It is proposed to use weighted least-norm solution to avoid joint limits for redundant joint manipulators. A comparison is made with the gradient projection method for avoiding joint limits. While the gradient projection method provides the optimal direction for the joint velocity vector within the null space, its magnitude is not unique and is adjusted by a scalar coefficient chosen by trial and error. It is shown in this paper that one fixed value of the scalar coefficient is not suitable even in a small workspace. The proposed manipulation scheme automatically chooses an appropriate magnitude of the self-motion throughout the workspace. This scheme, unlike the gradient projection method, guarantees joint limit avoidance, and also minimizes unnecessary self-motion. It was implemented and tested for real-time control of a seven-degree-of-freedom (7-DOF) Robotics Research Corporation (RRC) manipulator. >

A weighted least-norm solution based scheme for avoiding joint limits for redundant joint manipulators

Kinematically redundant manipulator arms and other robotic mechanisms provide a means for solving sophisticated motion tasks but require complex research on both mechanical and control problems. So far, many works have been published on kinematic redundancy, however, a systemization is missing. In this article an attempt for such a systemization is presented. It has been limited to methods for redundancy resolution through local optimization. Until now, these methods are most widely used, and it is expected also that they will prevail in the near future. A classification is suggested and the performance capabilities of the methods are discussed and compared. Two reference tables are provided; One of them lists references for different problems on kinematic redundancy as: mechanical design, dexterity measures, multicriteria optimization, global optimization, control design and computational considerations. The other table displays existing publications classified according to the application area of redundant robotic-mechanisms.

Redundancy resolution through local optimization: A review

Redundant manipulators provide increased flexibility for the execution of complex tasks. Redundancy is often required to maintain manipulability and avoid obstacles while completing the required task. Self-motion is the internal (joint) motion of the manipulator that does not contribute to the end effector motion. In this article we provide a dynamic feedback control law that guarantees the tracking of a desired end effector trajectory and provides redundancy resolution by making the self-motion of the manipulator flow along the projection of a given arbitrary vector field. By choosing this vector field to be the gradient of a cost function, for example, the manipulator can be made to seek an optimum configuration. The effectiveness of the control law is illustrated with simulation results.

Dynamic control of redundant manipulators

The loss of independent degrees of freedom at singular configurations is an inherent characteristic of robotic manipulators. Due to the unavoidable singularity of mechanical wrists, singular configurations cannot be avoided by simply restricting the bounds of the workspace. Techniques for operating at singular configurations without inducing unacceptably high joint velocities or end effector tracking errors are presented. Extensions to the damped least-squares formulation which incorporate estimates of the proximity to singularities and selective filtering of singular components are illustrated. The generality of the technique presented is illustrated in a computer simulation of a commercially available manipulator operating through singular configurations.

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Numerical filtering for the operation of robotic manipulators through kinematically singular configurations

The singular value decomposition has been extensively used for the analysis of the kinematic and dynamic characteristics of robotic manipulators. Due to a reputation for being nu merically expensive to compute, however, it has not been used for real-time applications. This work illustrates a for mulation for the singular value decomposition that takes advantage of the nature of robotics matrix calculations to ob tain a computationally feasible algorithm. Several applica tions, including the control of redundant manipulators and the optimization of dexterity, are discussed. A detailed illus tration of the use of the singular value decomposition to deal with the general problem of singularities is also presented.

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The singular value decomposition: computation and applications to robotics

The joint velocities required to move the robot end-effector with a desired speed depend on the direction of motion. Robot's mobility, i.e., its ability to move, is better in the directions requiring lower joint velocities. When the robot is near a singularity configuration, the joint velocities required to attain the end-effector velocity in certain directions are extremely high. Thus arbitrary directional changes become more difficult. Robot's flexibility, defined as its ability to change the direction of the end-effector motion, is low in the vicinity of singular configurations. Addition of redundant joints can greatly enhance their flexibility. However, this requires a proper utilization of redundancy. A control scheme is presented to improve the flexibility of redundant robots. The feasibility and effectiveness of this control scheme are demonstrated through simulation.

J. Luh

Papers

Redundant robot control for higher flexibility