A kinematic model is a mathematical abstraction that describes the geometry of a robot’s motion by relating joint-space variables (angles and displacements) to the position and orientation of the end-effector in Cartesian space, without accounting for the forces or torques that produce that motion. Forward kinematics maps joint configurations to end-effector poses using homogeneous transformation matrices or Denavit-Hartenberg parameters, whereas inverse kinematics solves the reverse problem of finding joint configurations that achieve a desired pose. Kinematic models are foundational to trajectory generation, motion planning, and simulation in robotic systems.
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- Kinematic models form the geometric backbone of all robotics control and planning software. They are typically constructed using the Denavit-Hartenberg (DH) convention, which provides a systematic method for assigning coordinate frames to each link in a serial manipulator chain and expressing the 4×4 homogeneous transformation matrix between consecutive frames with four parameters.
- Forward kinematics (FK) computes the end-effector pose given all joint angles and is a straightforward application of matrix multiplication along the kinematic chain. Inverse kinematics (IK) is substantially more complex: closed-form analytical solutions exist only for special geometries (e.g., six-degree-of-freedom manipulators with a spherical wrist), while general solutions require iterative numerical methods such as Jacobian pseudo-inverse or gradient-descent schemes.
- The Jacobian matrix, derived from differential kinematics, relates joint velocities to end-effector velocities and is central to velocity control, singularity analysis, and force control. In robot simulation environments such as ROS 2, kinematic models are specified in the URDF or SDF formats, which encode link geometry, joint limits, and joint types. Accurate kinematic models are prerequisites for trajectory generation, motion planning algorithms (such as RRT or CHOMP), and closed-loop control strategies including Model Predictive Control.