding system motion. It is shown that because all degrees of freedom are not actuated, the control forces may lose the ability to make an instantaneous effect on the end-effector acceleration at certain configurations, yielding the dynamical equation set of the system to be singular. The dynamical equations are modified in the neighborhood of the singular configurations by utilizing higher-order derivative information, so that the singularities in the numerical procedure are avoided. Asymptotically stable inverse dynamics closed-loop control in the presence of perturbations is also discussed. The algorithm is further generalized to closed chain manipulators. Three-link and two-link redundant planar manipulators are analyzed to illustrate the validity of the approach. © 2995 John Wiley & Sons, Inc.     

Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms

By a mobile manipulator we mean a robotic system composed of a non-holonomic mobile platform and a holonomic manipulator fixed to the platform. A taskspace of the mobile manipulator includes positions and orientations of its end effector relative to an inertial coordinate frame. The kinematics of a mobile manipulator are represented by a driftless control system with outputs. Admissible control functions of the platform along with joint positions of the manipulator constitute the endogenous configuration space. Endogenous configurations have a meaning of controls. A map from the endogenous configuration space into the taskspace is referred to as the instantaneous kinematics of the mobile manipulator. Within this framework, the inverse kinematic problem for a mobile manipulator amounts to defining an endogenous configuration that drives the end effector to a desirable position and orientation in the taskspace. Exploiting the analogy between stationary and mobile manipulators we present in the paper a collection of regular and singular Jacobian inverse kinematics algorithms. Their performance is evaluated on the basis of intense computer simulations.     

A Lagrangian network for kinematic control of redundant robotmanipulators

A recurrent neural network, called the Lagrangian network, is presented for the kinematic control of redundant robot manipulators. The optimal redundancy resolution is determined by the Lagrangian network through real-time solution to the inverse kinematics problem formulated as a quadratic optimization problem. While the signal for a desired velocity of the end-effector is fed into the inputs of the Lagrangian network, it generates the joint velocity vector of the manipulator in its outputs along with the associated Lagrange multipliers. The proposed Lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.     

A comparison between the Denavit–Hartenberg and the screw-based methods used in kinematic modeling of robot manipulators

This paper aims to integrate didactically some engineering concepts to understand and teach the screw-based methods applied to the kinematic modeling of robot manipulators, including a comparative analysis between these and the Denavit–Hartenberg-based methods. In robot analysis, kinematics is a fundamental concept to understand, since most robotic mechanisms are essentially designed for motion. The kinematic modeling of a robot manipulator describes the relationship between the links and joints that compose its kinematic chain. To do so, the most popular methods use the Denavit–Hartenberg convention or its variations, presented by several author and robot publications. This uses a minimal parameter representation of the kinematic chain, but has some limitations. The successive screw displacements method is an alternative representation to this classic approach. Although it uses a non-minimal parameter representation, this screw-based method has some advantages over Denavit–Hartenberg. Both methods are here presented and compared, concerning direct/inverse kinematics of manipulators. The differential kinematics is also discussed. Examples of kinematic modeling using both methods are presented in order to ease their comparison.