What is the core function of Denavit-Hartenberg (DH) parameters in robotics?

The core function of Denavit-Hartenberg (DH) parameters in robotics is to provide a standardized method for describing the kinematic structure of a robot arm. Kinematics refers to the study of motion without considering the forces that cause it, focusing instead on position, velocity, and acceleration. DH parameters achieve this by assigning a coordinate frame to each link of the robot arm and defining four parameters that relate each frame to the next. These four parameters are: link length (a), which is the distance between the Z axes of two consecutive coordinate frames along the X axis; link twist (alpha), which is the angle between the Z axes of two consecutive coordinate frames measured about the X axis; joint offset (d), which is the distance between the X axes of two consecutive coordinate frames along the Z axis; and joint angle (theta), which is the angle between the X axes of two consecutive coordinate frames measured about the Z axis. By systematically defining these parameters for each joint, DH parameters enable the creation of a homogeneous transformation matrix that describes the position and orientation of each link relative to the base frame of the robot. This matrix is crucial for performing forward kinematics, which calculates the position and orientation of the robot's end-effector given the joint angles, and inverse kinematics, which calculates the joint angles required to reach a desired position and orientation of the end-effector. Without a standardized system like DH parameters, accurately controlling robot motion and predicting its behavior would be significantly more complex.