CS545_Lecture_9

CS545_Lecture_9 - CS545Contents IX Inverse Kinematics...

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Unformatted text preview: CS545Contents IX Inverse Kinematics Analytical Methods Iterative (Differential) Methods Geometric and Analytical Jacobian Jacobian Transpose Method Pseudo-Inverse Pseudo-Inverse with Optimization Extended Jacobian Method Reading Assignment for Next Class See http://www-clmc.usc.edu/~cs545 The Inverse Kinematics Problem Direct Kinematics Inverse Kinematics Possible Problems of Inverse Kinematics Multiple solutions Infinitely many solutions No solutions No closed-form (analytical solution) x = f ( ) = f 1 x The Inverse Kinematics Problem Direct Kinematics Inverse Kinematics Possible Problems of Inverse Kinematics Multiple solutions Infinitely many solutions No solutions No closed-form (analytical solution) x = f ( ) = f 1 x ( ) Analytical (Algebraic) Solutions Analytically invert the direct kinematics equations and enumerate all solution branches Note: this only works if the number of constraints is the same as the number of degrees-of-freedom of the robot What if not? Iterative solutions Invent artificial constraints Examples 2DOF arm See S&S textbook 2.11 ff Analytical Inverse Kinematics of a 2 DOF Arm Inverse Kinematics: l 1 l 2 x y F x = l 1 cos 1 + l 2 cos 1 + 2 ( ) y = l 1 sin 1 + l 2 sin 1 + 2 ( ) l = x 2 + y 2 l 2 2 = l 1 2 + l 2 2 l 1 l cos = arccos l 2 + l 1 2 l 2 2 2 l 1 l y x = tan 1 = arctan y x 2 = arctan y l 1 sin x l 1 cos 1 1 Iterative Solutions of Inverse Kinematics Resolved Motion Rate Control Properties Only holds for high sampling rates or low Cartesian velocities a local solution that may be globally inappropriate Problems with singular postures...
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This note was uploaded on 02/24/2011 for the course CSCI 545 taught by Professor Schaal during the Spring '08 term at USC.

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CS545_Lecture_9 - CS545Contents IX Inverse Kinematics...

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