Neuromorphic solution to the inverse kinematic, problem of serial manipulators

Abstract

A serial manipulator is a chain of alternating 搄oints� (revolute or prismatic) and 搇inks,� with one end fixed and the free end having an end?effector attached. For a manipulator to perform any task, one of the main problems to be solved is generating a joint?space trajectory that makes the end?effector follow a given task?space trajectory (the inverse kinematics problem). This may have to be done in the presence of additional constraints such as avoiding obstacles and keeping within joint limits. The inverse kinematics problem in serial manipulators can be solved in closed form for certain types of non?redundant manipulators, and numerically for general non?redundant or redundant manipulators. In both these techniques, additional effort is required to obtain solutions that satisfy joint?motion constraints or that avoid singularities and obstacles. In this dissertation, we propose a self?organised neural architecture for solving the inverse kinematics for any serial manipulator. The architecture consists of three neural networks and concurrently transforms a given task?space trajectory into a configuration? or joint?space trajectory. We show that the architecture automatically eliminates solutions that violate joint limits. In addition, we obtain error bounds on the solution. We present simulation results for a planar two?degree?of?freedom manipulator and a planar three?degree?of?freedom redundant manipulator.