Forward Kinematics (FK)

Forward kinematics computes the end-effector's pose in Cartesian space given the robot's joint angles (or displacements for prismatic joints). For a serial chain robot, FK is computed by multiplying a sequence of homogeneous transformation matrices (one per joint), typically derived from Denavit-Hartenberg (DH) parameters or a URDF description. FK always has a unique solution — given joint angles, there is exactly one end-effector pose — unlike the inverse problem (IK), which may have zero, one, or many solutions. FK is used in simulation, collision checking, visualization, and real-time robot state monitoring.