Jan R. Sagli

A damped least-squares solution to redundancy resolution

Singularity robust redundancy resolution with task priority can be implemented using the extended Jacobian technique with weighted damped least-squares. The resulting scheme is simple to implement and involves less computation than the task priority scheme. The minimum singular value of the Jacobian can be estimated reliably and accurately with little computation, and this estimate was used to calculate an appropriate damping factor. A constant damping factor was also used with good results. The scheme was successfully implemented in a simulation study with a seven-joint manipulator with a kinematic design derived from the PUMA geometry.<<ETX>>

Coordination of Motion in a Spacecraft/ Manipulator System

A control scheme for the coordination of motion in a space craft/manipulator system is presented. It is shown how end- effector motion can be decoupled from satellite motion, satellite rotation, or total system momentum by selecting suitable gen eralized speeds for the satellite. The schemes are based on recursive calculation of kinematics and dynamics, and 12 degrees of freedom can be controlled without excessive com putational effort. Feedback linearization and decoupling of end-effector motion and total system momentum are discussed in detail. The satellite controller can then be developed in dependently of the manipulator controller, and reaction jets and momentum wheels are used only to reposition the satel lite. The end effector can be controlled accurately with a high bandwidth, while a slow, gross positioning can be used for the satellite. The resulting controller is very efficient in terms of fuel. The spacecraft/manipulator system is regarded as a re dundant manipulator of the macro-micro type with 12 degrees of freedom, and a redundancy resolution scheme based on the augmented task space approach is used to generate the position and orientation reference for the spacecraft. The proposed con troller was simulated with a 12-degrees-of-freedom model that was generated with a recursive formulation of the Jacobians. The results are presented in this article.

Optimal Continuous-Path Control for Manipulators with Redundant Degrees of Freedom

Abstract A control system for macro-micro manipulators is presented. A position transformation from the end-effector reference to joint coordinates is found using kinematic optimization. Decoupling and optimal control is used to coordinate the motion of the macro and micro part. The redundant manipulator will then have the speed of the micro manipulator and the large workspace of the macro manipulator. When optimal control is used, the redundant manipulator may be even faster than the micro manipulator provided that a suitable performance index is used. The performance of the manipulator is optimized over the whole reference, and this will give better results than the purely kinematic instantaneous optimization which is the dominating technique in research litterature.

Dynamic coordination and actuator efficiency using momentum control for macro-micro manipulators

A control scheme for the coordination of motion in a macro-micro manipulator system is presented. The motion of the end-effector is decoupled from the rest of the system using resolved acceleration control, while a slow gross positioning is used for the macro part. To avoid saturated inputs and excessive use of energy for systems with limited fuel, the end-effector is not decoupled from macro part motion, but from selected directions of the linear momentum of the total system. For the vehicle-manipulator case, the end-effector is decoupled also from the angular momentum. This leads to lower force and torque peaks in the actuators, and control force is used on the macro part only when it is necessary to reposition this to keep the micro part inside its workspace.<<ETX>>

Dynamics coordination in a manipulator with 7 joints

A control system for a 7-joint manipulator with three intersecting shoulder axes is presented. A singularity avoidance scheme is developed, where the redundancy is resolved through a position transformation. The internal and external motions are decoupled using nonlinear feedback linearization in an augmented task space. It is then possible to use linear controllers both for the internal nullspace and for the end-effector coordinates. It is shown how optimal control theory can be applied to coordinate the motion in the arm, and how to do this so that the input generalized forces are minimized. This gives a coordination of internal and external motion which resembles the motion of the human arm; this is demonstrated by simulating a throwing motion with the manipulator.<<ETX>>

Bounds on the largest singular value of the manipulator Jacobian

It is proved that if the manipulator Jacobian is properly scaled, the largest singular value is bounded within a small interval close to unity. In this case, the inverse of the smallest singular value is a good estimate of the condition number. This is useful in singularity analysis. Bounds are derived for a general six-joint manipulator and for the ABB IRb 2000 industrial robot in a case study. >

Optimal continuous-path control for manipulators with redundant degrees of freedom

Abstract A control system for macro-micro manipulators is presented. A position transformation from the end-effector reference to joint coordinates is found using kinematic optimization. Decoupling and optimal control is used to coordinate the motion of the macro and micro part. The redundant manipulator will then have the speed of the micro manipulator and the large workspace of the macro manipulator. When optimal control is used, the redundant manipulator may be even faster than the micro manipulator provided that a suitable performance index is used. The performance of the manipulator is optimized over the whole reference, and this will give better results than the purely kinematic instantaneous optimization which is the dominating technique in research litterature.

RESOLVING REDUNDANCY THROUGH A WEIGHTED DAMPED LEAST-SQUARES SOLUTION

Abstract Singularity robust redundancy resolution with task priority can be implemented using the extended Jacobian technique with weighted damped least-squares. The resulting scheme is simple to implement and involves less computation than the task priority scheme. The minimum singular value of the Jacobian can be estimated reliably and accurately with little computation, and this estimate was used to calculate an appropriate damping factor. A constant damping factor was also used with good results. The scheme was successfully implemented in a simulation study with a seven-joint manipulator with a kinematic design derived from the PUMA geometry.