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A 7 (or 4) degree-of-freedom limb

An Analytical Algorithm for a Seven-DOF Limb “Real-time inverse kinematics techniques for anthropomorphic limbs” Deepak Tolani, Ambarish Goswami, Norman I. Badler University of Pennsylvania. A 7 (or 4) degree-of-freedom limb. Numerical approaches : Jacobian singularites, local minima

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A 7 (or 4) degree-of-freedom limb

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  1. An Analytical Algorithm for a Seven-DOF Limb“Real-time inverse kinematics techniques for anthropomorphic limbs”Deepak Tolani, Ambarish Goswami, Norman I. BadlerUniversity of Pennsylvania

  2. A 7 (or 4) degree-of-freedom limb • Numerical approaches : Jacobian singularites, local minima • Analytical approaches : efficient and reliable 3 DOF 3 DOF L3 S1 S2 1 DOF L1 F L2

  3. Inverse Kinematics • Rotation matrices at joints S1, F, and S2 • 2 constant transformation matrices • A desired goal • The equation to solve

  4. Step 1: Solving for • Only affects the distance of S2 relative to S1. • If the normal vector of the plane containing S1, S2, and F is parallel to the axis of rotation of F, then can be computed trivially using the law of cosines. • Else, …

  5. Step 2: Solving for Elbow Position

  6. Step 3: Solving for R1 and R2

  7. Class PV_IK \\vrs4\opensources\xmath \\vrs4\opensources\ik #include “pv_ik.h” … float t4, r1[4][4]; … PV_IK ik(L1, L2); ik.setGoal(gx, gy, gz); ik.solve(); //or ik.solve(psi); t4 = ik.getTheta4(); ik.getR1(r1);

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