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Robots move themselves or move objects around them. Motion of the robot itself is sometimes called egomotion or locomotion. Motion of objects is called manipulation. Here we begin with a general framework for motion algebra. We then introduce specific representations and parameterizations of motion. These representations lead to algorithms that control motion or estimate the state of the environment from a motion model. A self-driving car and a humanoid robot may require different motion representations. The choice depends on the robot vendor or application domain (e.g., the aeronautical industry). We use motion representations to model: Kinematics: Kinematics describes the motion of bodies in a robotic mechanism without considering the forces or torques that cause the motion. Dynamics: The dynamic equations of motion relate the actuation and contact forces on a robot mechanism to the resulting acceleration and motion trajectories. Kinematic and dynamic models describe the robot’s mechanisms, including the actuators that exert forces on the links and joints of each mechanism.