Motion Control

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Motion Control

1. Locomotion
2. Legged Locomotion
3. Snake Locomotion
4. Free-Floating Motion
5. Wheeled Locomotion
6. Mobile Robot Kinematics
7. Models
8. Maneuverability
9. Motion Control

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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.

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Locomotion - Issues

• Stability
• 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

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Locomotion in Nature
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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

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Locomotion in Robots Examples

• Locomotion via Climbing

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Locomotion in Robots Examples

• Locomotion via Hopping

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Locomotion in Robots Examples

• Locomotion via Sliding

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Locomotion in Robots Examples

• Locomotion via Dancing

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Locomotion in Robots Examples

• Other types of motion

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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

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Legged Locomotion

• Nature inspired.
• The movement of walking biped is close to rolling.

• Number of legs determines stability of locomotion

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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.

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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

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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.

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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.

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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

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Examples of Legs with 3 DOF
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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.

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Most Obvious Gaits with 4 legs
Changeover Galopping
walking
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Most Obvious Gait with 6 legs
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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)!
  

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The number of possible gaits

• For a biped walker (k2) the number of possible
  events N is
  
  N (2k - 1) ! 3 ! 3 2 1 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

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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 63

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Humanoid Robots

• P2 from Honda, Japan
• Maximum Speed 2 km/h
• Autonomy 15 min
• Weight 210 kg
• Height 1.82 m
• Leg DOF 26
• Arm DOF 27

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Humanoid Robots

• Wabian build at Waseda University in Japan
• Weight 107 kg
• Height 1.66 m
• DOF in total 43

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Walking with Three Legs
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Walking Robots with Four Legs

• Artificial Dog Aibo from Sony, Japan

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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 63
• Power Consumption 10 W

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Wheeled Locomotion
a) b)

• Wheel type
• Standard Wheel
• 2 DOF
• Castor Wheel
• 3 DOF

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Wheeled Locomotion

• Wheel types
• c) Swedish Wheel
• 3 DOF
• d) Spherical Wheel
• Technically difficult

c) d)
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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

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Wheeled Locomotion

• 2 Wheel arrangements
• a) One steering and one traction wheel
• b) Differential drive with COM below the axle

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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

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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

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Wheeled Locomotion

• 4 Wheel arrangements

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Wheeled Locomotion

• Uneven Terrain
• Suspension required to maintain contact
• Bigger wheels can be used, but require greater
  torques

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Adapt Optimally to Rough Terrain