In computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a given position and orientation relative to the start of the chain.
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Inverse kinematics is used to recover the movements of an object in the world from some other data, such as a film of those movements, or a film of the world as seen by a camera which is itself making those movements.
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In robotics, inverse kinematics makes use of the kinematics equations to determine the joint parameters that provide a desired configuration for each of the robot's end-effectors.
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Forward kinematics uses the joint parameters to compute the configuration of the chain, and inverse kinematics reverses this calculation to determine the joint parameters that achieve a desired configuration.
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Inverse kinematics is an example of the kinematic analysis of a constrained system of rigid bodies, or kinematic chain.
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Inverse kinematics is important to game programming and 3D animation, where it is used to connect game characters physically to the world, such as feet landing firmly on top of terrain .
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The inverse kinematics problem computes the joint angles for a desired pose of the figure.
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Therefore, inverse kinematics is used in computer-aided design systems to animate assemblies and by computer-based artists and animators to position figures and characters.
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For example, inverse kinematics allows an artist to move the hand of a 3D human model to a desired position and orientation and have an algorithm select the proper angles of the wrist, elbow, and shoulder joints.
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One issue with these solvers, is that they are known to not necessarily give locally smooth solutions between two adjacent configurations, which can cause instability if iterative solutions to inverse kinematics are required, such as if the IK is solved inside a high-rate control loop.
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The core idea behind several of these methods is to model the forward Inverse kinematics equation using a Taylor series expansion, which can be simpler to invert and solve than the original system.
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