Near-pseudoinverse control of kinematically redundant manipulators with the constraint of repeatability

Abstract

The issue of repeatability is addressed for a particular redundant manipulator. This particular manipulator is a planar three-link manipulator with two orthogonal, prismatic joints and a third revolute joint. This manipulator can be thought of as a mobile robot with one revolute joint. It is shown that pseudoinverse control has no stable surfaces for this robotic manipulator. A class of repeatable inverses is then derived. Finally the repeatable inverse which is closest in an integral norm sense to the pseudoinverse is found from this class.If it turns out that this surface is in fact an integral surface, then a choice of initial joint settings which lies on this surface will guarantee repeatability. An integral surface is stable in the sense that if the manipulator starts on the surface then it will continue to stay on that surface. An example is given in [5]

Derivation of three closed loop kinematic velocity models using normalized quaternion feedback for an autonomous redundant manipulator with application to inverse kinematics

“…On the other hand, a critical view of the literature on the theory, modeling, and control of kinematically redundant autonomous manipulators [12,13,14,15,16,17,18,19,20] reveals that the spatial orientation control problem has largely been ignored. These literature resolve the redundancy based on open loop kinematic velocity and/or acceleration models of a serial link manipulator which could conceivably be applied to a spatial arm with N (>_ 7) joints.…”

“…These literature resolve the redundancy based on open loop kinematic velocity and/or acceleration models of a serial link manipulator which could conceivably be applied to a spatial arm with N (>_ 7) joints. But the proof of principle simulation examples presented in these literature mostly focus on the inverse kinematics of redundant planar manipulators with revolute joints or as in [17], a 3 DOF planar " manipulator with two prismatic and one revolute joint. But the orientation of a planar rigid body, e.g., the end effector of a planar revolute serial link manipulator, can " be represented by a single Euler angle measured about an axis perpendicular to the plane of motion.…”

Derivation of three closed loop kinematic velocity models using normalized quaternion feedback for an autonomous redundant manipulator with application to inverse kinematics

“…On the other hand, a critical view of the literature on the theory, modeling, and control of kinematically redundant autonomous manipulators [12,13,14,15,16,17,18,19,20] reveals that the spatial orientation control problem has largely been ignored. These angle measured about that axis.…”

The design of repeatable controls for kinematically redundant robots

“…These inverses, like the extended Jacobian [1], have foliations of stable surfaces and so are guaranteed to be repeatable. The inverses under consideration are generalized inverses like those described by (3). For a manipulator with a single degree of redundancy, any of these inverses can be written in the form (5) where ftJ is the unit length null vector of the Jacobian J and w is a vector which uniquely determines G. This follows from the fact that…”

“…Due to the extra degrees of freedom, redundant manipulators possess an infinite number of local control schemes of the form (3) where JG = I (except at singularities of J or possibly G) in order to satisfy the constraint of a given end effector velocity. A popular local control scheme is pseudoinverse control due to its desirable minimum norm property.…”