Kinematics is fundamentally used in robotics to understand, predict, and control the motion of robot arms and manipulators without considering the forces that cause the motion.
In robotics, robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems. This core principle means that the structure of a robot, composed of links connected by joints, is analyzed purely based on its geometric configuration. The emphasis on geometry means that the links of the robot are modeled as rigid bodies and its joints are assumed to provide pure rotation or translation. This simplified, geometric model is crucial for computationally solving complex movement problems.
Key Applications of Kinematics in Robotics
The geometric study provided by robot kinematics forms the basis for several essential robot functions, primarily revolving around determining the relationship between the robot's joints and its end-effector (the 'hand' or tool at the end of the arm). The two main applications are forward and inverse kinematics.
Forward Kinematics
Forward kinematics answers the question: "Given the angles or positions of all the robot's joints, where is the end-effector located in space?"
- Input: Joint variables (angles for revolute joints, displacements for prismatic joints).
- Output: The pose (position and orientation) of the end-effector.
- Method: It involves using the known lengths and configurations of the rigid links, and the joint variables, to calculate the transformation matrix from the robot's base frame to the end-effector frame using geometric or algebraic methods (like Denavit-Hartenberg parameters).
Uses of Forward Kinematics:
- Simulation: Predicting the path of the end-effector based on planned joint movements.
- Visualization: Displaying the robot's configuration in simulation software.
- Safety Checks: Determining if the robot's end-effector or links will collide with obstacles or limits within its workspace.
Inverse Kinematics
Inverse kinematics is often considered more complex and addresses the question: "Given a desired position and orientation for the end-effector, what are the required angles or positions for each joint?"
- Input: The desired pose (position and orientation) of the end-effector.
- Output: The set(s) of joint variables needed to achieve that pose.
- Method: This is typically solved using geometric techniques (for simpler robots) or iterative numerical methods (for more complex or redundant robots). Unlike forward kinematics, inverse kinematics can have multiple solutions (different joint configurations for the same end-effector pose), or no solution if the desired pose is outside the robot's reach.
Uses of Inverse Kinematics:
- Task Planning: Commanding the robot to reach specific points or follow paths in its workspace (e.g., picking up an object, welding a seam).
- Trajectory Generation: Calculating the sequence of joint movements needed to smoothly move the end-effector from one point to another.
- Obstacle Avoidance: Finding joint configurations that allow the robot to reach a target while avoiding objects in its environment.
Why Kinematics is Essential
Understanding robot kinematics is foundational for:
- Robot Control: Implementing algorithms to move the robot precisely.
- Path Planning: Generating safe and efficient movements for the robot.
- Design: Evaluating the reach, dexterity, and workspace of potential robot designs.
- Calibration: Correcting discrepancies between the theoretical kinematic model and the physical robot.
By modeling the robot as a series of rigid bodies connected by ideal joints, kinematics provides the mathematical framework necessary to translate desired tasks in the real world (like "move to coordinates X, Y, Z") into the specific joint commands the robot needs to execute.
