Robotics
Forward kinematics
Definition
Forward kinematics calculates the position and orientation of a robot link or end-effector from the robot geometry and joint positions. It maps a robot configuration to a pose.
Also known as: FK
Updated
From joint readings to a hand pose
A robot arm reports joint angles, but a manipulation task usually concerns the hand's position and orientation. Forward kinematics connects the two. Starting from a reference frame at the base, it composes the transformations along the links to the end-effector.
Modern Robotics develops this mapping with the product-of-exponentials formula: each joint contributes motion about its screw axis, combined with the robot's home pose. Denavit-Hartenberg parameters provide another way to organize the link transforms.
The reference frame is part of the result
A hand pose relative to the torso is different from its pose relative to the floor. For a moving robot, the base transform must be included when expressing the hand in world coordinates. MIT's manipulation notes demonstrate this by composing transforms through a kinematic tree to the world frame.
The same process can locate an elbow, camera, or tool frame, provided its connection to the modeled links is known.
What the calculation leaves out
Forward kinematics uses geometry. It does not calculate the forces required to move, which belong to dynamics. The reverse problem, finding joint positions for a requested pose, is inverse kinematics.
Sources
Related terms
Inverse kinematics
Inverse kinematics finds joint positions that produce a desired robot end-effector position, orientation, or other geometric task. A target can have multiple solutions, no solution, or a continuous family of solutions.
Denavit-Hartenberg parameters
Denavit-Hartenberg parameters are four geometric quantities that describe the relative placement of successive link frames in a robot kinematic chain. They provide a systematic way to construct the transformations used in forward kinematics.
Homogeneous transformation
In rigid-body robotics, a homogeneous transformation is a 4-by-4 matrix that combines a three-dimensional rotation and translation. It represents a pose or changes coordinates between reference frames.