07_num_ik.pdf - COMS W4733 Computational Aspects of Robotics Lecture 7 Numerical Inverse Kinematics S R Buss"Introduction to Inverse Kinematics with

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COMS W4733: Computational Aspects of Robotics Lecture 7: Numerical Inverse Kinematics Instructor: Tony Dear S. R. Buss. "Introduction to Inverse Kinematics with Jacobian Transpose, Pseudoinverse and Damped Least Squares methods."
Review: Inverse Differential Kinematics Linear mapping between joint and end effector velocities 𝑟 × 𝑛 configuration-dependent Jacobian: 𝒗 ? = ? ? ሶ? 𝑟 rows for each end effector velocity 𝑛 columns for each joint velocity Inverse problem: Find joint velocities to achieve desired end effector velocities 𝑟 = 𝑛 : Invert the Jacobian (assuming non-singular) 𝑟 < 𝑛 : Underconstrained, right pseudoinverse can optimize different criteria 𝑟 > 𝑛 : Overconstrained, left pseudoinverse can minimize resulting error Singular (or near singular): damped least-squares to move Jacobian away from singularities
Back to Inverse Kinematics Moving a robot to a desired pose still a hard problem Inverting nonlinear FK equations was too difficult Can we use the simpler IDK problem with velocities?

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• Fall '19
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