Lecture 3: Introduction to Concepts in Robotics

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Lecture 3Introduction to Concepts in Robotics

• In this lecture, you will learn
• - Basic Robotics Concepts
• Start discussion on geometric aspects frames,
  positions, orientations.
• Homogenous transforms
• Some math recap

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Reading Assignment for Weeks 1-2

• To cover History of Robotics and Basic Concepts,
  (Lectures 1-3)
• Required Reading is
• Chapters 1 F. Lewis
• Chapter 1 R. Murray
• Chapter 1 McKerrow
• Chapter 1 JJ Craig
• To cover Intro to Robot Kinematics Geometry,
  Frames, Transformations (Lectures 3, 4)
• Required Reading is
• Chapter 2.5 from F. Lewis text
• Chapter 2.1-2.6 from J. J. Craig text

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Robot Subsystems

• A mechanical structure.
• For manipulators this structure consists of a set
  of rigid bodies (links), connected by means of
  articulations (joints). Links and joints can also
  be described in terms of an arm (for mobility), a
  wrist (for dexterity) and an end-effector (for
  performing the task).
• For mobile robots, the structure consists of a
  chassis with a locomotion mechanism, in the form
  of legs, wheels, rotor blades, etc.
• Actuators. These set the robot in motion through
  actuation of its joints, and are typical electric
  or hydraulic.
• Sensors. These measure the status of the
  manipulator (propriceptive sensors) and the
  status of the environment (heteroceptive
  sensors).
• A control system. This enables control and
  supervision of the robot, and is usually a
  computer with a graphical user interface, and/or
  a pendant.

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Typical Industrial Robot

• 6 DOFs
• Controller

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Mechanics of Manipulators

• We describe robotic manipulators in terms of
  their degrees of freedom (DOFs).
• 6 DOFs are needed to position and orient an
  object in a unique way in the 3D space.
• Most robots have no more than 6 degrees of
  freedom. If they do, they are called redundant
  robots. Redundant robots can be ideal for
  situations requiring reaching out behind certain
  obstacles.
• The manipulator links are connected together in
  chains. Chains can be open or closed.
• Manipulators with open chains are also called
  serial, while the ones with closed chains are
  called parallel.
• Joints allow relative motion between links, and
  can be rotary (revolute R ) or linear
  (prismatic P ).
• The workspace of the manipulator is the total
  volume swept out by the end-effector of the
  manipulator.
• The workspace may be constrained by the fact that
  not all joints can rotate 360 degrees.
• The workspace is defined in terms of point
  reachable with arbitrary orientations (dextrous
  workspace) or fixed orientations (reachable
  workspace).

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Examples of industrial manipulator geometries

• Revolute
• RRR

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Examples of industrial manipulator geometries

• Cartesian
• PPP

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Examples of industrial manipulator geometries

• Spherical
• RRP

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Examples of industrial manipulator geometries

• SCARA
• 3RP

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Examples of industrial manipulator geometries

• Parallel
• Stewart platform

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Workspace Examples

• Revolute

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Workspace Examples

• Cartesian, Scara

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Properties of Manipulators

• The most important considerations for the
  application of an industrial robot are
• Manipulator performance
• System integration
• Reconfigurability/modularity
• Manipulator performance is defined as
• Reach (size of workspace), and dexterity (angular
  displacement of individual joints). Some robots
  can have unuseable workspace due to dead-zones,
  singular poses, wrist-wrap poses.
• Payload (weight that can be carried). Inertial
  loading for rotational wrist axes can be
  specified for extreme velocity and reach
  conditions.
• Quickness (how fast it can move). Critical in
  determining robot throughput but rarely
  specified. Maximum speeds of joints are usually
  specified, but average speeds while carrying
  payloads in a working cycle is of interest.
• Duty-cycle (how fast it can repeat motions
  without breaking down).

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Properties of Manipulators

• Precision is defined by using 3 metrics
  resolution, repeatability and accuracy.
• These concepts are usually static, and dynamic
  precision is usually not specified.
• Accuracy is defined as how close the manipulator
  can come to a given point within its workspace.
• Accuracy varies with the location of the point
• Repeatability is how close the manipulator
  returns to the same point in space.
• Most present day manipulators are highly
  repeatable but not very accurate.
• Repeatability for the manipulator is also defined
  as the ability to return to a so called taught
  position.
• Resolution is defined as the minimum motion
  increment that the manipulator can perform and
  detect.
• example a robot controller has 12-bit storage
  capacity, the full range of the robot 1.0 cm
  for one joint
• spatial resolution 1.0cm/212 1.0 cm/4096
  2.44 µm

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Basic Concepts

• In robotics we are constantly concerned with the
  location of objects in 3D space.
• In order to describe it we attach a coordinate
  frame rigidly to an object, or to the
  manipulator. We then transform the position and
  orientation from one frame to another. The frame
  associated with the non-moving parts of the
  manipulator is called the base frame, and the one
  attached to the end-effector is called the tool
  frame.

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Basic Concepts

• Kinematics is the science of motion based on
  geometric description, regardless of the forces
  which cause it. Kinematics deals with positions
  and its derivatives (velocity/acceleration).
• The number of DOFs of the manipulator equals the
  number of independent position variables that
  would have to be specified in order to locate all
  parts of the mechanism. It equals the number of
  joints in an open kinematic chain.
• Forward Kinematics refers to the problem of
  computing the position and orientation of the
  end-effector relative to the base frame given a
  set of joint angles.
• Cartesian space (or task space, operational
  space) is the usual 3D Euclidian space for
  position and orientation (6 DOFs). The joint
  space (or configuration space) is the space in
  which the manipulator is described by its joint
  angles.
• Inverse kinematics is the problem of inverse
  mapping between end-effector positions and
  orientation and the joint angles. We need to map
  locations in task space to the robots internal
  joint space. Early robots lacked this algorithm
  and they were simply taught joint spaces by
  moving the end-effector (by hand) to the desired
  position. The inverse kinematics problem is
  considerably harder than forward kinematics
  because it involves solving a non-linear equation
  which may not have a closed form solution. Also,
  no solution, or multiple solutions may exist.

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Basic Concepts

• The manipulator Jacobian is a matrix that relates
  the velocities of the joints to the velocities of
  the end-effector. When this matrix becomes
  singular (non-invertible), such points are called
  singularities. Example WW I rear gunner.
• Open chain manipulators are designed as a cascade
  of revolute or prismatic joints. They usually
  have up to six degrees of freedom depending on
  the task. For example a pick and place tasks from
  a 2D plane requires only 4 degrees of freedom. A
  welding operation on a car requires all 6 degreed
  of freedom. By using two manipulators to carry a
  load, one forms a closed kinematic chain. By
  using multiple kinematic chains, one can form
  much stiffer and precise robots called parallel
  manipulators.
• Manipulators dont always move through free
  space. They are sometimes required to touch a
  workpiece and apply a force. It turns out that we
  can use the manipulator Jacobian to calculate the
  relationship between joint torques and the forces
  exerted.
• The joint actuators of the manipulators are
  electric or hydraulic motors used to create
  motion of the joints.

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Basic Concepts

• Dynamics is devoted to studying the forces
  required to cause motion.
• The relationship between the joint actuator
  torques, the accelerations of the robot, and the
  other external forces (gravity of links and
  payload, external forces exerted) is studied
  within the context of dynamics.
• Dynamics is important if we use high velocities
  to actuate the system.
• If there is no motion involved, the force/torque
  balancing analysis is also called manipulator
  statics
• Kinematics is usually sufficient if the robot is
  gravity compensated and moves at slow speeds.
• Dynamics is necessary for simulation and control.
• Motion planning refers to the study of generating
  motion for the robot to accomplish a task. This
  consists of
• Path planning - generating a feasible path from
  an initial position to a final position by
  describing the geometric position and orientation
  of the robot during the transition. Sometimes
  this path must avoid obstacles in the task space,
  and it may be described by intermediate points
  (also called via-points). Sometimes the path is a
  spline (e.g. a smooth function that passes
  through a set of via points).
• Trajectory generation attaching a time frame to
  the paths generates a trajectory. The trajectory
  not only describes the position of the robot
  during motion, but also how that position changes
  with time.

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Basic Concepts

• Manipulator control refers to a closed-loop
  feedback system that uses sensory information to
  control the motion of the manipulator. A
  controller accomplishes
• Trajectory tracking following the prescribed
  trajectory for the manipulation.
• End-point control - reaching a goal
  configuration in either task or joint space
  irrespective of the trajectory it is achieved.
  This is also called the stabilization problem.
• Position/velocity control compensates for
  errors in knowledge of the systems parameters and
  suppresses disturbances. Control algorithms can
  be linear or nonlinear.
• Force control Controlling the force exerted by
  the manipulator onto an object in a single or
  multiple degrees of freedom. Can be reduced to
  position control if the stiffness of the
  manipulator and object are known, but it usually
  requires force sensing. Sometimes a scheme called
  hybrid control is used, e.g. controlling force
  along certain DOFs and position along other DOFs.
• Robot Programming Modern robots use robot
  programming languages to describe tasks from
  users. Programming could be on-line (with the
  robot attached) and off-line (with a dynamic
  simulation model of the robot). The issue of
  safety should be carefully considered when
  implementing on-line robot motion. Often time
  robotic cells have interlocked protective
  enclosures and fences.

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Robot Control Architectures

• 1) Functional (deliberative) vs. 2) Behavioral
  Model
• 1) Sense-Think-Act cycle in serial mode with five
• Think functional modules
• Perception, Modeling, Planning, Task Execution,
  Motor Control.
• Internal model maintenance/update consumes
  resources. This model has problems with long
  reaction times.
• Symbols are used to represent knowledge and
  generate actions.
• This approach dominated robotics in the first 30
  years.

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Robot Control Architectures

• 2) Sense-Think-Act cycle is decentralized in
  parallel mode. Brooks proposes a subsumption
  architecture (1985) with 8 behaviors
• - reason about objects, plan changes to world,
  identify objects, monitor changes, build maps,
  explore, wander, avoid objects.
• Advantages quick reaction, multiple goals, no
  conflict resolution needs, easy to extend, debug,
  etc.
• Disadvantages sub-optimal, not clear how to
  describe and implement complex plans.

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Recap of Math Concepts

• Vector space
• Subspace
• Vector norm
• Matrix norm
• Inner product
• Groups
• Special matrices
• Eigenvectors, eigenvalues
• Singular value decomposition