1. Motion Control Locomotion Mobile Robot Kinematics Legged Locomotion
Snake Locomotion
Free-Floating Motion
Wheeled Locomotion
Mobile Robot Kinematics
Models
Maneuverability
Motion Control

2. Locomotion Locomotion is the act of moving from place to place.
Locomotion relies on the physical interaction between the vehicle and its environment.
Locomotion is concerned with the interaction forces, along with the mechanisms and actuators that generate them.

3. Locomotion - Issues Stability Contact Environment
Number of contact points
Center of gravity
Static versus Dynamic stabilization
Inclination of terrain
Contact
Contact point or area
Angle of contact
Friction
Environment
Structure
Medium

4. Locomotion in Nature

5. Locomotion in Robots Many locomotion concepts are inspired by nature
Most natural locomotion concepts are difficult to imitate technically
Rolling, which is NOT found in nature, is most efficient

6. Locomotion in Robots: Examples
Locomotion via Climbing

7. Locomotion in Robots: Examples
Locomotion via Hopping

8. Locomotion in Robots: Examples
Locomotion via Sliding

9. Locomotion in Robots: Examples
Locomotion via Dancing

10. Locomotion in Robots: Examples
Other types of motion

11. Locomotion Concepts Concepts found in nature
difficult to imitate technically
Most technical systems use wheels or caterpillars
Rolling is most efficient, but not found in nature
Nature never invented the wheel !
However, the movement of a walking biped is close to rolling

12. Legged Locomotion Nature inspired.
The movement of walking biped is close to rolling.
Number of legs determines stability of locomotion

13. Walking of a Biped Biped walking mechanism
not too far from real rolling.
rolling of a polygon with side length equal to the length of the step.
the smaller the step gets, the more the polygon tends to a circle (wheel).
However, fully rotating joint was not developed in nature.

14. Walking or rolling? structural complexity control expense
energy efficient
number of actuators
terrain (flat ground, soft ground, climbing..)
movement of the involved masses
walking / running includes up and down movement of COG
some extra losses

15. Mobile Robots with legs
The fewer legs the more complicated becomes locomotion
stability, at least three legs are required for static stability
During walking some legs are lifted
thus loosing stability?
For static walking at least 6 legs are required
babies have to learn for quite a while until they are able to stand or even walk on there two legs.

16. Number of Joints of Each Leg
A minimum of two DOF is required to move a leg forward
a lift and a swing motion.
sliding free motion in more then only one direction not possible
Three DOF for each leg in most cases
Fourth DOF for the ankle joint
might improve walking
however, additional joint (DOF) increase the complexity of the design and especially of the locomotion control.

17. Legged Locomotion Degrees of freedom (DOF) per leg
Trade-off exists between complexity and stability
Degrees of freedom per system
Too many, needed gaited motion

18. Examples of Legs with 3 DOF

19. Legged Locomotion Walking gaits
The gait is the repetitive sequence of leg movements to allow locomotion
The gait is characterized by the sequence of lift and release events of individual legs.

20. Most Obvious Gaits with 4 legs
Changeover Galopping walking

21. Most Obvious Gait with 6 legs

22. The number of possible gaits
The gait is characterized as the sequence of lift and release events of the individual legs
it depends on the number of legs.
the number of possible events N for a walking machine with k leg s is: N = (2k - 1)!

23. The number of possible gaits
For a biped walker (k=2) the number of possible events N is: N = (2k - 1) ! = 3 ! = = 6
The 6 different events are: lift right leg / lift left leg / release right leg / release left leg / lift both legs together / release both legs together
For a robot with 6 legs (hexapod) N = 11! = 39'916'800

24. Walking Robots with Six Legs
Most popular because static stable walking possible
The human guided hexapod of Ohio State University
Maximum Speed: 2,3 m/s
Weight: 3.2 t
Height: 3 m
Length: 5.2 m
No. of legs: 6
DOF in total: 6*3

25. Humanoid Robots P2 from Honda, Japan Maximum Speed: 2 km/h
Autonomy: 15 min
Weight: 210 kg
Height: 1.82 m
Leg DOF: 2*6
Arm DOF: 2*7

26. Humanoid Robots Wabian build at Waseda University in Japan
Weight: 107 kg
Height: 1.66 m
DOF in total: 43

27. Walking with Three Legs

28. Walking Robots with Four Legs
Artificial Dog Aibo from Sony, Japan

29. Walking Robots with Six Legs
Lauron II, University of Karlsruhe
Maximum Speed: 0.5 m/s
Weight: 6 kg
Height: 0.3 m
Length: 0.7 m
No. of legs: 6
DOF in total: 6*3
Power Consumption: 10 W

30. Wheeled Locomotion a) b) Wheel type Standard Wheel Castor Wheel 2 DOF

31. Wheeled Locomotion Wheel types c) d) c) Swedish Wheel
3 DOF
d) Spherical Wheel
Technically difficult
c) d)

32. Wheeled Locomotion Wheel Arrangements
Three issues: Stability, Maneuverability and Controllability
Stability is guaranteed with 3 wheels, improved with four.
Tradeoff between Maneuverability and Controllability
Combining actuation and steering on one wheel increases complexity and adds positioning errors

33. Wheeled Locomotion 2 Wheel arrangements
a) One steering and one traction wheel
b) Differential drive with COM below the axle

34. Wheeled Locomotion 3 Wheel arrangements
c) Differential drive with third point of contact
d) Two connected traction wheels plus one steered
e) Two free wheels plus one steered traction wheel

35. Wheeled Locomotion 3 Wheel arrangements
f) Three swedish or omni- d wheels: omni- directional movement
g) Three synchronously driven and steered wheels: orientation not controllable

36. Wheeled Locomotion
4 Wheel arrangements

37. Wheeled Locomotion Uneven Terrain
Suspension required to maintain contact
Bigger wheels can be used, but require greater torques

38. Adapt Optimally to Rough Terrain