Lecture4

Lecture4 - 2/21/2010 Path and Trajectory Planning ME 598A:...

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2/21/2010 1 Path and Trajectory Planning ME 598A: Introduction to Robotics Spring 2010 ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning Homework 2 Solutions ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning
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2/21/2010 2 Review: Jacobian ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning Review: Jacobian Example 1: Planar RR ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning
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2/21/2010 3 Review: Singularities ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning [i.e. all columns of J are not linearly independent] Review: Identifying Singularities ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning [http://en.wikipedia.org/wiki/Determinant]
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2/21/2010 4 Review: Singularities Example 1: Planar RR ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning Review: Jacobian Transpose ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning
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2/21/2010 5 Review: Inverse Jacobian The Jacobian relationship: Specifies the end effector velocity that will result when the joints move with velocity Inverse problem: Find the joint velocities that produce the desired end effector velocity q q ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning p J q 1 ) ( q p [Hard if have non square J pseudo inverse (pinv)] Path and Trajectory Planning ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning
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2/21/2010 6 Path and Trajectory Planning •G i v en : –In i t ia l configuration of robot, q s (initial joint coordinates) –F ina l configuration of robot, q f (final joint coordinates) •Go al: ind a collision free path connecting q s and q f •P a th Planning – Provides geometric description (q) of the robot motion (no dynamics) ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning • Trajectory Planning – Provides time function to specify velocities and accelerations as robot moves along path q Configuration Space End effector • Configuration Space = C Obstacle Obstacle ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning • Obstacle Configuration Space = CO •F ree Configuration Space = C–CO = C free
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2/21/2010 7 Configuration Space •V e r y expensive to compute exactly •C om p l e x i t y grow exponentially with degrees of freedom ME 598A: INTRODUCTION TO ROBOTICS Path and Trajectory Planning intractable • Need methods that avoid explicit construction of CO or C free
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This note was uploaded on 02/28/2010 for the course ME 598 taught by Professor Staf during the Spring '09 term at Stevens.

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Lecture4 - 2/21/2010 Path and Trajectory Planning ME 598A:...

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