Explain the difference between forward and inverse kinematics.

Forward kinematics and inverse kinematics are two fundamental concepts in robotics that describe the relationship between a robot's joint angles and the position and orientation of its end-effector (the tool or hand at the end of the robot arm). Forward kinematics is the process of calculating the end-effector pose (position and orientation) given the joint angles and the robot's physical parameters (link lengths, joint offsets, etc.). In other words, if you know the angles of all the joints in the robot arm, forward kinematics allows you to determine exactly where the end-effector is located in space and how it is oriented. This calculation typically involves using transformation matrices based on Denavit-Hartenberg (DH) parameters to represent the relationships between the robot's links. Inverse kinematics is the opposite problem. Given a desired end-effector pose, inverse kinematics calculates the joint angles required to achieve that pose. This is a more complex problem than forward kinematics because there may be multiple solutions (multiple sets of joint angles that can achieve the same end-effector pose) or no solutions at all (the desired pose is outside the robot's workspace). Furthermore, inverse kinematics solutions are often non-unique and can be computationally expensive to calculate. Therefore, they are opposite equations.