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1 Inverse Kinematics

CS W4733 NOTES - Inverse Kinematics1 Inverse Kinematics1. Forward Kinematics is a mapping from joint spaceQto Cartesian spaceW:F(Q) =WThis mapping is one to one - there is a unique Cartesian configuration for the robot for a givenset of joint variables. Inverse Kinematics is a method to findthe Inverse mapping fromWtoQ:Q=F 1(W)2. The Inverse Kinematics problem has a wide range of applications in robotics. Most of our highlevel problem solving about the physical world is posed in Cartesian space. While we can reasonabout the physical world in Cartesian terms, the robot is actuated in joint space - that is what weultimately can control.

SPHERICAL robot has 3 variables: Radius r, Longitude angle Θ and latitude angle Φ. For the Spherical robot the final matrix is: T0 3 = SinΘCosΦ CosΘ SinΘSinΦ rCosΦSinΘ 0 0 0 1 1. r is the length of the the spherical arm radius and is equal to: r = ± q P2 X + P2 y + P2 z 2. To solve for Φ, Pz−1(Pz / − r). Note r has 2 values from ...

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