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ik_handout - Inverse Kinematics ME/ECE 739 Notes Professor...

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Inverse Kinematics – ME/ECE 739 Notes – Professor Nicola J. Ferrier – Spring 2006 1 Iterative Kinematic Inverse for Pose Goal: For a desired end-effector pose 0 N T * , find joint position q to attain that pose. Algorithm IKPose[ 0 N T * , q (0) ] I Input: - The desired configuration 0 N T * - initial joint configuration q (0) II Initialize: q = q (0) III Iterate: 1. Compute for current joint position, q : 0 N T - 1 ( q ) 0 J - 1 ( q ) 2. Calculate the error: ˆ E ( k ) = 0 N T * 0 N T - 1 ( q ) - I = * - #6 +#5 +#1 +#6 * - #4 +#2 - #5 #4 * +#3 0 0 0 0 3. Map to 6-vector: * - #6 +#5 +#1 +#6 * - #4 +#2 - #5 #4 * +#3 0 0 0 0 #1 #2 #3 #4 #5 #6 = ˆ E 6 ( k ) 4. Estimate the joint increments: ˆ δ q = 0 J - 1 ( q ) ˆ E 6 5. Move joints virtually q = q + ˆ δ q 6. if ˆ δ q < joint resolution, stop , otherwise repeat iteration IV Output: q Kinematic Inverse for Trajectories Goal: find joint positions to follow a desired end- effector trajectory.
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