Lecture «Robot Dynamics» · Lecture 10 17.11.2015 Fixed Wing General Introduction, Basics of...

||Autonomous Systems Lab

Marco Hutter, Michael Blösch, Roland Siegwart, Konrad Rudin and Thomas Stastny

15.09.2015Roland Siegwart 1

Lecture «Robot Dynamics»

151-0851-00 Vlecture: Tuesday 10:15 – 12:00exercise: Tuesday 14:15 – 16:00 every 2nd week

||Autonomous Systems Lab 15.09.2015Roland Siegwart 2

Fascinating Robots

DARPA Robotics Challenge| Team Kaist

FESTO | BionicOpter

Spot | hydraulic quadruped

Designing and controlling such systems requires appropriate dynamic models


Kinematic and dynamic modeling of robot systems: Manipulator Legged robot Rotary wing systems Fixed wing airplanes

Objective of the course Deepening an applied understanding of how to model the most

common robotic systems. Extending the background in rotations, kinematics, dynamics, and

of multi-body systems. Modeling of actuation forces Tools to work in the field of design or control of robotic systems.


Content of the Lecture


Lecture 1 15.09.2015 Intro and OutlineLecture 2 22.09.2015 Kinematics 1 Lecture 3 29.09.2015 Kinematics 2 Lecture 4 06.10.2015 Multibody Dynamics Lecture 5 13.10.2015 Legged robots Lecture 6 20.10.2015 Introduction to Rotorcraft Lecture 7 27.10.2015 Dynamic Modeling of Rotorcraft I Lecture 8 03.11.2015 Dynamic Modeling of Rotorcraft II Lecture 9 10.11.2015 Control of Rotorcraft, Robots Case Study Lecture 10 17.11.2015 Fixed Wing General Introduction, Basics of Aerodynamics Lecture 11 24.11.2015 Stability and Derivation of a Dynamic Model Lecture 12 01.12.2015 Control and Solar Airplanes Lecture 13 08.12.2015 Some Aspects of Flight Dynamics and Flight Control,

Challenges of UAV AutoFlight System Design Lecture 14 15.12.2015 Backup, Summary


Lecture Program


“Soft Robots” | torque / force controlled robots

lightweight robot

BaxterYuMi


Tactility, key for controlling the real worldRobot Manipulator | torque controlled actuation

Courtesy of Albu-Schaeffer & Hirzinger, DLR, Germany


||Autonomous Systems Lab Roland Siegwart 7

Legged Locomotion | efficient, agile and robust

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serial elastic actuation


Helicopters: < 20 minutes Highly dynamic and agility

Fixed Wing Airplanes: > some hours; continuous flights possible Non-holonomic constraints

Blimp: lighter-than-air > some hours (dependent on wind conditions); Sensitive to wind Large size (dependent on payload)

Flapping wings < 20 minutes; gliding mode possible Non-holonomic constraints Very complex mechanics

8

UAV (Unmanned Aerial Vehicles) | flight concepts

Festo BionicOpter 15.09.2015Roland Siegwart

||Autonomous Systems Lab 9

UAV | collision avoidance and path planning

Proto 1

Proto 2

Proto 315.09.2015Roland Siegwart

Real time 3D mapping (on-board) optimal path planning considering localization uncertainties


Based on Mass & Power Balance Need for precise scaling laws (mass models)

Roland Siegwart 10

Solar Airplane |design methodology for continuous flights

Airplane Parts• Solar cells• Battery• Airframe• …

Total massAerodynamic & Conditions Power for level Flight

15.09.2015


Design space at 38° N, June 21st

Fixed Aspect Ratio: 18.5

Flat optimum at wingspan 11.5 mWingspan [m]

Bat

tery

mas

s [k

g]

Excess Time [h]

3 4 5 6 7 8 90

2

4

6

8

10

12

0

5

10

15


Solar Airplane | Optimization

Chosen AtlantikSolarconfiguration: Wingspan 5.65 m Total weight 6.2 kg. Battery mass 2.9 kg Structural weight 1.8 kg Predicted: 1‘317 g Prediction [Noth’08]: 4‘638 g

81 hours non-stop flight in July, 2015


Solar Airplane | visual navigation

Visual-inertial sensor with multiple camerasIntegrated thermal vision

Robust state estimation and flight controlAutonomous planning for complete inspection

Long endurance solar powered fight


… describe the relationship between forces/torques and motion (in joint space or workspace variables)

Two possible goals:1. Given joint torques ( ) or end-effector forces ( ), what

motions (e.g. or ), would result? (this is forward dynamics)

2. Given motion variables (e.g. or ), what joint torques ( ) or end-effector forces ( ) would have been the cause? (this is inverse dynamics)


Equations of Motion / Robot Dynamics

f, , , ,x x x

, , , ,x x x f


The main elements (general for all mechanical systems) Generalized coordinates Coordinate transformation Kinematics and Jacobian Multi-body dynamics

System dependent Actuator External forces (interaction, aerodynamics, …)


Equation of Motion / Robot Dynamics


Forward kinematics: Transformation from joint- to physical space

Inverse kinematics Transformation from physical- to joint space Required for motion control

Roland Siegwart 315

Forward and Inverse (backward) Kinematics

P

YR

XR

XI

(nonintegrable) Robot Model

(x,y,theta)(v, omega)-

Control law

15.09.2015


A set of independent variables that uniquely describe the robot’s configuration

Express all quantities as a function of generalized coordinates, e.g.

16

Generalized coordinates

I OP I OPr r q

xy

q

15.09.2015Roland Siegwart


Reference frames Coordinate system I (inertial, not moving) Coordinate system B (body-fixed, moving)

Translation vector from O to P, expressed in I:

Rotation matrix from frame B to frame I:

Homogeneous transformation Combination of translation and rotation

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Coordinate transformation

3 1I P I OP

v r

3 1I IB

ω

I P I OP I OB I IB I BP v r r ω r

3 1I OP

r

3 3IB

R

15.09.2015Roland Siegwart


How to represent position and orientationof the end-effector

Forward Kinematics

Instantaneous (or differential) Kinematics


Kinematics and Jacobian

{I}

{E}

x

x f

x x

Jacobian Matrix0 6 1

6 1

( )EI n n

EI

v

J


Manipulator (fully actuated, no interaction force)

Floating base, i.e. under-actuated systems with interaction forces


Multi-body Dynamics - General Formulation

, T Tc c act M q q b q q g q J F S τ

mass matrix

coriolis/centrifugal

gravity

contact jacobian and force

Selection matrix andactuation torque

, act M q q b q q g q τ


Newton-Euler: Impulse and angular momentum for all bodies “intelligent” selection of generalized coordinates to get rid of

internal forces

Lagrange (Energy)kinetic energypotential energynon-conservative generalized forces

For both you need to get the angular and linear velocity of CoG (as a function of generalized coordinates) and the mass/inertial properties


How to Get the Dynamic Model

TV

L T V jj j

d L L Qdt q q

Q


Roland Siegwart

15.09.2015((Vorname Nachname)) 21

Lecturer

MarcoHutter

MichaelBloesch

ThomasStastny

KonradRudin


Lecture 1 15.09.2015 Intro and OutlineLecture 2 22.09.2015 Kinematics 1 Lecture 3 29.09.2015 Kinematics 2 Lecture 4 06.10.2015 Multibody Dynamics Lecture 5 13.10.2015 Legged robots Lecture 6 20.10.2015 Introduction to Rotorcraft Lecture 7 27.10.2015 Dynamic Modeling of Rotorcraft I Lecture 8 03.11.2015 Dynamic Modeling of Rotorcraft II Lecture 9 10.11.2015 Control of Rotorcraft, Robots Case Study Lecture 10 17.11.2015 Fixed Wing General Introduction, Basics of Aerodynamics Lecture 11 24.11.2015 Stability and Derivation of a Dynamic Model Lecture 12 01.12.2015 Control and Solar Airplanes Lecture 13 08.12.2015 Some Aspects of Flight Dynamics and Flight Control,

Challenges of UAV AutoFlight System Design Lecture 14 15.12.2015 Backup, Summary


Lecture Program

Lecture «Robot Dynamics» · Lecture 10 17.11.2015 Fixed Wing General Introduction, Basics of...

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