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Introduction to Robotics © L. Itti & M. J. Mataric’
Introduction to RoboticsIntroduction to Robotics
� CSCI 445
� Amin Atrash
� Lecture #3: Effectors and Actuators
Introduction to Robotics © L. Itti & M. J. Mataric’
Today’s Lecture OutlineToday’s Lecture Outline
�Degrees of Freedom (DOF)� holonomicity, redundancy
� Legged locomotion� stability (static and dynamic)
� polygon of support
� Wheeled locomotion
� Trajectory/motion planning
Introduction to Robotics © L. Itti & M. J. Mataric’
Definition of EffectorDefinition of Effector
� An effector is any device that has an effect on the environment.
� A robot’s effectors are used to purposefully create an effect on the environment.
� E.g., legs, wheels, arms, fingers...
� The role of the controller is to get the effectors to produce the desired effect on the environment, based on the robot’s task.
Introduction to Robotics © L. Itti & M. J. Mataric’
Definition of ActuatorDefinition of Actuator
� An actuator is the actual mechanism that enables the effector to execute an action.
� E.g, electric motors, hydraulic or pneumatic cylinders, pumps…
� Actuators and effectors are not the same thing.
� Incorrectly thought of the same; “whatever makes the robot act”
Introduction to Robotics © L. Itti & M. J. Mataric’
Degrees of FreedomDegrees of Freedom
� Most simple actuators control a single
degree of freedom (DOF)
� Think of DOFs as ways in which a
motion can be made (e.g., up-down, left-
right, in-out)
� E.g., a motor shaft controls one rotational
DOF; a sliding part on a plotter controls
one translational DOF.
Introduction to Robotics © L. Itti & M. J. Mataric’
Counting DOFCounting DOF
� A free body in space has 6 DOF� 3 are translational (x, y, z)
� 3 are rotational (roll, pitch, and yaw)
� Every robot has a specific number of DOF
� If there is an actuator for every DOF, then all of the DOF are controllable
� Usually not all DOF are controllable
� This makes robot control harder
Introduction to Robotics © L. Itti & M. J. Mataric’
Example: DOF of a CarExample: DOF of a Car
� A car has 3 DOF: position (x,y) and orientation (theta)
� Only 2 DOF are controllable� driving: through the gas pedal and the
forward-reverse gear
� steering: through the steering wheel
� Since there are more DOF than are controllable, there are motions that cannot be done, like moving sideways (that’s why parallel parking is hard)
Introduction to Robotics © L. Itti & M. J. Mataric’
Actuators and DOFsActuators and DOFs
� We need to make a distinction between what an actuator does (e.g., pushing the gas pedal)
and what the robot does as a result (moving forward)
� A car can get to any 2D position but it may have to follow a very complicated trajectory
� Parallel parking requires a discontinuous trajectory w.r.t. velocity, i.e., the car has to stop and go
Introduction to Robotics © L. Itti & M. J. Mataric’
HolonomicityHolonomicity
� When the number of controllable DOF is equal to the total number of DOF on a robot, it is holonomic.
� If the number of controllable DOF is smaller than total DOF, the robot is non-holonomic.
� If the number of controllable DOF is larger than the total DOF, the robot is redundant.
Introduction to Robotics © L. Itti & M. J. Mataric’
RedundancyRedundancy
� A human arm has 7 DOF (3 in the shoulder, 1 in the elbow, 3 in the wrist), all of which can be controlled.
� A free object in 3D space (e.g., the hand, the
finger tip) can have at most 6 DOF!
� => There are redundant ways of putting the hand at a particular position in 3D space.
� This is the core of why robot manipulation is very hard!
Introduction to Robotics © L. Itti & M. J. Mataric’
Uses of EffectorsUses of Effectors
� Two basic ways of using effectors:� to move the robot around
=>locomotion
� to move other object around =>manipulation
� These divide robotics into two mostly separate categories:� mobile robotics
� manipulator robotics
Introduction to Robotics © L. Itti & M. J. Mataric’
LocomotionLocomotion
� Many different kinds of effectors and actuators are used for locomotion:� legs (walking, crawling, climbing,
jumping, hopping…)
� wheels (rolling)
� arms (swinging, crawling, climbing…)
� flippers (swimming)
� Most animals use legs, but most mobile robots use wheels, why?
Introduction to Robotics © L. Itti & M. J. Mataric’
StabilityStability
� Stability is a necessary property of mobile robots
� Stability can be� static (standing w/o falling over)
� dynamic (moving w/o falling over)
� Static stability is achieved through the mechanical design of the robot
� Dynamic stability is achieved through control
Introduction to Robotics © L. Itti & M. J. Mataric’
More on StabilityMore on Stability
� E.g., people are not statically stable but dynamically
stable! It takes active control to balance. This is
mostly unconscious.
� Static stability becomes easier with more
legs.
� To remain stable, a robot’s center of gravity
(COG) must fall under its polygon of support
(the area of the projection of its points of
contact onto the surface)
Introduction to Robotics © L. Itti & M. J. Mataric’
Polygon of SupportPolygon of Support
� In two-legged robots/creatures, the polygon
of support is very small, much smaller than
the robot itself, so static stability is not
possible (unless the feet are huge!)
� As more legs are added, and the feet spread
out, the polygon gets larger
� Three-legged creatures can use a tripod
stance to be statically stable
Introduction to Robotics © L. Itti & M. J. Mataric’
Statically Stable WalkingStatically Stable Walking
� Three legs are enough to balance, but what about walking?
� If a robot can stay continuously balanced while walking, it employs statically stable walking
� That is impossible with 3 legs; as soon as one is off the ground, only 2 are left, which is unstable
� How many legs are needed for statically stable walking?
Introduction to Robotics © L. Itti & M. J. Mataric’
Good Numbers of LegsGood Numbers of Legs
� Since it takes 3 legs to be statically stable, it takes at least 4 for statically stable walking
� Various such robots have been built
� 6 legs is the most popular number as they allow for a very stable walking gait, the tripod gait
� 3 legs are kept on the ground, while the other 3 are moved forward
Introduction to Robotics © L. Itti & M. J. Mataric’
The Tripod GaitThe Tripod Gait
� If the same three legs move at a time, this
is called the alternating tripod gait
� if the legs vary, it is called the ripple gait
� All times, a triangle of support stays on the
ground, and the COG is in it
� This is very stable and thus used in most
legged robots
Introduction to Robotics © L. Itti & M. J. Mataric’
Tripod GaitTripod Gait
See JPL MRE movie
Introduction to Robotics © L. Itti & M. J. Mataric’
Introduction to Robotics © L. Itti & M. J. Mataric’
Tripod Gait in BiologyTripod Gait in Biology� Numerous insects have 6 legs; cockroaches and
many others use the alternating tripod gait
� Insects with many more than 6 legs (e.g., centipedes and millipedes) use the ripple gate
� Insects can also run very fast by letting go of the
ground completely and going airborne…
Introduction to Robotics © L. Itti & M. J. Mataric’
How did they do it?How did they do it?
Introduction to Robotics © L. Itti & M. J. Mataric’
Defying physicsDefying physics
Patented design.
See USPTO for
more info.
Introduction to Robotics © L. Itti & M. J. Mataric’
Dynamic StabilityDynamic Stability� Statically stable walking is very energy
inefficient
� As an alternative, dynamic stability enables a robot to stay up while moving
� This requires active control (i.e., the inverse pendulum problem)
� Dynamic stability can allow for greater speed, but requires harder control
Introduction to Robotics © L. Itti & M. J. Mataric’
Dynamic StabilityDynamic Stability
Introduction to Robotics © L. Itti & M. J. Mataric’
Wheels v. LegsWheels v. Legs� Because balance is such a hard control
problem, most mobile robots have wheels, not legs, and are statically stable
� Wheels are more efficient than legs, and easier to control
� There are wheels in nature, but legs are far more prevalent (though in terms of population sizes, more than 2 legs greatly surpass bipedal locomotion)
Introduction to Robotics © L. Itti & M. J. Mataric’
Biological wheels?Biological wheels?
Introduction to Robotics © L. Itti & M. J. Mataric’
Introduction to Robotics © L. Itti & M. J. Mataric’
Varieties of WheelsVarieties of Wheels
� Wheels are the locomotion effectors of choice in most mobile robots
� Wheels can be as innovative as legs� size and shape variations
� tire shapes and patterns
� tracks
� wheels within wheels and cylinders
� different directions of rotation
� ...
Introduction to Robotics © L. Itti & M. J. Mataric’
Wheels and HolonomicityWheels and Holonomicity
� Having wheels does not imply holonomicity
� 2 or 4-wheeled robots are not usually holonomic
� A very popular and
efficient design involves
2 differentially-actuated
wheels and a passive
caster
Introduction to Robotics © L. Itti & M. J. Mataric’
LocomotionLocomotion
�Common Drives
�Differential – rotation by speed of wheels
�Synchronous – can steer wheels
�Tracked – tanks
�Car – Ackerman steering
y
rolly
x
z motion
Introduction to Robotics © L. Itti & M. J. Mataric’
Differential SteeringDifferential Steering
� Differential steering means that the two
(or more) wheels can be steered
separately (individually)
� If one wheel can turn in one direction and the
other in the opposite direction, the robot can spin in place: this is very helpful for following
arbitrary trajectories
� Tracks/treads are often
used (e.g., tanks)
Introduction to Robotics © L. Itti & M. J. Mataric’
Omni-Directional RobotsOmni-Directional Robots
� Omni-directional (holonomic) robots can be built using special wheels
� A minimum of 3 wheels (arranged in opposition) is needed
� Mechanically inefficient
Introduction to Robotics © L. Itti & M. J. Mataric’
An Omni-Directional RobotAn Omni-Directional Robot
Introduction to Robotics © L. Itti & M. J. Mataric’
Instantaneous Center of CurvatureInstantaneous Center of Curvature
� Instantaneous Center of Curvature
� Intersection of x-axis of wheels
Good!
Bad!!!
Bad!!!
ICC
Introduction to Robotics © L. Itti & M. J. Mataric’
Differential DrivesDifferential Drives
ICC
R
l/2
Vl
Vr
θθθθ
ω
Introduction to Robotics © L. Itti & M. J. Mataric’
Differential DriveDifferential Drive
Introduction to Robotics © L. Itti & M. J. Mataric’
Synchronous DriveSynchronous Drive
Introduction to Robotics © L. Itti & M. J. Mataric’
Ackerman Steering
(Kingpin Steering)
Ackerman Steering
(Kingpin Steering)
From
wikipedia.org
Introduction to Robotics © L. Itti & M. J. Mataric’
Other examplesOther examples
�Bicycle
�Tricycle
Introduction to Robotics © L. Itti & M. J. Mataric’
TrajectoriesTrajectories
� In locomotion we may be
concerned with:� getting to a particular location
� following a particular trajectory (path)
� Following an arbitrary given trajectory is harder, and is impossible for some robots (depending on their DOF)
� For others, it is possible, but with discontinuous velocity (stop, turn, and then go again)
Introduction to Robotics © L. Itti & M. J. Mataric’
Trajectory PlanningTrajectory Planning
� A large area of traditional robotics is
concerned with following arbitrary trajectories
� Why? Because planning can be used to
compute optimal (and thus arbitrary)
trajectories for a robot to follow to get to a
particular goal location
� Practical robots may not be so concerned
with specific trajectories as with just getting
to the goal location
Introduction to Robotics © L. Itti & M. J. Mataric’
More Trajectory PlanningMore Trajectory Planning
� Trajectory planning is a computationally complex process
� All possible trajectories must be found (by using search) and evaluated� Since robots are not points, their
geometry (i.e., turning radius) and steering mechanism (holonomicity properties) must be taken into account
� This is also called motion planning
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