presentazione standard di powerpoint · 2019. 6. 6. · prof.fanny ficuciello robotics for...

Prof. Fanny Ficuciello Robotics for Bioengineering • Differential Kinematics

Relationship between the joint velocities and the corresponding end-effector linear and angular velocity Differential kinematics Geometric Jacobian Jacobian of typical manipulator structures Kinematic singularities Analysis of redundancy Use of redundancy Inverse differential kinematics Analytical Jacobian Inverse kinematics algorithms Comparison among inverse kinematics algorithms Statics Manipulability ellipsoids

Differential Kinematics


drift phenomena of the solution

error in the operational space

find

Inverse Kinematics Algorithms


linearization of the error dynamics

For a redundant manipulator

Jacobian (Pseudo-)inverse


without linearization of the error dinamics Lyapunov method

where

Jacobian Transpose


the choice

Imply

If with If limited,

Jacobian Transpose


Jacobian Transpose


Second-order Algorithms


Comparison Among Inverse Kinematics Algorithms

Three planar arm


Open-loop vs closed-loop inverse Jacobian algorithm


End-effector orientation is not constrained


Exploiting redundancy


Kineto-Statics Duality

absorbed by the structure


consider the set of joint velocities of constant (unit) norm

the operational space velocities that can be generated

the principal axes of the ellipsoid are determined by the eigenvectorsof

the dimensions of the axes are given by the singular values of

volume of the ellipsoid is a measure of manipulation ability

Velocity manipulability Ellipsoids


kineto-statics duality an effective interpretation of the above results can be achieved by

regarding the manipulator as a mechanical transformer of velocities and forces from the joint space to the operational space Conservation of energy dictates that an amplification in the velocity

transformation is necessarily accompanied by a reduction in the force transformation, and vice versa

Force manipulability ellipsoid


Velocity Force

Two-link planar arm


Typical task of writing/throwing a weight in the horizontal direction

Velocity and force manipulability ellipses for a 3-link planar arm in atypical configuration for a task of actuating force and velocity

Velocity and force manipulability ellipses for a 3-link planar arm in atypical configuration for a task of controlling force and velocity

presentazione standard di powerpoint · 2019. 6. 6. · prof.fanny ficuciello robotics for...

Documents