Redundant Non-Serial Implicit Manipulator Kinematics and Dynamics

Abstract

Redundant non-serial manipulators that encompass a broad spectrum of parallel and non-parallel heavy load bearing construction and material handling equipment are treated, using foundations of differential geometry. Kinematics of this category of manipulator are defined in configuration space by algebraic equations in input and output coordinates that cannot be explicitly solved for either set of coordinates as a function of the other. New sets called assembly components of manipulator configuration space are defined that partition the space into disjoint topological components whose assembled configurations cannot be connected by continuous trajectories. Forward and inverse kinematically singular configurations are characterized by criteria that partition each assembly component into singularity free assembly components in which equations of kinematics and dynamics are well behaved. Three typical applications and associated simplified model problems are studied throughout the paper to illustrate methods and results presented. Singularity free differentiable configuration space manifolds are parameterized by both input and operational coordinates, leading to well posed ordinary differential equations of manipulator dynamics in both input and operational coordinates. It is shown that generalized inverse velocity kinematic equations that are problematic for serial manipulators are likewise plagued with problems for non-serial implicit manipulators that can be avoided using the methods presented.