Fast Numerical Methods for Inverse Kinematics

Bill Baxter
Dept of Computer Science
University of North Carolina at Chapel Hill

February 21, 2000
COMP 290-72, Physically Based Modeling

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Table of contents

Fast Numerical Methods for Inverse Kinematics

Introduction

Overview

The IK Problem

Joint Types

More Joint types

Forward Kinematics

So what is f ?

So what is f ?

Other Representations

Kinematics

So what is f -1 ?

An idea

The Jacobian

The Jacobian

The Jacobian

Computing the Jacobian

Matrix Derivatives

Rotation Matrix Derivatives

The Angular Velocity Matrix

Simple Answer

T he Jacobian Inverse

What's Wrong with J+?

Jacobian Transpose

Principal of Virtual Work

Jacobian Transpose

Jacobian Transpose

Jacobian Transpose

Good and Bad of JT

Cyclic Coordinate Descent

CCD Math - Prismatic

CCD Math - Revolute

CCD Math - Revolute

Good and Bad of CCD

Wrap up

Bibliography

Author: Bill Baxter

E-mail: baxter@cs.unc.edu

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