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Navigation Robot control architectures for goal-directed navigation Prehension: Reaching and Grasping Classical Control Paradigm: “SPA” SPA lacks SPA is serial ad hoc analytical assumptous speed and efficiency flexibility and adaptivity modularity and scalability

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Navigation l.jpg
Navigation

  • Robot control architectures for goal-directed navigation

  • Prehension: Reaching and Grasping


Slide2 l.jpg

Classical Control Paradigm: “SPA”

SPA lacks

SPA is

  • serial

  • ad hoc

  • analytical

  • assumptous

  • speed and efficiency

  • flexibility and adaptivity

  • modularity and scalability

  • error-tolerance and robustness


Quotations by r brooks fast cheap and out of control l.jpg
Quotations by R. Brooks”fast, cheap, and out of control”

  • Planning is just a way of avoiding figuring out what to do next.

  • The world is its own best model

  • Complex behavior need not necessarily be the product of a complex control system

  • Simplicity is a virtue

  • Robots should be cheap

  • All on-board computation is important

  • Systems should be build incrementally

  • Intelligence is in the eye of the observer

  • No representation, no calibration, no complex computers


Objections that can be misleading l.jpg
Objections that can be misleading

  • In a different environment the robot will fail. [a function that deals with this problem will create more problems]

  • The system cannot be debugged [bugs, too, are in the eye of the observer]

  • It’s not scalable! [“Elephants don’t play chess”]


Slide5 l.jpg

Subsumption Architecture

Evaluation of progress

if not

Scheduling of subtasks

if not

(sub-) Goal approach

if not

Path planning

if not

Self-localization & -calibration

if not

Obstacle avoidance

if not

Move when clear

act

sense


Evaluation of the subsumption architecture l.jpg
Evaluation of the Subsumption Architecture

  • “I wouldn’t want one to be my chauffeur” (C. Torpe)

  • Modifications at low-levels affect higher levels

  • Often there the hierarchy is not strict

  • Priorities rather than inhibition

  • Representations, plans, and models do help

  • Reproducibility is a virtue

  • SPA is top-down, SubsArc is bottom-up

  • “neats vs. scruffies”


Modular architectures l.jpg
Modular architectures

  • Schemas (M. Arbib)

  • Circuit architecture: Situated automata (L. Kaelbling)

  • Action selection (P. Maes), behavior-based robotics (R. Arkin)

  • Dynamical systems and ant colonies

  • Cognitive architectures


Three layer architecture tla l.jpg

Deliberator

Sequencer

Controller

Three-layer architecture (TLA)

Erann Gat, 1998

Planning, search, reasoning

standard programming

Competition, scheduling,

and adaptation of behaviours

Elementary behaviours


Architectures summary l.jpg
Architectures Summary

  • Simplicity is a virtue

  • The subsumption architecture is simple and extendable and usually good to start with

  • 3. The ultimate goal is to interface reasoning with the real world

  • 4. Limited resources, noise and complexity are problems in any approach to robot control


Prehension l.jpg
Prehension

Goal : understand ideal robot mechanisms for

reaching, grasping and manipulation

Robot positions and shapes as a function of

control parameters – kinematics

Need to know:

  • Representing mechanism geometry

  • Standard configurations

  • Degrees of freedom

  • Grippers and graspability conditions


3d coordinate systems l.jpg
3D Coordinate Systems

Left handed (Right handed reverses +Z direction)


Vectors points in 3d l.jpg

Point Vector

Vectors & Points in 3D


Local reference frames l.jpg

can be expressed as

Local Reference Frames

  • Local (translated) coordinates

  • Global (untranslated) coordinates

Local could also have further sub-local frames


Translations l.jpg
Translations

Move to


Slide15 l.jpg

  • A lot of conventions

  • Here: positive is anti-clockwise when looking along +Z

  • in local (rotated) coordinates is (a,b,c)’

  • in global (unrotated) coordinates is

  • (a cos( )-b sin( ), a sin( )+b cos( ),c)’

Rotations

Rotate about Z axis


Slide16 l.jpg

Rotation Matrix Representation I

Much more compact and clearer



Other rotation representations l.jpg
Other Rotation Representations

  • All equivalent but different parameters:

  • Yaw, pitch, roll

  • Azimuth, elevation, twist

  • Axis + angle

  • Slant, tilt, twist

  • Quaternion

roll

pitch

yaw


Full rotation specification l.jpg
Full Rotation Specification

  • Need 3 angles for arbitrary 3D rotation

  • Lock & key example

  • Rotation angles :

  • Warning: rotation order by convention but

    must be used consistently:


Full transformation specification l.jpg
Full Transformation Specification

Each connection has a new local coordinate system

Need to specify 6 degrees of freedom

3 rotation + 3 translation


Kinematic chains l.jpg
Kinematic Chains

is at:

In C2:

In C1:

In C0:


Homogeneous coordinates i l.jpg
Homogeneous Coordinates I

Messy when more than 2 links, as in robot

So: pack rotation and translation into

Homogeneous coordinate matrix

Extend points with a 1 from 3-vector to 4-vector

Extend vectors with a 0 from 3-vector to 4-vector

Pack rotation and translation into 4x4 matrix:

3 rotation parameters:

3 translation parameters:


Homogeneous matrices l.jpg
Homogeneous matrices

scaling

translation

projection

perspective

rotations


Homogeneous coordinates ii l.jpg
Homogeneous coordinates II

In C2:

In C1:

In C0:

Longer chains for robot arms (e.g. 6 links):


Joint geometry l.jpg
Joint geometry

Linear (prismatic) joint:

slides

parametrize one translation

direction per joint

E.g.: sliding in the X direction

Hinge (revolute) joint:

rotates

parametrize one

rotation angle per joint

E.g. Rotation about x-axis

trf(θ,0,0,0,0,0)‏

trf(0,0,0,λ,0,0)‏


Slide26 l.jpg

Degrees of Freedom

  • Controllable DoF: number of joints

  • Effective DoF: number of DoF you can get after multiple

  • motions

  • car has 2 controllable (move, turn) but can adjust XY

  • position and orientation so 3 effective DoF

  • Task DoF: configurations in space dimensionality:

  • 2D : 3 (x,y,angle)

  • 3D : 6 (x,y,z,3 angles)


Forward and inverse kinematics l.jpg
Forward and Inverse Kinematics

Forward:

Given joint angles, find gripper position

Easy for sequential joints in robot arm: just multiply

matrices

Inverse:

Given desired gripper position, find joint angles

Hard for sequential joints – geometric reasoning


Configuration space i l.jpg
Configuration Space I

Alternative representation to scene coordinates

Number of joints=J

J-dimensional space

Binary encoding: 0:invalid pose, 1: free space

Real encoding: “distance” from goal configuration

Point in C.S = configuration in real space

Curve in C.S. = motion path in real space


Continuous configuration space l.jpg
(continuous) Configuration Space

What is the shortest path in configuration space?

At what speed the path is traversed?

  • Cost to go (energy or wear)‏

  • Time to goal

  • Least perturbations (predictability)‏

  • Maximal smoothness

  • Minimal intervention

A

B



Slide31 l.jpg

Sequential & Parallel Mechanisms

Simplified into 2D

Serial manipulator Parallel manipulator

vary: vary:


Equilibrium point hypothesis l.jpg
Equilibrium point hypothesis

A. G. Feldman 66

Bizzi et al. 78

Gribble et al. 98

  • Extensors: rubrospinal tract

  • Flexors: pontine reticulospinal tract

  • Force-field experiments: violation of equifinality at variations of velocity-dependent load (Hinder & Milner 03)

Solution: Internal dynamics models (Shadmehr & Mussa-Ivaldi 94)



Specifying robot positions l.jpg
SPECIFYING ROBOT POSITIONS

  • Actuator level: specify voltages that generate

  • required joint angles.

  • 2. Joint level: specify joint angles and let system

  • calculate voltages.

  • 3. Effector level: specify tool position and let

  • system compute joint angles.

  • 4. Task level: specify the required task and let the

  • system compute the sequence of tool positions

Most robot programming is at level 2 or 3.


Grippers and grasping l.jpg
Grippers and Grasping

  • Gripper: special tool for general part manipulation

  • Fingers/gripper: 2, 3, 5

  • Joints/finger: 1, 2, 3

Your hand: 5 fingers * 3 DoF + wrist position (6) = 21 DoF. Whew!



Barret hand l.jpg
Barret Hand

2 parallel fingers (spread uniformly)

1 opposable finger

DoF: 4 fingers (2 finger joints bend uniformly)



Finger contact geometry l.jpg
Finger Contact Geometry

Coefficient of friction at fingertip:

Surface normal: direction perpendicular to surface:

Friction cone: angles within about surface normal

Force direction: direction finger pushed

No-slip condition:


Force closure l.jpg

Need balanced forces or else object twists

2 fingers – forces oppose:

3 fingers – forces meet at point:

Force closure: point where forces meet lies within

3 friction cones otherwise object slips

Force Closure


Other grasping criteria l.jpg
Other Grasping Criteria

  • Some heuristics for a good grasp:

  • Contact points form nearly equilateral triangle

  • Contact points make a big triangle

  • Force focus point near centre-of-mass


Grasp algorithm l.jpg
Grasp Algorithm

  • Isolate boundary

  • Locate large enough smooth graspable sections

  • Compute surface normals

  • Pick triples of grasp points

  • Evaluate for closure & select by heuristics

  • Evaluate for reachability and collisions

  • Compute force directions and amount

  • Plan approach and finger closing strategy

  • Contact surface & apply grasping force

  • Lift (& hope)


Kinematics summary l.jpg
Kinematics Summary

  • Need vector & matrix form for robot geometry

  • Geometry of joints & joint parameters

  • Forward & inverse kinematics

  • Degrees of freedom

  • Grippers & grasping conditions


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