- Forward Kinematics Forward kinematics involves computing the position and orientation of the robot's end-effector based on its joint angles. For a 7-DOF arm like the KUKA LBR iiwa, the forward kinematics solution calculates the transformation matrix from the base to the end-effector, describing the robot's pose in 3D space. This process is crucial for tasks where precise positioning is required, allowing us to understand where the end-effector will be when the joints are set to specific angles.
- Workspace of the Arm Robot The workspace of the LBR iiwa 7 R800 robot is the set of all positions and orientations that the robot's end-effector can reach. This workspace is determined by the robot's joint limits, link lengths, and configurations. Understanding the workspace is essential for ensuring that the robot can perform tasks within its physical limits. The KUKA LBR iiwa has a versatile workspace due to its 7-DOF configuration, allowing it to reach a wide range of positions with flexibility.
- Inverse Kinematics using Jacobian Inverse kinematics (IK) involves calculating the joint angles required to achieve a desired position and orientation of the robot's end-effector. Using the Jacobian matrix, which relates joint velocities to end-effector velocities, we solve for the joint configurations that produce a specific end-effector pose. This is a critical process in robotics, enabling precise control of the robot's movements to reach target positions, especially in complex environments.
- Dynamic Control Dynamic control of the robot arm is governed by the equation B (q) ̈q + C (q, ̇q) ̇q + G (q) =τ, where B(q) represents the inertia matrix, C (q, ̇q) is the Coriolis and centrifugal force matrix, G(q) is the gravity vector, and τ is the torque applied at the joints. This equation models the robot's dynamics, enabling precise control over its movement by considering the effects of inertia, Coriolis forces, and gravity.
- Final Task: Precision Placement The final task involves using the above methods to design a trajectory controller that accurately places a custom flange at a location identified by a camera. By integrating forward kinematics, inverse kinematics, and dynamic control, the trajectory controller achieves a precision of 0.00001m in all directions, ensuring that the flange is placed with exceptional accuracy. This task demonstrates the practical application of robotic control principles in a real-world scenario.