Answer

2D and 3D Velocity Measurement

2D Velocity: Vector $\vec{v}=(v_x,v_y)$ in plane. Methods:

• Wheel odometry: $v = \omega r$, two wheels → $v_x, \omega_z$.
• Optical flow: Camera estimates $(u,v)$ pixel/frame → $v_{world}$.
• 2D LIDAR Doppler: Frequency shift $\Delta f = 2v/\lambda$.
• IMU + GPS: Integrate $a_x,a_y$.

3D Velocity: $\vec{v}=(v_x,v_y,v_z)$.

• 3D optical flow / stereo vision: Depth $Z$ via disparity, $v_z = \Delta Z/\Delta t$.
• Doppler LIDAR / Radar: 3D $f_d$.
• IMU 6-DOF: Accelerometer + gyro fusion (Kalman) → $v_{3D}$.
• VIO: Visual-Inertial Odometry.

Comparison:

Feature	2D	3D
Sensors	Encoders, 2D LIDAR, single camera	Stereo camera, 3D LIDAR, IMU
Complexity	Low	High
Applications	Mobile base, AGV	Drone, manipulator

Final: 2D = planar $(v_x,v_y)$ via odometry/optical flow, 3D adds $v_z$ via stereo/Doppler/IMU fusion.