Manipulator Kinematics and Dynamics On Differentiable Manifolds: Part II Dynamics

The manipulator differentiable manifold formulation presented in Part I of this paper is used to create algorithms for forward and inverse kinematics on maximal, singularity free, path connected manifold components. Existence of forward and inverse configuration mappings in manifold components is extended to obtain forward and inverse velocity mappings. Computational algorithms for forward and inverse configuration and velocity analysis on a time grid are derived for each of the four categories of manipulator treated. Manifold parameterizations derived in Part I are used to transform variational equations of motion in Cartesian generalized coordinates to second order ordinary differential equations of manipulator dynamics, in terms of both input and output coordinates, avoiding ad-hoc derivation of equations of motion. This process is illustrated in evaluating terms required for equations of motion of the four model manipulators analyzed in Part I. It is shown that computation involved in forward and inverse kinematics and in evaluation of equations of manipulator dynamics can be carried out in real-time on modern microprocessors, supporting on-line implementation of modern methods of manipulator control.