csci 445 amin atrash - usc robotics research labaatrash/cs445/lec03.pdf · csci 445 amin atrash...

Introduction to Robotics © L. Itti & M. J. Mataric’

Introduction to RoboticsIntroduction to Robotics

� CSCI 445

� Amin Atrash

� Lecture #3: Effectors and Actuators


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


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.


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”


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.


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


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)


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


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.


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!


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


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?


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


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)


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


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?


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


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


Tripod GaitTripod Gait

See JPL MRE movie


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…


How did they do it?How did they do it?


Defying physicsDefying physics

Patented design.

See USPTO for

more info.


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


Dynamic StabilityDynamic Stability


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)


Biological wheels?Biological wheels?


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

� ...


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


LocomotionLocomotion

�Common Drives

�Differential – rotation by speed of wheels

�Synchronous – can steer wheels

�Tracked – tanks

�Car – Ackerman steering

y

rolly

x

z motion


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)


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


An Omni-Directional RobotAn Omni-Directional Robot


Instantaneous Center of CurvatureInstantaneous Center of Curvature

� Instantaneous Center of Curvature

� Intersection of x-axis of wheels

Good!

Bad!!!

Bad!!!

ICC


Differential DrivesDifferential Drives

ICC

R

l/2

Vl

Vr

θθθθ

ω


Differential DriveDifferential Drive


Synchronous DriveSynchronous Drive


Ackerman Steering

(Kingpin Steering)

Ackerman Steering

(Kingpin Steering)

From

wikipedia.org


Other examplesOther examples

�Bicycle

�Tricycle


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)


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


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

csci 445 amin atrash - usc robotics research labaatrash/cs445/lec03.pdf · csci 445 amin atrash...

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