PLANNING THE JOINT TRAJECTORY OF REDUNDANT KINEMATICS CHAIN

Abstract

In a number of technological operations, the end-effector of an open kinematic chain must follow a spatial trajectory, and a necessary condition for the realization of the movement is the smooth change of the generalized coordinates. An analogous problem exists in the development of drugs when a molecular configuration requiring minimal energy for its realization must be provided. A task of this nature must be solved in order to find the missing segments of a partially known protein structure. These problems lead to the more general task of ensuring a smooth change of the joint coordinates of the kinematic chain while performing a continuous spatial movement of the end-effector of the chain. An algorithm for planning a smooth reconfiguration of a redundant kinematics chain is proposed in the present work. The chain is decomposed into a countable number of substructures, each of which provides a unique solution of inverse kinematics for a target point. This makes it possible to select substructures during the spatial movement of the kinematic chain, ensuring a smooth change of the joint coordinates. The redundant generalized coordinates are force controlled, given the necessary values to ensure a smooth reconfiguration. The inverse kinematics problem is solved for the other joints.