Probabilistic Robotics Wheeled Locomotion SA1 Locomotion of Wheeled

Probabilistic Robotics Wheeled Locomotion SA-1

Locomotion of Wheeled Robots Locomotion (Oxford Dict. ): Power of motion from place to place • Differential drive (Amigo. Bot, Pioneer 2 -DX) • Car drive (Ackerman steering) • Synchronous drive (B 21) • Mecanum wheels, XR 4000 2

Instantaneous Center of Curvature ICC • For rolling motion to occur, each wheel has to move along its y-axis 3

Differential Drive ICC y w vl q R x (x, y) vr l/2 4

Differential Drive: Forward Kinematics ICC R P(t+dt) P(t) 5

Differential Drive: Forward Kinematics ICC R P(t+dt) P(t) 6

Ackermann Drive ICC w y j j vl q R d x (x, y) vr l/2 7

Synchonous Drive y q v(t) x w(t ) 8

Synchro-Drive Robot 9

XR 4000 Drive y vi(t) q wi(t) x ICC 10

XR 4000 [courtesy by Oliver Brock & Oussama Khatib] 11

Mecanum Wheels 12

Example: Priamos (Karlsruhe) 13

Example 14

Odometry 15

Non-Holonomic Constraints • Non-holonomic constraints limit the possible incremental movements within the configuration space of the robot. • Robots with differential drive or synchro-drive move on a circular trajectory and cannot move sideways. • XR-4000 or Mecanum-wheeled robots can move sideways. 16

Holonomic vs. Non-Holonomic • Non-holonomic constraints reduce the control space with respect to the current configuration (e. g. , moving sideways is impossible). • Holonomic constraints reduce the configuration space. 17