Repeatable Joint Displacement Generation for Redundant Robotic Systems

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Abstract
This paper presents a novel, practical, and theoretically sound kinematic control strategy for serial redundant manipulators. This strategy yields repeatability in the joint space of a serial redundant manipulator whose end effector undergoes some general cyclic type motion. This is accomplished by deriving a new inverse kinematic equation that is based on springs being theoretically or conceptually located in the joints of the manipulator (torsional springs for revolute joints, translational springs for prismatic joints). Previous researchers have also derived an inverse kinematic equation for serial redundant manipulators. However, to the authors’ knowledge, the new strategy is the first to include the free angles of torsional springs and the free lengths of translational springs. This is important because it ensures the repeatability in the joint space of a serial redundant manipulator whose end effector undergoes a cyclic type motion. Numerical verification for repeatability is done in terms of Lie bracket condition. Choices for the free angle and torsional stiffness of a joint (or the free length and translational stiffness) are made based upon the mechanical limits of the joint.

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