Robotics (Locomotion)
Winter 1393
Bonab University
Locomotion “Movement or the ability to move”
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Locomotion
Locomotion mechanisms used in biological
systems:
-Successful in harsh environments
-Inspired most engineered locomotion
systems
Exception: wheels
However,
Our walking ~= rolling polygon
Locomotion – Can we copy nature?
• Extremely difficult because:• Mechanical complexity is achieved by: Structural replication
(cell division) like: millipede
• Man-made structure: fabrication=individual
• Miniaturization : extremely difficult
• Nature’s energy storage and activation (torque, response time,
And conversion efficiency) unachievable
Example: insects (robust)
Such limitations locomotion choice:• Wheeled (simpler, suitable for flat ground)
• Small # of legs ( higher DOFs mechanical complexity)
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Locomotion
Locomotion -- efficiency
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Locomotion
• on flat surfaces wheeled locomotion 1-2 orders of magnitude more efficient than legged locomotion• Example: railway with rolling friction = ideal
But, as the ground gets softer !!
• Legged locomotion = only point contacts
A biped walking system
~= by a rolling polygon,
with sides = d to the
span of the step.
As the step size
decreases
circle/wheel
Locomotion -- efficiency
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Locomotion
• Efficiency of wheeled locomotion depends on:• Environment (specially on ground)
• Flatness
• Hardness
• Efficiency of legged locomotion depends on:• Mass (that robot needs to support at all parts of gait)
• Leg
• Body
• So, it’s clear why• nature chooses legged rough/unstructured env.
(insect vertical variation > 10 it’s height)
• Human environments = engineered, smooth surfaces so, choice= wheeled
• Recently, for more natural outdoor environments hybrid
General Considerations (all forms of mobile robot locomotion)
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Locomotion
• Locomotion vs. Manipulation both study:• Actuators generate interaction forces
• Mechanisms desired kinematic & dynamic properties
• Key issues for locomotion:• stability
- number and geometry of contact points
- center of gravity
- static/dynamic stability
- inclination of terrain
• characteristics of contact- contact point/path size and shape
- angle of contact
- friction
• type of environment- structure
- medium, (e.g. water, air, soft or hard ground)
Legged Mobile Robots
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Locomotion:
Legged
• Legged locomotion = a series of point contacts between the robot & ground
• Advantages: • Adaptability
• Maneuverability in rough terrain
• Quality of the ground: does not matter
• Cross holes so long as its reach exceeds the width
• Potential to manipulate objects in the environment with great skill, e.g.
• Disadvantages:• power and mechanical complexity (Leg, which may include several DoF, must be capable of
sustaining part/whole weight)
• high maneuverability = forces in different directions (if leg has enough DoFs)
Example of
manipulation:
Dung beetle
Leg configurations and stability
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• Some biologically successful legged systems• Large animals (reptiles, mammals): 4-legs
• Insects >= 6-legs
• Some mammals perfected for 2-leg locom.
Humans can even jump on 1-leg (balance)
Price = complex active control
In contrast: 3-legged static stability
(stool : balance without motion, passive)
• Robot: static walk (need to lift legs) = need 6-legs
(a tripod of legs in touch with ground at all times)
• Insects/spiders, Mammals, Human
Arrangement of the legs of various animals
Static walking with six legs
Standing/walking after birth is more difficult
6-legs 4-legs 2-legs
Locomotion:
Legged
Video demonstrating
tripod walk
Variety of successful legs: from very simple to complicated
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• Complexity of individual legs• Caterpillar (1-DoF)
• Hydraulic pressure extends leg
• Release in pressure + single tensile muscle retracts leg
• Complex overall locomotion
• Two robotic legs (with 3-DoFs):
• Human leg: (> 7 major DoFs)• Further actuation at toes
• > 15 muscle groups, 8-complex joints
leg is extended using hydraulic pressure
Locomotion:
Legged
Variety of successful legs: Example
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• 3-DoF cockroach leg
Locomotion:
Legged
http://www.manoonpong.com/AMOSWD06.html
Leg DoFs needed to Move
• At least 2-DoFs needed• Lift
• Swing forward
• More common is adding 1-dof for adding complex maneuvers
• 4th is in recent walking robots at ankle
• In general: adding dof = increase maneuverability
• Range of terrains
• Different gaits
• Main disadvantage: Added energy, control, and mass
• And leg coordination / gait control
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2-types of gaits in a 4-legged
robot, static walking is
impossible:
Locomotion:
Legged
Possible gaits
• Gait: a sequence of lift and release events for the individual legs.
• For a mobile robot with k legs:
1. lift right leg;
2. lift left leg;
3. release right leg;
4. release left leg;
5. lift both legs together;
6. release both legs together.
• K=6:
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Locomotion:
Legged
Examples of walking robots: One-legged
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• No high-volume industrial application (legged), but important research
• 1-leg • Minimizes mass
• No leg coordination
• Maximizes advantage of legged motion (1 contact point vs. whole track)
So, suitable for the roughest terrain
Hopper running start cross a gap > its stride
Multilegged can’t run limited to gap = its reach
• Major challenge: balance• Not only static walk = impossible
• Static stability while stationary = impossible
• Active balance:1-Change centre of gravity, 2-Corrective forces
Locomotion:
Legged
Examples of walking robots: One-legged
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• Raibert hopper (well-known single legged hopping robot)
• Actuators: hydraulic (large off-board pump)
• Continuous corrections (body attitude, velocity)
• By adjusting leg angle
Locomotion:
Legged
Not very energy efficient
Examples of walking robots: One-legged
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• 2D single bow leg hopper• More energy efficient
• Hydraulic actuator bow leg
(85% of landing energy is returned, means:
Stable hopping with 15%)
• 1 battery set 20 minutes of hop
• controls velocity by changing the angle
of the leg to the body at the hip
• An important aspect in hopping robots:
Duality: mechanics vs. controls• Mechanical design can help simplify control
• Dynamic stability with more passivity
Locomotion:
Legged
The 2D single bow leg hopper from CMU
Video: Robots from MIT’s Leg Lab
• Past 10 years: many successful bipedal robots demonstrated:• Walking-run
• Jumping
• Up-down stairs
• Even aerial tricks
• In the commercial sector:• Honda
• Sony
• They both designed:• Servos for small power joints
• Great: power/weight (small & strong)
• Intelligent (with sensors, so compliant actuation)
Examples of walking robots: 2-legged
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Locomotion:
Legged
significant advances highly capable 2-leg robots
SonyHonda
• Result of research begun in 1997
• Objective: motion/ communication entertainment
(dancing & singing)
• 38 DOF
• 7 microphones fine sound localization
• Person recognition (image)
• Stereo map reconstruction
• Speech recognition (limited)
• For this goal, Sony spent considerable effort designing
a motion prototyping application system to enable engineers to
script dances in a straightforward manner
Examples of walking robots: 2-legged (Sony SDR-4X II)
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Locomotion:
Legged
NAO – biped robot video
• Long history Asimo P2
• Much larger than Sony SDR-4X
• Practical mobility in the human world of stairs
• The first robot that famously (biomimetic): stair up/down
• Goal: not entertainment, but human aids in society
• Height ~= humans operate in their world
(say, control light switches)
important feature (2-leg robots): anthropomorphic shape
• Can have same approximate dimensions as humans
• Makes them excellent vehicles for research in human-robot interaction
Examples of walking robots: 2-legged (Honda P2)
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Locomotion:
Legged
• WABIAN-2R developed at Waseda University in Japan• designed to emulate human motion (even to dance like a human)
• DOF= leg:6x2, foot:1x2(passive), waist:2, trunk:2, arm:7x2, hand:3x2,
Neck:3
• Spring flamingo of MIT:• Springs in series with leg actuators =
More elastic gait
• Combined with kneecaps
• Very biomimetic
• 2-leg robots:• can only be statically stable within
some limits
• must perform continuous
balance-correcting even when
standing still
Examples of walking robots: 2-legged
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Locomotion:
Legged
• Standing still = passively stable, walking remains challenging (CoG needs to be actively shifted during gait)
• Sony invested several $million on AIBO:
Examples of walking robots: 4-legged
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Locomotion:
Legged
Sony produced:• A new robot operating system that is near real-time
• New geared servomotors:
• Sufficiently high torque to support the robot
• Yet back drivable for safety
• A color vision system -> AIBO can chase a brightly
colored ball
• function for 1-hour -> recharging
• > 60,000 units sold in the first year
• ~ $1500
• 4-leg: the potential to serve as effective artifacts for research in human-robot interaction:• As a pet (might develop an emotional relationship)
• They can emulate learning and maturation (AIBO does)
Examples of walking robots: 4-legged (AIBO, artificial dog from Sony)
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Locomotion:
Legged
• Extremely popular for their static stability in walking
So, less control complexity
• In most cases, each leg has 3DOF:• hip flexion, knee flexion, & hip abduction
Examples of walking robots: 6-legged (hexapods)
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Locomotion:
Legged
Lauron II, a hexapod platform developed at
the University of Karlsruhe, GermanyPlustech developed the first application-
driven walking robot
• Genghis is a commercially available hobby robot• has six legs, each 2DOF provided by hobby servos
(hip flexion - hip abduction)
• Such robots has less maneuverability in rough
terrain but performs quite well on flat ground.
• Straightforward arrangement of servomotors,
straight legs -> easily built
• Insects (the most successful locomoting creatures
on earth), excel at traversing all forms of terrain
with 6-legs, even upside down.
• The gap of capability (insects-robots) is still huge• Not lack of DOF in robots
• Insects combine few active DOFs with passive structures (microscopic barbs, textured pads) -> grip strength
Examples of walking robots: 6-legged (hexapods)
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Locomotion:
Legged
Genghis, one of the most famous walking robots
from MIT, uses hobby servomotors as its actuators
Wheeled Mobile robots
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• Wheeled locomotion: the design space• Wheel design
• Wheel geometry
• Stability
• Maneuverability
• Controllability
• Wheeled locomotion: case studies• Synchro drive
• Omnidirectional drive (locomotion)
• with three spherical wheels
• with four Swedish wheels
• with four castor wheels and eight motors
• Tracked slip/skid locomotion
• Walking wheels
Locomotion:
Wheeled
Uranus
from CMU
Nomad X4000
Has 4 castor
Wheels all
-steered
-driven
Wheeled Mobile robots: Design space - wheel design
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• 4 basic wheel types (large effect on the overall kinematics)
(a) Standard wheel 2DOF; rotation around the (motorized) wheel axle
and the contact point
b) castor wheel: 2DOF; rotation around an offset steering joint
c) Swedish wheel: 3DOF; rotation around the (motorized) wheel axle,
around the rollers, and around the contact point
(d) Ball or spherical
Locomotion:
Wheeled
Highly directional
steering
Wheeled Mobile robots: Design space - wheel geometry
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Choice of wheel • Types
• Arrangement, or wheel geometry
• Why not common car configuration (Ackerman)?
Locomotion:
Wheeled
strongly linked affects:• Maneuverability
• Controllability
• Stability
Wheeled Mobile robots: Design space - wheel geometry
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Locomotion:
Wheeled
Wheeled Mobile robots: Design space - wheel geometry
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Locomotion:
Wheeled
Wheeled Mobile robots: Design space - Stability
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• Minimum # wheel for stability?• Surprisingly, 2 (CoM below axle)
• But wheel diameter = impractically large
• Dynamics (high enough torque) can also cause instability
• Conventionally, static (Not dynamic) stability requires
3-wheels• CoG be contained in the triangle of contacts
• Otherwise it needs controller to be stabilized
• Stability further improves by adding wheels• But we’ll need flexible suspension on uneven terrain
Locomotion:
Wheeled
Cye does vacuum and deliveries
Wheeled Mobile robots: Design space - Maneuverability
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• Maneuverability: Overall DoF that robot can manipulate:• Mobility
• Steerability
• Omnidirectional Robot?• Can move at any time in any direction on the ground plane (x,y)
• Regardless of robot’s orientation around it’s vertical axix
• requires wheels to move in more than just 1-direction
• So, usually employ powered Swedish (Mecanum) or
spherical wheels
Locomotion:
Wheeled
Wheeled Mobile robots: Design space - Maneuverability
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• Examples of robot direction based on wheels’ rotation:
Locomotion:
Wheeled
Uranus: uses four Swedish wheels to rotate and
translate independently and without constraints
Wheeled Mobile robots: Design space - Maneuverability
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• A disadvantage for Swedish/spherical wheels:• Limited ground clearance (mechanical limitations)
• A solution: 4-castor wheels:• All actively translated
• All actively steered -> truly omnidirectional (although robot moves with this steering)
• Other classes of robots are highly popular: • High maneuverability slightly inferior to Omnidirectional:
• Motion in any direction:• May require initial rotation
• If a circular robot with rotation axis at the centre, footprint also won’t change
• The simplest is 2-wheel differential drive
• 1-2 more contact points for improved stability
• Ackerman config. (lower maneuverability)
• Turning diameter > car
• Moving sideways very difficult
• advantage: its directionality ->
very good lateral stability in high-speed turns (popular)
Locomotion:
Wheeled
Wheeled Mobile robots: Design space - Controllability
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• Controllability vs. Maneuverability (inverse correlation)
• E.g., 4-castor wheel -> significant processing (desired rotational/translational velocities -> individual wheel commands)
• Omnidirectional designs greater DOF at the wheel (the Swedish wheel has a set of free rollers) -> accumulation of slippage ->
• reduce dead-reckoning accuracy
• increase the design complexity
• For specific direction of travel:
• Ackerman: just lock the steering
• 2-wheel diff. drive : Challenging for the 2 motors to have the same velocity profile
• Variations between wheels, motors, environmental differences
• Uranus: even more difficult
• Summary: no ideal configuration maximizes
Locomotion:
Wheeled
• Stability
• Maneuverability
• Controllability
-> Design based on: Application
Wheeled Mobile robots: Case studies
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• 1-Synchro drive:• Popular for indoor applications
• Only 2-motors
• Translation motor
• Steering motor
• No direct way of reorienting the chassis
• It drifts with time (uneven tire slippage)
• Rotational dead reckoning problem
• Can add extra motor for this purpose
• Dead reckoning: True omnidirectional < Synch. < Ackerman
• Closest wheel starts spinning first (single belt for translation)
Locomotion:
Wheeled
Omnidirectional, but orientation of chassis is not controllable
B21r: sold with such capability
Wheeled Mobile robots: Case studies
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• 2-Omnidirectional drive:• Complete maneuverability = high interest
• In any direction (x,y,θ) holonomic (Every DoF is controllable)
a) With 3 spherical wheels
• Suspended by 3 contact points (2 bearing, 1 by wheel connected to motor axle)
• Simple design, but limited to flat surfaces & small loads
b) With 4 Swedish wheels (or with 3 90o wheel because we have 3 DoF in the plane)
• One motor for each wheel
• Direction & relative speed of each motor omnidirectionality
• Even can simultaneously rotate around its vertical axis
• One application: Mobile manipulator (gross motion by robot chassis)
c) With 4 castor wheels & 8 motors
• Requires precise synchronization and coordination for
Precise motion (x,y,θ)
Locomotion:
Wheeled
XR4000 from
Nomadic
Wheeled Mobile robots: Case studies
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• 3-Tracked slip/skid locomotion:• Assumption in wheel configurations: wheels are not
allowed to skid
• Alternatively: reorient the robot by spinning wheels that
are facing the same direction
• at different speeds
• in opposite directions
• Example: army tank, Nanokhod
• Large ground contact patches better:
• maneuverability in loose terrains
• traction
• Disadvantage: changing orientation (=skidding turn)
• Most of the track must slide
• Exact centre of turn is difficult to predict
• Dead reckoning: inaccurate
• Power efficiency: good on loose train, bad otherwise
Locomotion:
Wheeled
Walking wheels
• Walking robots:• best maneuverability in rough terrain
• Inefficient on flat ground & need sophisticated control
• Hybrid solutions: combining• adaptability of legs
• efficiency of wheels
• Example:• Shrimp: 6 motorized wheels
• Front-back motors are steered
• 4 on the side help steering by
speed control
• Personal rover
• Actively shifts CoM
• By identifying the terrain
• Then moving the boom
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Shrimp, an all-terrain robot with
outstanding passive climbing abilities (EPFL)
Supplement
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Locomotion
Extra explanation – Mecanum Wheel
Figure 2 provides a top view of a (rectangular) vehicle featuring four Mecanum
wheels, along with its attached coordinate system (x,y), the origin of which is assumed to be the geometrical centre of the rectangle; the wheels are identifed by the numbers 1 : : : 4, starting from the right-bottom corner (i.e., from the
right-rear wheel of the vehicle) and proceeding in the counter-clockwise direction. The angular velocities w1:::4 are designed positive for translational motion in the forward direction (increasing y).
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Extra explanation – Mecanum Wheel
• The driving (motor) force (thrust) ~Fi acting on wheel iof the vehicle (chosen to be wheel 2), along with its decomposition into one force ( ~Fi;p) parallel to the rotational axis of the roller (which is in contact with the ground at that moment) and one in the transverse direction ( ~Fi;t), are shown in Fig. 3. The angle between the transverse direction and the rotational plane of the wheel is denoted as α [0,π ). (The quantity sin α is also known as the efficiency of the wheel'.) Since the rollers rotate freely around their axle, there is no traction along the transverse direction; therefore, the force ~Fi;t can safely be ignored when studying the motion of the vehicle. The relation between Fi;p
• and Fi (indicating the corresponding moduli of the two vectors) reads as:
• Fi;p = Fi sin α.
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The rollers shown are assumed to be those
corresponding to the lower part of the wheel,
part of which is in contact with the ground.
Extra explanation – Mecanum Wheel
• Finally, the only relevant force, Fi,p, may be decomposed into forces along the axes of the attached coordinate system (see Fig. 4). The geometry dictates that Fi,x = Fi,p cos α= Fi sin αcos α and Fi,y = Fi,p sin α = Fi sin2 α .
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The rollers shown are assumed to be those
corresponding to the lower part of the wheel,
part of which is in contact with the ground.
Control scheme for mobile robots
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Locomotion
Main bodies of knowledge associated
with mobile robotics