MTRX 4700 Experimental Robotics

Transcription

1 Course Outline Mtrx 4700: Experimental Robotics Dr. Stefan B. Williams Slide 1 Wk. Date Content Labs Due Dates 1 4 Mar Introduction, history & philosophy of robotics 2 11 Mar Robot kinematics & dynamics Kinematics/Dynamics Lab 3 18 Mar Sensors, measurements and perception 4 25 Mar Robot ision and ision processing. Processing laser data Kin. Lab 5 1 Apr Extra tutorial session Processing ision data No Tute (Good Friday) 8 Apr BREAK 6 15 Apr Localization and naigation Naigation exercise beacon based na 7 22 Apr Estimation and Data Fusion Naigation exercise beacon based na 8 29 Apr Obstacle aoidance and path planning Sensing Lab 9 6 May Robotic architectures, multiple robot systems Major project Na Lab May Robot learning May Case Study May Case Study 13 3 June Major Project demonstration Major Project 14 Spare Slide 2 Agenda Introduction Autonomous Naigation Localisation Mapping The SLAM Problem Autonomous Exploration Conclusions Introduction Deployment of Autonomous Systems in unknown enironments remains difficult Requires reliable, long-term autonomous naigation One of the fundamental questions in robotics is Where am I? Naigation : Localisation and Mapping Naturally leads to Simultaneous Localisation and Mapping (SLAM) Slide 3 Slide 4 1

2 Autonomous Naigation Localisation Fundamental competence for mobile robotics Two major components Localisation Vehicle models Internal sensing (INS, laser, ision, maps) External sensing (GPS, LBL, off-board cameras) Mapping Raw maps s. Feature maps Representation? Slide 5 There are two fundamental sources of localisation information Proprioceptie sensors Include encoders, inertial sensing, and sensors capable of obsering the internal state of the system Generally gie us a differential equation which relates to the motion of the ehicle Exteroceptie sensors Include laser, sonar, ision, GPS, acoustic positioning systems, off-board sensors capable of obsering ehicle such as radar and ision Generally relies on soling geometric constraints to identify the position or pose of the ehicle Slide 6 Mobile Robotic Kinematics Recall from Week 2 that we suggested Kinematics plays an important role in mobile robotics We typically assign a frame to the some location on the ehicle Additional frames are assigned to the sensors We use kinematic relationships to estimate where objects of interest are in the enironment Mobile Robot Kinematics A ehicle model describes how the motion of the ehicle eoles oer time The complexity of the model will depend largely on the accuracy with which the motion must be tracked It will also depend on the nature of the mechanism a ehicle model of a legged robot will necessarily be more complicated than a two wheeled ehicle Slide 7 Slide 8 2

3 Vehicle Model Vehicle Model For a mobile ehicle, we are usually interested in the ehicle pose If we can measure the ehicle elocity and sense heading changes we can write a differential equation describing the eolution of the ehicle pose x = V cos( ψ ) + x y = V sin( ψ ) + y ψ = ( ψ ) + turnrate ψ Y (X, Y ) X Slide 9 V To implement this on a digital controller, we discretize the update equations Y (X, Y ) x ( k) = x ( k 1) + Δt V ( k 1)cos( ψ ( k 1)) y ( k) = y ( k 1) + Δt V ( k 1)sin( ψ ( k 1)) ψ ( k) = ψ ( k 1) + Δt ψ ( k 1) turnrate X Slide 10 V Vehicle Model Differential Drie Vehicle Model Differential Drie r = r ω L L L = r ω R R R R L L L + R = 2 L ω = L R R A ehicle like our pioneers relies on differential drie (i.e. two powered wheels) elocity and turn rate is achieed by turning the two wheels If one wheel turns, the body centre will moe at half the instantaneous elocity. The body will rotate about the stationary wheel Slide 11 = r ω L L L = r ω R R R L L L + R = 2 tan( γ ) ω = L R More complex ehicles, such as a car, are often modelled using the tricycle model Velocity and turn rate is measured about the centre of the rear axis The angle,, of the front steering wheel, determines the turn rate of the ehicle Slide 12 3

4 Vehicle Model Sensing How do we sense motion of the ehicle? For a wheeled ehicle we can use encoders to measure wheel rotation. This can tell us something about how the ehicle is moing oer the ground For other ehicles, such as airborne and underwater, other sensors must be employed In the last two lectures, we hae looked at sensors suitable for obsering the enironment around a ehicle. These hae included ision and laser, although we hae also touched on things like radar We will now look more closely at sensors suitable for use in naigation Slide 13 Slide 14 Proprioceptie Sensing Acceleration What quantities might we be interested in measuring? Position Velocity Acceleration Heading How can we sense these quantities? In some instances we can obsere them directly in others we must infer them Slide 15 Accelerometers used to measure Vibration Accelerations of a moing body All accelerometers operate by measuring relatie displacement of a small mass constrained within an accelerating case An accelerometer s output is produced by transducing the deflection of the elastic restraint into an electrical signal. The signal is proportional to the displacement of the proof mass Distortion of a piezo Motion of a cantileer Strain on mass restraints Single Axis, 10,000g Shielded for Seere enironment EMI shielded Slide 16 4

5 Silicon Machined Accelerometers Accelerometers Used in eg air-bags Cantileer beams Slide 17 Total Force (Newton s Second Law) F g = mx Specific Force F g = x + m m Accelerometers measure specific force, not acceleration When the case is accelerated in zero g, the spring will deflect allowing us to measure the acceleration. When the case is placed upright on a table, it will measure the influence of graitation because the spring will deflect with the weight of the mass. The deflection of the elastic restraint is directly influenced by the total force on the mass and not only by its acceleration. When measuring arbitrary accelerations in a graitational field, the output is a linear combination of the two effects and the contribution of each cannot be deduced from the accelerometer Slide output 18 alone Tri-axial Accelerometers Inclinometer Triaxial accelerometers used in mobile systems In high-performance cars Inside rotating elements of turbines In aircraft elements Can be used to estimate graity ector Proide ibration information Proide short-term position data Triple axis Accelerometer For racing cars An inclinometer measures the inclination of a body by estimating the graity ector In an analogous manner to which graity affects accelerometer readings, accelerations will affect the inclinometer reading Slide 19 Slide 20 5

6 Compass Gyroscope A compass measures the local magnetic field This can be used to infer the direction of North Other sources of magnetic fields must be taken into account Fixed magnetic fields from metals and other sources in the enironment. The processes of metal fabrication often result in latent magnetic fields Electromagnetic sources, such as motors. These are much more difficult to account for Slide 21 A 2π r + rωt t = c 2π r rωt t = c 2 4π r ω Δt 2 c + + A gyroscope measures the rotational rate of a body Early gyros were mechanical and relied on sensing the torques induced by a change of a spinning mass More recent gyros rely on optical properties Ring laser gyros conert differences in arrial time into beat frequency Fiber optic gyros increase the pathlength by using coils of fibre optic cable Slide 22 Silicon Gyroscopes Structural arrangement of silicon which records centrifugal acceleration and thus angular speed Use strain-gauge bridges and/or piezo structure to record deformations Multiple component elements to calibrate other accelerations Inertial Systems Together in an orthogonal arrangement of accelerometers and gyroscopes, these comprise an inertial measurement unit (IMU) An IMU that is used for naigation is called an inertial naigation system (INS) These are widely used in aircraft and missile naigation and guidance. They are also seeing increasing integration into robotic and other autonomous guidance systems Slide 23 Slide 24 6

7 Aerospace INS Tachometers Aircraft Ballistic Missile Measurement of rotary speed using a DC generator Essentially a motor running in reerse Used to be common to hae these attached to motors to enable direct analog feedback Much less common now with digital control (use incremental encoders) Tacho generator for large industrial plant (GE) Slide 25 Slide 26 Optical Encoders Encoder Internal Structure Encoders are digital Sensors commonly used to proide position feedback for actuators Consist of a glass or plastic disc that rotates between a light source (LED) and a pair of photo-detectors Disk is encoded with alternate light and dark sectors so pulses are produced as disk rotates Slide 27 Slide 28 7

8 Incremental Encoders Exteroceptie Sensing Pulses from leds are counted to proide rotary position Two detectors are used to determine direction (quadrature) Index pulse used to denote start point Otherwise pulses are not unique What quantities might we be interested in measuring? Range Bearing Temperature Light intensity How can we sense these quantities? In some instances we can obsere them directly in others we must infer them Slide 29 Slide 30 GPS Lasers The Global Positioning System consists of a number of satellites orbiting the earth The satellites transmit time coded signals Receiers on earth listen for the signal and effectiely triangulate position Only works when sufficient satellites are in iew Satellite Satellite Satellite We hae seen how laser range finders gie us access to high resolution range and bearing information about the enironment We hae also looked at methods for identifying features in this data. This includes lines and corners If we hae a map of an enironment we can match obserations against the map to proide us with positioning information Other methods exist which use the raw laser data for localisation Slide 31 Slide 32 8

9 Vision Beacon Based Naigation We hae examined a few techniques for extracting corners and lines from images These features can be used with appropriate camera models to proide obserations of eleation and azimuth to these features What if I knew the location of some features in the enironment? Obserations of the relatie position between myself and these beacons would tell me something about my own position 1 TY 2 T Y1 1 R2 sinθ2 R1 sinθ 1 ψ = tan tan T T R cosθ R cosθ X 2 X ( θ ψ ) ( θ ψ ) X = T R cos X Y = T R sin Y Y (T X2, T Y2 ) y R 2 (X, Y ) X Y X 2 x 1 R 1 (T, T ) X1 Y1 Slide 33 Slide 34 Beacon Based Naigation Data Fusion Other systems proide range or bearing only obserations to these beacons These can also yield appropriate methods for estimating the position or pose of the ehicle Y (T X2, T Y2 ) R 2 y x Based on the preceding deelopment, we may hae a number of sources of information about how a ehicle is moing We need a mechanism for putting this information together in a consistent manner This is referred to as data fusion ( X ) ( Y ) ( ) ( ) X T + Y T = R X 2 + Y 2 = 2 X T Y T R (X V, Y V ) R 1 (T X1, T Y1 ) X Slide 35 Slide 36 9

10 Data Fusion The Estimation Process In essence, data fusion methods are designed to proide us with the best estimate of the our states of interest x k gien the information aailable to us P(x k Z k, U k, x 0 ) where x k is the state at time k Z k is a sequence of obserations up to time k U k is a sequence of actions up to time k x 0 is the initial state How best is defined depends on the situation. We also need to make decisions about how to model any potential errors in the sensors Slide 37 Recursie three stage update procedure F 0 x Vehicle Path Vehicle Path Z 2 Vehicle Path Z 1 Z 3 Z x x 0 x 0 0 x 3 0 x 4 Slide 38 Data Fusion Mapping Dead Reckoning Triangulation Signal True Path True Path Triangulation path Dead Reckoning path Update stage Fused path estimate Triangulation obseration Dead Reckoning prediction Dead Reckoning prediction at Obseration Fused estimate Assuming that we know where the ehicle is, what can we do? We might wish to build a map of the enironment in which the ehicle is moing What will be in this map? This will depend on the requirements of the application Estimate Obserati on Update Stage Obseration Initial Estimate Slide 39 Slide 40 10

11 Occupancy Grid 3D Mapping A simple approach to mapping is to discretize the enironment and map occupied and free space We might wish to generate a richer description of an enironment 3D models can be built using a small indoor robot We are looking at methods for building more compact models of this data Slide 41 Slide 42 3D Point Set 3D Plane Fitting Slide 43 Slide 44 11

12 IMAGING LASER ALTIMETRY IMAGING LASER ALTIMETRY BUILDINGS LASER AND RADAR ALTIMETERS USE TIME OF FLIGHT TO MEASURE THE DISTANCE TO THE GROUND. HIGH QUALITY IMAGES ARE PRODUCED BY COMBINING ACCURATE HEIGHT MEASUREMENTS WITH DGPS POSITIONING. Slide 45 Slide 46 IMAGING LASER ALTIMETRY HIGHWAY IMAGING LASER ALTIMETRY BONN FLOODED BY THE RHINE Slide 47 Slide 48 12

13 0 0 x 4 4 The SLAM Problem The Estimation Process Estimated Landmark Correlated Landmark Errors Estimated Vehicle Path True Vehicle Path Simultaneous Localisation and Map Building (SLAM) Start at an unknown location with no a priori knowledge of landmark locations From relatie obserations of landmarks, compute estimate of ehicle location and estimate of landmark locations While continuing in motion, build complete map of landmarks and use these to proide continuous estimates of ehicle location Recursie three stage update procedure Vehicle Path Z 2 Vehicle Path Z 1 Z 3 0 x 5 Z 4 0 x 0 2 x 2 0 x 6 True Landmark 0 0 x 0 x 0 0 x 3 3 F 0 0 x Slide 49 Slide 50 Algorithms for Mapping and Exploration Building Maps Unknown Enironment Sensing and naigation Locating areas of interest Applications Security Tour Guide Domestic Underwater Vehicles GPS is not aailable underwater. The high frequency carrier signal is attenuated ery quickly by water Many systems rely on acoustic positioning to determine the position of the ehicle We are currently deeloping methods for applying SLAM in highly unstructured underwater enironments Slide 51 Slide 52 13

14 The AUV platform Stereo Odometry Fully autonomous operation, 1. Find Features in Left Image no tether Control of ehicle performed using on-board computer Sensors include Sonar (imaging and fwd obstacle aoidance) Vision (stereo) DVL Compass Pressure Mission Time ~4 hours (up to 8 hours with current housing 2. Measure Altitude and bound search for features in Right Image 3. Estimate Feature Locations 4. Check consistency with Epipolar Geometry 5. Use DVL displacement to estimate motion to next pair. Find correspondences 6. Confirm consistency using RANSAC 7. Bundle adjustment to refine estimate Slide 53 Managing Loop Closure Slide 54 Simultaneous Localisation and Mapping Gien the planned ehicle path, we can manage the search for loop closure based on our estimate of the ehicle pose Characterization of the drift rates allows us to bound the search area Incorporating the pose estimates into the SLAM state rather than feature poses will allow us to manage the complexity of the mapping process Slide 55 Slide 56 14

15 Simultaneous Localisation and Mapping Sureys on the Great Barrier Reef Slide 57 Terrain Eleation Maps Slide 58 Sydney Harbour Demonstrations What about more complex map information? Sydney Harbour presents an Terrain eleation maps ideal enironment in which to alidate these algorithms Detailed bathymetric maps of the harbour are aailable A beautiful spot for field work as well! aailable for some deployment areas Obserations of altitude can be used to bound likely position of ehicle Slide 59 Slide 60 15

16 Ship transect Sydney Harbour Bathymetry Ship data from DSTO, including Sydney Harbour Harbour Tunnel Bathymetry from DSTO Shallow Water Surey Bathymetric data collected using multi beam echo sounder Resolution of 1m oer extent of inner harbour GPS position and depth soundings taken at 5s interals, during transect of the Harbour Particle based localisation and tracking of ship using depth soundings has been demonstrated using logged data Darling Harbour Slide 61 Particle Tracking of Ship Transect Slide 62 Particle Tracking of Ship Transect Lost Slide 63 Slide 64 16

17 Conclusions There are three fundamental competencies to enable deployment of autonomous systems A ehicle model tells us something about how the ehicle moes Localisation information can be fused to gie us an idea of where we are Mapping allows us to infer something about the enironment Slide 65 17