ROBOTICS Kinematics Degeneracies Redundancies Precision TEMPUS IV Project

ROBOTICS Kinematics: Degeneracies, Redundancies, Precision TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS

Redundancy and Degeneracies • Redundant: a manipulator can reach a specified position with more than one configuration of the linkages – More than one solution to the inverse kinematic transform (usually from a sqrt function or arccos) – Robot with more DOF than task demands • Redundancy is not bad – – Reach into holes keep away from joint limits avoid collisions with obstacles Avoid degenerate states where manipulator could lose degrees of freedom 2

Multiple Solutions 3

Redundancy and Degeneracies But redundancy can be useful…. 4

Redundancy and Degeneracies • Degenerate: infinitely many solutions – Lose control of one or more degrees of freedom – Occurs in wrist when two axes align 5

Infinitely Many Solutions! • Two link arm (L 1 = L 2) with the origin as the goal position: TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 6

Static Precision of Manipulators • Accuracy • difference between the actual location and the commanded location • Repeatability • variation in the actual location when the manipulator repeatedly moves the endeffector/tool center point, Pe, to the same commanded location • Resolution • the minimum distance that the tool center point can be guaranteed to move TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 7

Accuracy and Repeatability TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 8

Resolution TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 9

What causes inaccuracies? • Non geometric parameters: – Compliance – Gear backlash, eccentricity & transmission errors – Encoder resolution – Temperature related expansion – Linkage wobble due to bearing slop – Cross coupling between joints due to robot construction • Rotation of joint n due to a rotation about a joint n-I • Occurs in cable driven systems TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 10

What causes inaccuracies? • For a Cartesian robot (prismatic joints in orthogonal directions) errors do not accumulate • Errors accumulate for revolute robots TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 11

What causes inaccuracies? • Geometric parameters: – Errors in link parameters (manufacturing tolerances) • Axes can be up to 0. 5 o from the design angle – Error in joint placement (gripper flange not flat or not orthogonal to roll axis) TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 12

References: • Lessons of prof. N. Ferrier, Wisconsin, USA. Literature: J. M. Selig: Introductory Robotics, Prentice Hall, 1992 TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 13