Jorge Angeles

Singularity analysis of closed-loop kinematic chains

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. >

A Global Performance Index for the Kinematic Optimization of Robotic Manipulators

In this paper, a novel performance index for the kinematic optimization of robotic manipulators is presented. The index is based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the kinematic and static transformations between the joint and Cartesian spaces. Moreover, the index proposed here, termed global conditioning index (CGI), is meant to assess the distribution of the aforementioned condition number over the whole workspace. Furthermore, the concept of a global index is applicable to other local kinematic or dynamic indices. The index introduced here is applied to a simple serial two-link manipulator, to a spherical three-degree-of-freedom serial wrist, and to three-degree-of-freedom parallel planar and spherical manipulators. Results of the optimization of these manipulators, based on the GCI, are included.

Fundamentals of Robotic Mechanical Systems

From the Publisher: Modern robotics dates from the late 1960s, when progress in the development of microprocessors made possible the computer control of a multiaxial manipulator. Since then, robotics has evolved to connect with many branches of science and engineering, and to encompass such diverse fields as computer vision, artificial intelligence, and speech recognition. This book deals with robots-such as remote manipulators, multifingered hands, walking machines, flight simulators, and machine tools-that rely on mechanical systems to perform their tasks. It aims to establish the foundations on which the design, control and implementation of the underlying mechanical systems are based. The treatment assumes familiarity with some calculus, linear algebra, and elementary mechanics; however, the elements of rigid-body mechanics and of linear transformations are reviewed in the first chapters, making the presentation self-contained. An extensive set of exercises is included. Topics covered include: kinematics and dynamics of serial manipulators with decoupled architectures; trajectory planning; determination of the angular velocity and angular acceleration of a rigid body from point data; inverse and direct kinematics manipulators; dynamics of general parallel manipulators of the platform type; and the kinematics and dynamics of rolling robots. Since the publication of the previous edition there have been numerous advances in both the applications of robotics (including in laprascopy, haptics, manufacturing, and most notably space exploration) as well as in the theoretical aspects (for example, the proof that Hustys 40th-degree polynomial is indeed minimal - mentioned as an open question in the previous edition). This new edition has been revised and updated throughout to include these new

Kinematic isotropy and the optimum design of parallel manipulators

The differential kinematic equations (DKE) of parallel manip ulators usually involve two Jacobian matrices that, depending on the role they play in the kinetostatic transformation between the joint and Cartesian variables, are commonly referred to as the forward and the inverse Jacobians. In this article, we make use of the special structure of these Jacobians to define a set of conditions under which a parallel manipulator can be rendered isotropic. These conditions are general, and pro vide a systematic method for the optimum kinematic design of parallel manipulators, with or without introducing structural constraints. The application of the proposed conditions is illus trated in detail through a few examples, one of which pertains to the design of a 6-DOF isotropic parallel manipulator.

Kinematic isotropy and the conditioning index of serial robotic manipulators

The conditioning index of a serial robotic manipulator is de fined in this article in terms of the reciprocal of its minimum condition number. The condition number of a manipulator is defined, in turn, as that of its Jacobian matrix. Moreover, in defining the Jacobian condition number, a quadratic norm of the Jacobian matrix is needed. However, this norm, or for that matter any other norm, brings about dimensional inho mogeneities. It is shown here that by properly defining the said norm based on a weighting positive definite matrix, the dimensional inhomogeneity is resolved. Manipulators with a conditioning index of 100% are termed isotropic, a six-axis isotropic manipulator being introduced. This manipulator has all its angles between neighboring revolute axes at 90° and all its distances between neighboring axes identical; more over, these distances are identical to the offsets of those axes. The kinematic conditioning of wrist-partitioned manipulators is given due attention, and illustrated with some examples of industrial robots of this type.

Architecture singularities of platform manipulators

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.<<ETX>>

The Qualitative Synthesis of Parallel Manipulators

As shown in this paper, when designing parallel manipulators for tasks involving less than six degrees of freedom, the topology can be laid out by resorting to qualitative reasoning. More specifically, the paper focuses on cases whereby the manipulation tasks pertain to displacements with the algebraic structure of a group. Besides the well-known planar and spherical displacements, this is the case of displacements involving: rotation about a given axis and translation in the direction of the same axis (cylindrical subgroup); translation in two and three dimensions (two- and three-dimensional translation subgroups); three independent translations and rotation about an axis of fixed direction, what is known as the Schonflies subgroup; and similar to the Schonflies subgroup, but with the rotation and the translation in the direction of the axis of rotation replaced by a screw displacement. For completeness, the fundamental concepts of motion representation and groups of displacements, as pertaining to rigid bodies, are first recalled. Finally, the concept of H-joint, introduced elsewhere, is generalized to two and three degrees of freedom, thereby ending up with the Π 2 -and the Π 3 -joints, respectively.

On the Numerical Solution of the Inverse Kinematic Problem

Solved in this paper is the inverse kinematic problem asso ciated with manipulators of arbitrary architecture. Its formu lation is based on invariants in the rotational part of the closure equations, which produces a formally overdetermined nonlinear algebraic system. In the translational part, a recur sive scheme similar to that of Horners for polynomial evalu ation is introduced. This leads to a reduced number of com putations, which allows an efficient numerical solution of the problem. Velocity and acceleration kinematic inversions are also included. The procedure is illustrated with the analysis of a six-degree-of-freedom, revolute-coupled manipulator of an architecture that makes a closed-form solution difficult. This method has been successfully applied to the analysis of 7R spatial linkages as well. Appendix A lists the nomenclature and notation used in this paper.

Real-time force optimization in parallel kinematic chains under inequality constraints

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 design of isotropic manipulator architectures in the presence of redundancies

The design of redundant isotropic architectures for robotic nia nipulators is the subject of this article. A manipulator is said to have a redundant isotropic architecture if (1) its number of controlled axes is greater than the dimension of its task space. and (2) it is possible for the manipulator to attain configura tions at which all the singular values of its Jacobian matrix are identical and nonzero. The concept of isotropy, which has already been applied to the design of nonredundant manip ulators, is applied to the design of redundant ones. General geometric conditions on the manipulator parameters and on its configuration variables under which isotropy is attained are derived.