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Unformatted text preview: CS545Contents IX Inverse Kinematics Analytical Methods Iterative (Differential) Methods Geometric and Analytical Jacobian Jacobian Transpose Method PseudoInverse PseudoInverse with Optimization Extended Jacobian Method Reading Assignment for Next Class See http://wwwclmc.usc.edu/~cs545 The Inverse Kinematics Problem Direct Kinematics Inverse Kinematics Possible Problems of Inverse Kinematics Multiple solutions Infinitely many solutions No solutions No closedform (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 closedform (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 degreesoffreedom 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.
 Spring '08
 Schaal

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