🦾 Inverse Kinematics

Inverse kinematics (IK) is the problem of computing the joint angles of a linked chain — such as a robot arm or an animated character's skeleton — needed to place its end effector at a desired position, the reverse of forward kinematics, which computes end-effector position from already-known joint angles. Because a chain with several joints usually has more degrees of freedom than the target has constraints, IK problems are often underdetermined and are solved iteratively rather than in closed form — for example with FABRIK (Forward And Backward Reaching Inverse Kinematics), which alternates forward and backward passes along the chain until it converges on a valid pose without requiring any matrix inversion. IK is essential to robotics, character animation and procedural motion, letting an artist or algorithm specify only where a hand or foot should go and letting the solver figure out every joint in between. Other common approaches include the Jacobian transpose and cyclic coordinate descent (CCD) methods, which likewise avoid the expensive matrix inversions of the classical Jacobian-inverse technique while still converging reliably for chains with many links. Because a target pose can often be reached in more than one way, real IK systems also apply joint-angle limits and preference costs so the resulting pose looks physically natural rather than merely mathematically valid.