Manipulator Mass Matrix Research Articles

A New Pseudoinverse for Manipulator Collision Avoidance

AbstractThis paper presents a control system architecture for robot manipulator suitable for on line path planning in a cluttered environment. The proposed technique fits for both redundant and non redundant manipulators. We use potential fields in order to control the joint velocities to make the manipulator escape from obstacles. We also propose a new weighted pseudoinverse matrix that improves the manipulator capability to find feasible paths moving around obstacles and passing through narrow corridors without calculating the manipulator mass matrix. The proposed solution is tested on two manipulators: a 7 degree-of-freedom (DOF) planar manipulator and a 7 degree-of-freedom spatial manipulator both moving in a cluttered environment.

Global Output Tracking Control of Flexible Joint Robots via Factorization of the Manipulator Mass Matrix

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper investigates the problem of global output feedback tracking control of flexible joint robots. Despite the fact that only link position and actuator position are available from measurements, the proposed controller ensures that the link position globally tracks the desired trajectory while keeping all the remaining signals bounded. The controller development uses a partial state-feedback linearization technique combined with the integrator backstepping control design method whereas a filter and an observer are utilized to remove the requirement of link and actuator velocity measurements. Partial state-feedback linearization of robot dynamics is performed by factoring the manipulator mass matrix into a quadratic form involving an integrable root matrix. The applicability of the proposed general design methodology is illustrated by an example of flexible joint planar robots. Numerical results for a two-link flexible joint planar robot are also provided. </para>

A nonlinear controller for rigid manipulators

A nonlinear controller for rigid manipulators is proposed in this paper. The controller is based on equations of motion arising from decomposition of the manipulator mass matrix and contains a vector of generalized velocity components (GVC). It is shown that dynamics description in terms of the GVC gives an further insight into the system dynamics which is also available if the presented controller is used. The theoretical considerations are illustrated by simulation on a 3 d.o.f. spatial manipulator.

Dynamical couplings reduction for rigid manipulators using generalized velocity components

A method for evaluation and reduction of dynamical couplings between the links of a rigid serial manipulator is presented. The approach is based on the first-order equations of motion expressed in terms of the generalized velocity components (GVC). The GVC obtained from decomposition of the manipulator mass matrix reflect the dynamics of the system. In order to reduce the dynamical couplings several criteria and indexes are introduced. As a result of the reduction, the time response of the system with a controller is improved. Moreover, the joint applied torques, the Coriolis and the gravitational term forces, and the kinetic energy are reduced too. The proposed method is tested via simulation on a spatial manipulator with three degrees of freedom.

Evaluation of the reduction of dynamical coupling for robot manipulators

The problem of evaluation of the reduction of dynamical coupling in rigid serial manipulators is presented in the current paper. The proposed strategy is based on first-order equations of motion expressed in terms of normalized generalized velocity components, which result from decomposition of the manipulator mass matrix. The principal activity of the study relies on an algorithm in which some evaluation criteria as well as some indexes are used. The presented approach is important, mainly for manipulators with a direct drive arm at their design stage. Simulation results on a three-degree-of-freedom (3-DOF) spatial manipulator are given in order to illustrate the offered method.

Proportional-derivative energy-based control for manipulator using normalized quasi-velocities

This paper presents a proportional-derivative (PD) controller for rigid manipulators whose dynamics is expressed in terms of the normalized quasi-velocities (NQV) described by Jain and Rodriguez. It is shown that using the NQV it is possible to shape the kinetic energy reduction of the manipulator and at the same time to realize the PD control in its joint space. The energy-based strategy gives an insight into the position control and allows a different method to be used instead of the classical PD controller in order to change the behaviour of the system. The controller uses quasi-velocities arising from a decomposition of the manipulator mass matrix. Its use yields a globally asymptotically stable closed-loop system. The performance of the controller is illustrated via experiment on a two-degree-of-freedom robot arm and in simulation on a three-degree-of-freedom spatial manipulator.

Investigation of manipulator dynamics with a viscous damping model

In this article, some remarks concerning dynamics investigation of a manipulator described using first-order equations of motion with a viscous damping model is conducted. The viscous damping model arises from the Rayleigh dissipation potential and decomposition of the manipulator mass matrix. As a result, it takes into account both kinematic and mechanical parameters of the system. Moreover, the use of first-order equations of motion leads to obtaining some interesting insight into the manipulator dynamics. The proposed approach was tested on a three-degrees-of-freedom, three-dimensional Yasukawa-like robot.

PD Controller for Manipulator with Kinetic Energy Term

A kinetic energy approach to PD control in joint space of a manipulator in terms of the eigenfactor quasi-coordinate velocity (EQV) vector is considered in this paper. The modified PD controller which contains quantities resulting from decomposition of a manipulator mass matrix is proposed. The obtained equations of motion are based on the eigenvalues and eigenvectors of the mass matrix (Junkins, J. L. and Schaub, H. [7]. It is shown that utilizing the EQV vector one can determine directly the kinetic energy of the manipulator and at the same time realize PD control in its joint space. This energy-based strategy gives an interesting insight into position control. The controller presented here was tested in simulation on a 3 d.o.f. direct drive arm manipulator and via experiment on a 2 d.o.f. manipulator. The results confirmed that one can directly determine the kinetic energy for the total manipulator as well for its each joint. Additionally, time response of the system under EQV controller is faster than for the classical controller if mechanical coupling are strong.

Application of unnormalized quasi-velocities integrals

This paper presents considerations concerning usefulness of integrals of unnormalized quasi-velocities. These quasi-velocities described by Jain and Rodriguez (IEEE Transactions on Robotics and Automation 11, 571 -84, 1995) are obtained as a result of diagonalization of the manipulator mass matrix in velocity space. Equations of motion are expressed in terms of generalized coordinates and an unnormalized velocity vector. Both quasi-velocities and their integrals can serve as a tool for improvement of manipulator dynamics. It is shown that sometimes there exist integrals of these quasi-velocities in explicit analytical form for a 2 d.o.f. manipulator. In other cases one can calculate integrals of unnormalized quasi-velocities using numerical methods. The numerically procedure was used for 3 d.o.f. three-dimensional DDArm robot.

Remarks concerning integrals of normalized quasi-velocities

In this paper, the problem of the integrals of normalized quasi-velocities is discussed. Introducing the quasi-velocities known from the robotic literature leads to diagonalization of the manipulator mass matrix in velocity space. It is shown here that, for a two-degree-of-freedom (2-DOF) manipulator, sometimes there exist analytical forms of integrals of normalized quasi-velocities. If the analytical method is not available, then a numerical method is used to calculate integrals of the quasi-velocities. This solution is presented for a 3-DOF three-dimensional DDArm (Direct Drive Arm) robot.

Spatial operator factorization and inversion of the manipulator mass matrix

This paper advances two linear operator factorizations of the manipulator mass matrix. Embedded in the factorizations are many of the techniques that are regarded as very efficient computational solutions to inverse and forward dynamics problems. The operator factorizations provide a high-level architectural understanding of the mass matrix and its inverse, which is not visible in the detailed algorithms. They also lead to an approach to the development of computer programs or the organisation of complexity in robot dynamics. >