Lecture «Robot Dynamics»: Dynamics and Control

Size: px
Start display at page:

Download "Lecture «Robot Dynamics»: Dynamics and Control"

Transcription

1 Lecture «Robot Dynamics»: Dynamics and Control V lecture: CAB G11 Tuesday 10:15 12:00, every week exercise: HG E1.2 Wednesday 8:15 10:00, according to schedule (about every 2nd week) Marco Hutter, Roland Siegwart, and Thomas Stastny Robot Dynamics - Dynamics

2 Intro and Outline Course Introduction; Recapitulation Position, Linear Velocity Kinematics 1 Rotation and Angular Velocity; Rigid Body Formulation, Transformation Exercise 1a Kinematics Modeling the ABB arm Kinematics 2 Kinematics of Systems of Bodies; Jacobians Exercise 1b Differential Kinematics of the ABB arm Kinematics 3 Kinematic Control Methods: Inverse Differential Kinematics, Inverse Kinematics; Rotation Error; Multi-task Control Exercise 1c Kinematic Control of the ABB Arm Dynamics L1 Multi-body Dynamics Exercise 2a Dynamic Modeling of the ABB Arm Dynamics L2 Floating Base Dynamics Dynamics L3 Dynamic Model Based Control Methods Exercise 2b Dynamic Control Methods Applied to the ABB arm Legged Robot Dynamic Modeling of Legged Robots & Control Exercise 3 Legged robot Case Studies 1 Legged Robotics Case Study Rotorcraft Dynamic Modeling of Rotorcraft & Control Exercise 4 Modeling and Control of Multicopter Case Studies 2 Rotor Craft Case Study Fixed-wing Dynamic Modeling of Fixed-wing & Control Exercise 5 Fixed-wing Control and Simulation Case Studies 3 Fixed-wing Case Study (Solar-powered UAVs - AtlantikSolar, Vertical Take-off and Landing UAVs Wingtra) Summery and Outlook Summery; Wrap-up; Exam Robot Dynamics - Dynamics

3 Recapitulation We learned how to get the equation of motion in joint space Newton-Euler Projected Newton-Euler Lagrange II Introduction to floating base systems Today: How can we use this information in order to control the robot, M q qb q q g S q M q T T q τ JF c c Generalized coordinates Mass matrix bqq, Centrifugal and Coriolis forces g q τ S F J c c Gravity forces Generalized fores c Selection matrix/jacobian External forces Contact Jacobian Robot Dynamics - Dynamics

4 Position vs. Torque Controlled Robot Arms Robot Dynamics - Dynamics

5 Setup of a Robot Arm System Control Actuator Control ( U, I) τ qqq,, Actuator (Motor + Gear) Robot Dynamics Robot Dynamics - Dynamics

6 Classical Position Control of a Robot Arm q, q High Actuator gain Control PID ( U, I) Actuator (Motor + Gear) τ Robot Robot Dynamics qqq,, Position Sensor Position feedback loop on joint level Classical, position controlled robots don t care about dynamics High-gain PID guarantees good joint level tracking Disturbances (load, etc) are compensated by PID => interaction force can only be controlled with compliant surface Robot Dynamics - Dynamics

7 Joint Torque Control of a Robot Arm q, q τ Actuator Control ( U, I) Actuator (Motor + Gear) τ Robot Dynamics qqq,, Torque Sensor Position Sensor Integrate force-feedback Active regulation of system dynamics Model-based load compensation Interaction force control Robot Dynamics - Dynamics

8 Setup of Modern Robot Arms Modern robots have force sensors Dynamic control Interaction control Safety for collaboration Robot Dynamics - Dynamics

9 FRANKA an example of a force controllable robot arm Robot Dynamics - Dynamics

10 ANYpulator An example for a robot that can interact Special force controllable actuators Dynamic motion Safe interaction position force motor gear spring link Series Elastic Actuator Robot Dynamics - Dynamics

11 Joint Impedance Control Torque as function of position and velocity error Closed loop behavior Static offset due to gravity Impedance control and gravity compensation Estimated gravity term Robot Dynamics - Dynamics

12 Inverse Dynamics Control Compensate for system dynamics In case of no modeling errors, the desired dynamics can be perfectly prescribed PD-control law Every joint behaves like a decoupled mass-spring-damper with unitary mass Robot Dynamics - Dynamics

13 Inverse Dynamics Control with Multiple Tasks Motion in joint space is often hard to describe => use task space A single task can be written as In complex machines, we want to fulfill multiple tasks (As introduced already for velocity control) Same priority, multi-task inversion Hierarchical Robot Dynamics - Dynamics

14 Task Space Dynamics Joint-space dynamics End-effector dynamics w e F e {E} Torque to force mapping Inertia-ellipsoid Kinematic relation Substitute acceleration {I} Robot Dynamics - Dynamics

15 End-effector Motion Control Determine a desired end-effector acceleration Note: a rotational error can be related to differenced in representation by Determine the corresponding joint torque E R χ R χ R w t e Trajectory control w e F e {E} {I} Robot Dynamics - Dynamics

16 Robots in Interaction There is a long history in robots controlling motion and interaction Robot Dynamics - Dynamics

17 Operational Space Control Generalized framework to control motion and force Extend end-effector dynamics in contact with contact force F c Introduce selection matrices to separate motion force directions w e F e F c {I} Robot Dynamics - Dynamics

18 Operational Space Control 2-link example Given: Find, s.t. the end-effector r accelerates with exerts the contact force T edes, 0 a y, 0 T contact des Fc F 1 y O l x l r edes, 0 a y P 2 F contact, des F 0 c Robot Dynamics - Dynamics

19 How to Find a Selection Matrix Selection matrix in local frame 1: it can move 0: it can apply a force Rotation between contact force and world frame Robot Dynamics - Dynamics

20 How to Find a Selection Matrix Selection matrix in local frame Rotation between contact force and world frame Robot Dynamics - Dynamics

21 Sliding a Prismatic Object Along a Surface Assume friction less contact surface Σ Mp Σ Fp Σ Σ Mr Σ Fr Robot Dynamics - Dynamics

22 Inserting a Cylindrical Peg in a Hole Find the selection matrix (in local frame) Σ Mp Σ Fp Σ Σ Mr Σ Fr Robot Dynamics - Dynamics

23 Inverse Dynamics of Floating Base Systems Robot Dynamics - Dynamics

24 Recapitulation: Support Consistent Dynamics Equation of motion (1) Cannot directly be used for control due to the occurrence of contact forces Contact constraint Contact force Back-substitute in (1), replace Jq s Jq s and use support null-space projection Support consistent dynamics Inverse-dynamics Multiple solutions Robot Dynamics - Dynamics

25 Some Examples of Using Internal Forces Robot Dynamics - Dynamics

26 Recapitulation: Quadrupedal Robot with Point Feet Floating base system with 12 actuated joint and 6 base coordinates (18DoF) Total constraints Internal constraints Uncontrollable DoFs Robot Dynamics - Dynamics

27 Internal Forces extreme example Robot Dynamics - Dynamics

28 Robot Dynamics - Dynamics

29 Least Square Optimization some notes on quadratic optimization Ax b 0 x=a b min Ax b min x 2 2 x x1 x1 Ax 1 1b Ax min 2 2 = A1 A2 b A1 A2 b x1, x2 x2 x 2 2 min x x Axb Axb Equal priority A1 b x= x x A 2 b min A b min x 2 A b Hierarchy x A b N A x N Axb A Ab A x b x A A b A A b min x min x st.. Axb Axb Axb c 0 2N Robot Dynamics - Dynamics

30 Least Square Optimization Application to Inverse Dynamics Mq b g τ Jq Jq w * e e e q M I bg 0 τ * J 0 Jq w e q τ e Single task min qτ, M Iq bg J 0 τ Jq w * e e q * min Je 0 Jq w e qτ, τ Priority 2 q st..m I bg0 τ 2 Robot Dynamics - Dynamics

31 Operational Space Control as Quadratic Program A general problem We search for a solution that fulfills the equation of motion Motion tasks: Force tasks: Torque min: min τ 2 Robot Dynamics - Dynamics

32 Solving a Set of QPs QPs need different priority!! Exploit Null-space of tasks with higher priority Every step = quadratic problem with constraints Use iterative null-space projection (formula in script) Robot Dynamics - Dynamics

33 Behavior as Multiple Tasks Robot Dynamics - Dynamics

34 Quasi-static: Virtual Model Control Pratt 2001 No dynamic effects Add virtual external forces to pull/support the robot Static equilibrium of forces and moments From principle of virtual work it follows directly that Robot Dynamics - Dynamics

35 Next Time Application of this technique for locomotion control of legged robots Robot Dynamics - Dynamics

36 Robot Dynamics - Dynamics

Lecture «Robot Dynamics»: Dynamics 2

Lecture «Robot Dynamics»: Dynamics 2 Lecture «Robot Dynamics»: Dynamics 2 151-0851-00 V lecture: CAB G11 Tuesday 10:15 12:00, every week exercise: HG E1.2 Wednesday 8:15 10:00, according to schedule (about every 2nd week) office hour: LEE

More information

Lecture «Robot Dynamics»: Kinematics 2

Lecture «Robot Dynamics»: Kinematics 2 Lecture «Robot Dynamics»: Kinematics 2 151-0851-00 V lecture: CAB G11 Tuesday 10:15 12:00, every week exercise: HG E1.2 Wednesday 8:15 10:00, according to schedule (about every 2nd week) Marco Hutter,

More information

Lecture «Robot Dynamics» : Kinematics 3

Lecture «Robot Dynamics» : Kinematics 3 Lecture «Robot Dynamics» : Kinematics 3 151-0851-00 V lecture: CAB G11 Tuesday 10:15-12:00, every week exercise: HG G1 Wednesday 8:15-10:00, according to schedule (about every 2nd week) office hour: LEE

More information

Robot Dynamics Instantaneous Kinematiccs and Jacobians

Robot Dynamics Instantaneous Kinematiccs and Jacobians Robot Dynamics Instantaneous Kinematiccs and Jacobians 151-0851-00 V Lecture: Tuesday 10:15 12:00 CAB G11 Exercise: Tuesday 14:15 16:00 every 2nd week Marco Hutter, Michael Blösch, Roland Siegwart, Konrad

More information

Artificial Intelligence & Neuro Cognitive Systems Fakultät für Informatik. Robot Dynamics. Dr.-Ing. John Nassour J.

Artificial Intelligence & Neuro Cognitive Systems Fakultät für Informatik. Robot Dynamics. Dr.-Ing. John Nassour J. Artificial Intelligence & Neuro Cognitive Systems Fakultät für Informatik Robot Dynamics Dr.-Ing. John Nassour 25.1.218 J.Nassour 1 Introduction Dynamics concerns the motion of bodies Includes Kinematics

More information

Dynamics. describe the relationship between the joint actuator torques and the motion of the structure important role for

Dynamics. describe the relationship between the joint actuator torques and the motion of the structure important role for Dynamics describe the relationship between the joint actuator torques and the motion of the structure important role for simulation of motion (test control strategies) analysis of manipulator structures

More information

Lecture Schedule Week Date Lecture (M: 2:05p-3:50, 50-N202)

Lecture Schedule Week Date Lecture (M: 2:05p-3:50, 50-N202) J = x θ τ = J T F 2018 School of Information Technology and Electrical Engineering at the University of Queensland Lecture Schedule Week Date Lecture (M: 2:05p-3:50, 50-N202) 1 23-Jul Introduction + Representing

More information

41514 Dynamics of Machinery

41514 Dynamics of Machinery 41514 Dynamics of Machinery Theory, Experiment, Phenomenology and Industrial Applications Ilmar Ferreira Santos 1. Recapitulation Mathematical Modeling & Steps 2. Example System of Particle 3. Example

More information

(W: 12:05-1:50, 50-N202)

(W: 12:05-1:50, 50-N202) 2016 School of Information Technology and Electrical Engineering at the University of Queensland Schedule of Events Week Date Lecture (W: 12:05-1:50, 50-N202) 1 27-Jul Introduction 2 Representing Position

More information

Lecture «Robot Dynamics»: Dynamics 1

Lecture «Robot Dynamics»: Dynamics 1 Leture «Robot Dynamis»: Dynamis 1 151-0851-00 V leture: CAB G11 uesday 10:15 12:00, every week exerise: HG E1.2 Wednesday 8:15 10:00, aording to shedule (about every 2nd week) offie hour: LEE H303 Friday

More information

Robot Dynamics - Rotary Wing UAS: Control of a Quadrotor

Robot Dynamics - Rotary Wing UAS: Control of a Quadrotor Robot Dynamics Rotary Wing AS: Control of a Quadrotor 5-85- V Marco Hutter, Roland Siegwart and Thomas Stastny Robot Dynamics - Rotary Wing AS: Control of a Quadrotor 7..6 Contents Rotary Wing AS. Introduction

More information

Adaptive Robust Tracking Control of Robot Manipulators in the Task-space under Uncertainties

Adaptive Robust Tracking Control of Robot Manipulators in the Task-space under Uncertainties Australian Journal of Basic and Applied Sciences, 3(1): 308-322, 2009 ISSN 1991-8178 Adaptive Robust Tracking Control of Robot Manipulators in the Task-space under Uncertainties M.R.Soltanpour, M.M.Fateh

More information

Robot Dynamics II: Trajectories & Motion

Robot Dynamics II: Trajectories & Motion Robot Dynamics II: Trajectories & Motion Are We There Yet? METR 4202: Advanced Control & Robotics Dr Surya Singh Lecture # 5 August 23, 2013 metr4202@itee.uq.edu.au http://itee.uq.edu.au/~metr4202/ 2013

More information

Robotics. Dynamics. University of Stuttgart Winter 2018/19

Robotics. Dynamics. University of Stuttgart Winter 2018/19 Robotics Dynamics 1D point mass, damping & oscillation, PID, dynamics of mechanical systems, Euler-Lagrange equation, Newton-Euler, joint space control, reference trajectory following, optimal operational

More information

q 1 F m d p q 2 Figure 1: An automated crane with the relevant kinematic and dynamic definitions.

q 1 F m d p q 2 Figure 1: An automated crane with the relevant kinematic and dynamic definitions. Robotics II March 7, 018 Exercise 1 An automated crane can be seen as a mechanical system with two degrees of freedom that moves along a horizontal rail subject to the actuation force F, and that transports

More information

In this section of notes, we look at the calculation of forces and torques for a manipulator in two settings:

In this section of notes, we look at the calculation of forces and torques for a manipulator in two settings: Introduction Up to this point we have considered only the kinematics of a manipulator. That is, only the specification of motion without regard to the forces and torques required to cause motion In this

More information

Inverse differential kinematics Statics and force transformations

Inverse differential kinematics Statics and force transformations Robotics 1 Inverse differential kinematics Statics and force transformations Prof Alessandro De Luca Robotics 1 1 Inversion of differential kinematics! find the joint velocity vector that realizes a desired

More information

Robotics. Dynamics. Marc Toussaint U Stuttgart

Robotics. Dynamics. Marc Toussaint U Stuttgart Robotics Dynamics 1D point mass, damping & oscillation, PID, dynamics of mechanical systems, Euler-Lagrange equation, Newton-Euler recursion, general robot dynamics, joint space control, reference trajectory

More information

Case Study: The Pelican Prototype Robot

Case Study: The Pelican Prototype Robot 5 Case Study: The Pelican Prototype Robot The purpose of this chapter is twofold: first, to present in detail the model of the experimental robot arm of the Robotics lab. from the CICESE Research Center,

More information

Introduction to centralized control

Introduction to centralized control Industrial Robots Control Part 2 Introduction to centralized control Independent joint decentralized control may prove inadequate when the user requires high task velocities structured disturbance torques

More information

Video 8.1 Vijay Kumar. Property of University of Pennsylvania, Vijay Kumar

Video 8.1 Vijay Kumar. Property of University of Pennsylvania, Vijay Kumar Video 8.1 Vijay Kumar 1 Definitions State State equations Equilibrium 2 Stability Stable Unstable Neutrally (Critically) Stable 3 Stability Translate the origin to x e x(t) =0 is stable (Lyapunov stable)

More information

Advanced Robotic Manipulation

Advanced Robotic Manipulation Advanced Robotic Manipulation Handout CS37A (Spring 017 Solution Set # Problem 1 - Redundant robot control The goal of this problem is to familiarize you with the control of a robot that is redundant with

More information

Robot Manipulator Control. Hesheng Wang Dept. of Automation

Robot Manipulator Control. Hesheng Wang Dept. of Automation Robot Manipulator Control Hesheng Wang Dept. of Automation Introduction Industrial robots work based on the teaching/playback scheme Operators teach the task procedure to a robot he robot plays back eecute

More information

Introduction to centralized control

Introduction to centralized control ROBOTICS 01PEEQW Basilio Bona DAUIN Politecnico di Torino Control Part 2 Introduction to centralized control Independent joint decentralized control may prove inadequate when the user requires high task

More information

Balancing of an Inverted Pendulum with a SCARA Robot

Balancing of an Inverted Pendulum with a SCARA Robot Balancing of an Inverted Pendulum with a SCARA Robot Bernhard Sprenger, Ladislav Kucera, and Safer Mourad Swiss Federal Institute of Technology Zurich (ETHZ Institute of Robotics 89 Zurich, Switzerland

More information

GAIN SCHEDULING CONTROL WITH MULTI-LOOP PID FOR 2- DOF ARM ROBOT TRAJECTORY CONTROL

GAIN SCHEDULING CONTROL WITH MULTI-LOOP PID FOR 2- DOF ARM ROBOT TRAJECTORY CONTROL GAIN SCHEDULING CONTROL WITH MULTI-LOOP PID FOR 2- DOF ARM ROBOT TRAJECTORY CONTROL 1 KHALED M. HELAL, 2 MOSTAFA R.A. ATIA, 3 MOHAMED I. ABU EL-SEBAH 1, 2 Mechanical Engineering Department ARAB ACADEMY

More information

The Dynamics of Fixed Base and Free-Floating Robotic Manipulator

The Dynamics of Fixed Base and Free-Floating Robotic Manipulator The Dynamics of Fixed Base and Free-Floating Robotic Manipulator Ravindra Biradar 1, M.B.Kiran 1 M.Tech (CIM) Student, Department of Mechanical Engineering, Dayananda Sagar College of Engineering, Bangalore-560078

More information

Manipulator Dynamics 2. Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

Manipulator Dynamics 2. Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA Manipulator Dynamics 2 Forward Dynamics Problem Given: Joint torques and links geometry, mass, inertia, friction Compute: Angular acceleration of the links (solve differential equations) Solution Dynamic

More information

Robotics & Automation. Lecture 25. Dynamics of Constrained Systems, Dynamic Control. John T. Wen. April 26, 2007

Robotics & Automation. Lecture 25. Dynamics of Constrained Systems, Dynamic Control. John T. Wen. April 26, 2007 Robotics & Automation Lecture 25 Dynamics of Constrained Systems, Dynamic Control John T. Wen April 26, 2007 Last Time Order N Forward Dynamics (3-sweep algorithm) Factorization perspective: causal-anticausal

More information

A Physically-Based Fault Detection and Isolation Method and Its Uses in Robot Manipulators

A Physically-Based Fault Detection and Isolation Method and Its Uses in Robot Manipulators des FA 4.13 Steuerung und Regelung von Robotern A Physically-Based Fault Detection and Isolation Method and Its Uses in Robot Manipulators Alessandro De Luca Dipartimento di Informatica e Sistemistica

More information

IROS 16 Workshop: The Mechatronics behind Force/Torque Controlled Robot Actuation Secrets & Challenges

IROS 16 Workshop: The Mechatronics behind Force/Torque Controlled Robot Actuation Secrets & Challenges Arne Wahrburg (*), 2016-10-14 Cartesian Contact Force and Torque Estimation for Redundant Manipulators IROS 16 Workshop: The Mechatronics behind Force/Torque Controlled Robot Actuation Secrets & Challenges

More information

Robust Control of Cooperative Underactuated Manipulators

Robust Control of Cooperative Underactuated Manipulators Robust Control of Cooperative Underactuated Manipulators Marcel Bergerman * Yangsheng Xu +,** Yun-Hui Liu ** * Automation Institute Informatics Technology Center Campinas SP Brazil + The Robotics Institute

More information

ME751 Advanced Computational Multibody Dynamics

ME751 Advanced Computational Multibody Dynamics ME751 Advanced Computational Multibody Dynamics Inverse Dynamics Equilibrium Analysis Various Odd Ends March 18, 2010 Dan Negrut, 2010 ME751, UW-Madison Action speaks louder than words but not nearly as

More information

41514 Dynamics of Machinery

41514 Dynamics of Machinery 41514 Dynamics of Machinery Theory, Experiment, Phenomenology and Industrial Applications Ilmar (Iumár) Ferreira Santos 1. Course Structure 2. Objectives 3. Theoretical and Experimental Example 4. Industrial

More information

In most robotic applications the goal is to find a multi-body dynamics description formulated

In most robotic applications the goal is to find a multi-body dynamics description formulated Chapter 3 Dynamics Mathematical models of a robot s dynamics provide a description of why things move when forces are generated in and applied on the system. They play an important role for both simulation

More information

Natural and artificial constraints

Natural and artificial constraints FORCE CONTROL Manipulator interaction with environment Compliance control Impedance control Force control Constrained motion Natural and artificial constraints Hybrid force/motion control MANIPULATOR INTERACTION

More information

MCE493/593 and EEC492/592 Prosthesis Design and Control

MCE493/593 and EEC492/592 Prosthesis Design and Control MCE493/593 and EEC492/592 Prosthesis Design and Control Control Systems Part 3 Hanz Richter Department of Mechanical Engineering 2014 1 / 25 Electrical Impedance Electrical impedance: generalization of

More information

Gain Scheduling Control with Multi-loop PID for 2-DOF Arm Robot Trajectory Control

Gain Scheduling Control with Multi-loop PID for 2-DOF Arm Robot Trajectory Control Gain Scheduling Control with Multi-loop PID for 2-DOF Arm Robot Trajectory Control Khaled M. Helal, 2 Mostafa R.A. Atia, 3 Mohamed I. Abu El-Sebah, 2 Mechanical Engineering Department ARAB ACADEMY FOR

More information

Force 9. Force Control

Force 9. Force Control 195 Multimedia Contents Force 9. Force Control Luigi Villani, Joris De Schutter A fundamental requirement for the success of a manipulation task is the capability to handle the physical contact between

More information

Game Physics. Game and Media Technology Master Program - Utrecht University. Dr. Nicolas Pronost

Game Physics. Game and Media Technology Master Program - Utrecht University. Dr. Nicolas Pronost Game and Media Technology Master Program - Utrecht University Dr. Nicolas Pronost Rigid body physics Particle system Most simple instance of a physics system Each object (body) is a particle Each particle

More information

Introduction to Robotics

Introduction to Robotics J. Zhang, L. Einig 277 / 307 MIN Faculty Department of Informatics Lecture 8 Jianwei Zhang, Lasse Einig [zhang, einig]@informatik.uni-hamburg.de University of Hamburg Faculty of Mathematics, Informatics

More information

Dynamics and control of mechanical systems

Dynamics and control of mechanical systems Dynamics and control of mechanical systems Date Day 1 (03/05) - 05/05 Day 2 (07/05) Day 3 (09/05) Day 4 (11/05) Day 5 (14/05) Day 6 (16/05) Content Review of the basics of mechanics. Kinematics of rigid

More information

Nonlinear PD Controllers with Gravity Compensation for Robot Manipulators

Nonlinear PD Controllers with Gravity Compensation for Robot Manipulators BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 4, No Sofia 04 Print ISSN: 3-970; Online ISSN: 34-408 DOI: 0.478/cait-04-00 Nonlinear PD Controllers with Gravity Compensation

More information

ELEC4631 s Lecture 2: Dynamic Control Systems 7 March Overview of dynamic control systems

ELEC4631 s Lecture 2: Dynamic Control Systems 7 March Overview of dynamic control systems ELEC4631 s Lecture 2: Dynamic Control Systems 7 March 2011 Overview of dynamic control systems Goals of Controller design Autonomous dynamic systems Linear Multi-input multi-output (MIMO) systems Bat flight

More information

Ch. 5: Jacobian. 5.1 Introduction

Ch. 5: Jacobian. 5.1 Introduction 5.1 Introduction relationship between the end effector velocity and the joint rates differentiate the kinematic relationships to obtain the velocity relationship Jacobian matrix closely related to the

More information

HADDONFIELD PUBLIC SCHOOLS Curriculum Map for AP Physics, Mechanics C

HADDONFIELD PUBLIC SCHOOLS Curriculum Map for AP Physics, Mechanics C Curriculum Map for AP Physics, Mechanics C September Enduring Understandings (The big ideas): Chapter 2 -- Motion Along a Straight Line Essential Questions: How do objects move? 1. Displacement, time,

More information

IMPROVING FORCE CONTROL THROUGH END- EFFECTOR VIBRATION REDUCTION AND VARIABLE STIFFNESS JOINT DESIGN LI RENJUN NATIONAL UNIVERSITY OF SINGAPORE

IMPROVING FORCE CONTROL THROUGH END- EFFECTOR VIBRATION REDUCTION AND VARIABLE STIFFNESS JOINT DESIGN LI RENJUN NATIONAL UNIVERSITY OF SINGAPORE IMPROVING FORCE CONTROL THROUGH END- EFFECTOR VIBRATION REDUCTION AND VARIABLE STIFFNESS JOINT DESIGN LI RENJUN NATIONAL UNIVERSITY OF SINGAPORE 2014 IMPROVING FORCE CONTROL THROUGH END- EFFECTOR VIBRATION

More information

Introduction to Control (034040) lecture no. 2

Introduction to Control (034040) lecture no. 2 Introduction to Control (034040) lecture no. 2 Leonid Mirkin Faculty of Mechanical Engineering Technion IIT Setup: Abstract control problem to begin with y P(s) u where P is a plant u is a control signal

More information

General procedure for formulation of robot dynamics STEP 1 STEP 3. Module 9 : Robot Dynamics & controls

General procedure for formulation of robot dynamics STEP 1 STEP 3. Module 9 : Robot Dynamics & controls Module 9 : Robot Dynamics & controls Lecture 32 : General procedure for dynamics equation forming and introduction to control Objectives In this course you will learn the following Lagrangian Formulation

More information

Operational Space Control of Constrained and Underactuated Systems

Operational Space Control of Constrained and Underactuated Systems Robotics: Science and Systems 2 Los Angeles, CA, USA, June 27-3, 2 Operational Space Control of Constrained and Underactuated Systems Michael Mistry Disney Research Pittsburgh 472 Forbes Ave., Suite Pittsburgh,

More information

Multibody simulation

Multibody simulation Multibody simulation Dynamics of a multibody system (Newton-Euler formulation) Dimitar Dimitrov Örebro University June 8, 2012 Main points covered Newton-Euler formulation forward dynamics inverse dynamics

More information

Linköping University Electronic Press

Linköping University Electronic Press Linköping University Electronic Press Report Simulation Model of a 2 Degrees of Freedom Industrial Manipulator Patrik Axelsson Series: LiTH-ISY-R, ISSN 400-3902, No. 3020 ISRN: LiTH-ISY-R-3020 Available

More information

WEEK 1 Dynamics of Machinery

WEEK 1 Dynamics of Machinery WEEK 1 Dynamics of Machinery References Theory of Machines and Mechanisms, J.J. Uicker, G.R.Pennock ve J.E. Shigley, 2003 Makine Dinamiği, Prof. Dr. Eres SÖYLEMEZ, 2013 Uygulamalı Makine Dinamiği, Jeremy

More information

Dynamics. 1 Copyright c 2015 Roderic Grupen

Dynamics. 1 Copyright c 2015 Roderic Grupen Dynamics The branch of physics that treats the action of force on bodies in motion or at rest; kinetics, kinematics, and statics, collectively. Websters dictionary Outline Conservation of Momentum Inertia

More information

Robotics I. Classroom Test November 21, 2014

Robotics I. Classroom Test November 21, 2014 Robotics I Classroom Test November 21, 2014 Exercise 1 [6 points] In the Unimation Puma 560 robot, the DC motor that drives joint 2 is mounted in the body of link 2 upper arm and is connected to the joint

More information

Rigid Manipulator Control

Rigid Manipulator Control Rigid Manipulator Control The control problem consists in the design of control algorithms for the robot motors, such that the TCP motion follows a specified task in the cartesian space Two types of task

More information

Virtual Passive Controller for Robot Systems Using Joint Torque Sensors

Virtual Passive Controller for Robot Systems Using Joint Torque Sensors NASA Technical Memorandum 110316 Virtual Passive Controller for Robot Systems Using Joint Torque Sensors Hal A. Aldridge and Jer-Nan Juang Langley Research Center, Hampton, Virginia January 1997 National

More information

Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy

Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy Stress Analysis Lecture 3 ME 276 Spring 2017-2018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress

More information

Design and Control of Compliant Humanoids. Alin Albu-Schäffer. DLR German Aerospace Center Institute of Robotics and Mechatronics

Design and Control of Compliant Humanoids. Alin Albu-Schäffer. DLR German Aerospace Center Institute of Robotics and Mechatronics Design and Control of Compliant Humanoids Alin Albu-Schäffer DLR German Aerospace Center Institute of Robotics and Mechatronics Torque Controlled Light-weight Robots Torque sensing in each joint Mature

More information

Video 5.1 Vijay Kumar and Ani Hsieh

Video 5.1 Vijay Kumar and Ani Hsieh Video 5.1 Vijay Kumar and Ani Hsieh Robo3x-1.1 1 The Purpose of Control Input/Stimulus/ Disturbance System or Plant Output/ Response Understand the Black Box Evaluate the Performance Change the Behavior

More information

EML5311 Lyapunov Stability & Robust Control Design

EML5311 Lyapunov Stability & Robust Control Design EML5311 Lyapunov Stability & Robust Control Design 1 Lyapunov Stability criterion In Robust control design of nonlinear uncertain systems, stability theory plays an important role in engineering systems.

More information

Dynamics. Basilio Bona. Semester 1, DAUIN Politecnico di Torino. B. Bona (DAUIN) Dynamics Semester 1, / 18

Dynamics. Basilio Bona. Semester 1, DAUIN Politecnico di Torino. B. Bona (DAUIN) Dynamics Semester 1, / 18 Dynamics Basilio Bona DAUIN Politecnico di Torino Semester 1, 2016-17 B. Bona (DAUIN) Dynamics Semester 1, 2016-17 1 / 18 Dynamics Dynamics studies the relations between the 3D space generalized forces

More information

Contents. Dynamics and control of mechanical systems. Focus on

Contents. Dynamics and control of mechanical systems. Focus on Dynamics and control of mechanical systems Date Day 1 (01/08) Day 2 (03/08) Day 3 (05/08) Day 4 (07/08) Day 5 (09/08) Day 6 (11/08) Content Review of the basics of mechanics. Kinematics of rigid bodies

More information

Lecture Note 12: Dynamics of Open Chains: Lagrangian Formulation

Lecture Note 12: Dynamics of Open Chains: Lagrangian Formulation ECE5463: Introduction to Robotics Lecture Note 12: Dynamics of Open Chains: Lagrangian Formulation Prof. Wei Zhang Department of Electrical and Computer Engineering Ohio State University Columbus, Ohio,

More information

Exercise 1b: Differential Kinematics of the ABB IRB 120

Exercise 1b: Differential Kinematics of the ABB IRB 120 Exercise 1b: Differential Kinematics of the ABB IRB 120 Marco Hutter, Michael Blösch, Dario Bellicoso, Samuel Bachmann October 5, 2016 Abstract The aim of this exercise is to calculate the differential

More information

Design and Control of Variable Stiffness Actuation Systems

Design and Control of Variable Stiffness Actuation Systems Design and Control of Variable Stiffness Actuation Systems Gianluca Palli, Claudio Melchiorri, Giovanni Berselli and Gabriele Vassura DEIS - DIEM - Università di Bologna LAR - Laboratory of Automation

More information

Center of Gravity Pearson Education, Inc.

Center of Gravity Pearson Education, Inc. Center of Gravity = The center of gravity position is at a place where the torque from one end of the object is balanced by the torque of the other end and therefore there is NO rotation. Fulcrum Point

More information

Week 3: Wheeled Kinematics AMR - Autonomous Mobile Robots

Week 3: Wheeled Kinematics AMR - Autonomous Mobile Robots Week 3: Wheeled Kinematics AMR - Paul Furgale Margarita Chli, Marco Hutter, Martin Rufli, Davide Scaramuzza, Roland Siegwart Wheeled Kinematics 1 AMRx Flipped Classroom A Matlab exercise is coming later

More information

INSTRUCTIONS TO CANDIDATES:

INSTRUCTIONS TO CANDIDATES: NATIONAL NIVERSITY OF SINGAPORE FINAL EXAMINATION FOR THE DEGREE OF B.ENG ME 444 - DYNAMICS AND CONTROL OF ROBOTIC SYSTEMS October/November 994 - Time Allowed: 3 Hours INSTRCTIONS TO CANDIDATES:. This

More information

Introduction MEAM 535. What is MEAM 535? Audience. Advanced topics in dynamics

Introduction MEAM 535. What is MEAM 535? Audience. Advanced topics in dynamics What is MEAM 535? Advanced topics in dynamics Audience Review of Newtonian mechanics MEAM 535 Introduction Analytical mechanics: Lagrangian and Hamiltonian Special topics: Stability of dynamical systems,

More information

Nonlinear Landing Control for Quadrotor UAVs

Nonlinear Landing Control for Quadrotor UAVs Nonlinear Landing Control for Quadrotor UAVs Holger Voos University of Applied Sciences Ravensburg-Weingarten, Mobile Robotics Lab, D-88241 Weingarten Abstract. Quadrotor UAVs are one of the most preferred

More information

Video 1.1 Vijay Kumar and Ani Hsieh

Video 1.1 Vijay Kumar and Ani Hsieh Video 1.1 Vijay Kumar and Ani Hsieh 1 Robotics: Dynamics and Control Vijay Kumar and Ani Hsieh University of Pennsylvania 2 Why? Robots live in a physical world The physical world is governed by the laws

More information

Control of industrial robots. Centralized control

Control of industrial robots. Centralized control Control of industrial robots Centralized control Prof. Paolo Rocco (paolo.rocco@polimi.it) Politecnico di Milano ipartimento di Elettronica, Informazione e Bioingegneria Introduction Centralized control

More information

Automatic Control Systems. -Lecture Note 15-

Automatic Control Systems. -Lecture Note 15- -Lecture Note 15- Modeling of Physical Systems 5 1/52 AC Motors AC Motors Classification i) Induction Motor (Asynchronous Motor) ii) Synchronous Motor 2/52 Advantages of AC Motors i) Cost-effective ii)

More information

Pierre Bigot 2 and Luiz C. G. de Souza 3

Pierre Bigot 2 and Luiz C. G. de Souza 3 INTERNATIONAL JOURNAL OF SYSTEMS APPLICATIONS, ENGINEERING & DEVELOPMENT Volume 8, 2014 Investigation of the State Dependent Riccati Equation (SDRE) adaptive control advantages for controlling non-linear

More information

Modelling and Control of Variable Stiffness Actuated Robots

Modelling and Control of Variable Stiffness Actuated Robots Modelling and Control of Variable Stiffness Actuated Robots Sabira Jamaludheen 1, Roshin R 2 P.G. Student, Department of Electrical and Electronics Engineering, MES College of Engineering, Kuttippuram,

More information

Robotics I. Test November 29, 2013

Robotics I. Test November 29, 2013 Exercise 1 [6 points] Robotics I Test November 9, 013 A DC motor is used to actuate a single robot link that rotates in the horizontal plane around a joint axis passing through its base. The motor is connected

More information

Robot Control Basics CS 685

Robot Control Basics CS 685 Robot Control Basics CS 685 Control basics Use some concepts from control theory to understand and learn how to control robots Control Theory general field studies control and understanding of behavior

More information

Exponential Controller for Robot Manipulators

Exponential Controller for Robot Manipulators Exponential Controller for Robot Manipulators Fernando Reyes Benemérita Universidad Autónoma de Puebla Grupo de Robótica de la Facultad de Ciencias de la Electrónica Apartado Postal 542, Puebla 7200, México

More information

1.053J/2.003J Dynamics and Control I Fall Final Exam 18 th December, 2007

1.053J/2.003J Dynamics and Control I Fall Final Exam 18 th December, 2007 1.053J/2.003J Dynamics and Control I Fall 2007 Final Exam 18 th December, 2007 Important Notes: 1. You are allowed to use three letter-size sheets (two-sides each) of notes. 2. There are five (5) problems

More information

Repetitive jumping control for biped robots via force distribution and energy regulation

Repetitive jumping control for biped robots via force distribution and energy regulation Repetitive jumping control for biped robots via force distribution and energy regulation Gianluca Garofalo and Christian Ott German Aerospace Center (DLR), Institute of Robotics and Mechatronics, Münchner

More information

Objectives. Fundamentals of Dynamics: Module 9 : Robot Dynamics & controls. Lecture 31 : Robot dynamics equation (LE & NE methods) and examples

Objectives. Fundamentals of Dynamics: Module 9 : Robot Dynamics & controls. Lecture 31 : Robot dynamics equation (LE & NE methods) and examples \ Module 9 : Robot Dynamics & controls Lecture 31 : Robot dynamics equation (LE & NE methods) and examples Objectives In this course you will learn the following Fundamentals of Dynamics Coriolis component

More information

ANALYSIS OF LOAD PATTERNS IN RUBBER COMPONENTS FOR VEHICLES

ANALYSIS OF LOAD PATTERNS IN RUBBER COMPONENTS FOR VEHICLES ANALYSIS OF LOAD PATTERNS IN RUBBER COMPONENTS FOR VEHICLES Jerome Merel formerly at Hutchinson Corporate Research Center Israël Wander Apex Technologies Pierangelo Masarati, Marco Morandini Dipartimento

More information

Robotics I. Figure 1: Initial placement of a rigid thin rod of length L in an absolute reference frame.

Robotics I. Figure 1: Initial placement of a rigid thin rod of length L in an absolute reference frame. Robotics I September, 7 Exercise Consider the rigid body in Fig., a thin rod of length L. The rod will be rotated by an angle α around the z axis, then by an angle β around the resulting x axis, and finally

More information

Robotics 2 Robot Interaction with the Environment

Robotics 2 Robot Interaction with the Environment Robotics 2 Robot Interaction with the Environment Prof. Alessandro De Luca Robot-environment interaction a robot (end-effector) may interact with the environment! modifying the state of the environment

More information

A Blade Element Approach to Modeling Aerodynamic Flight of an Insect-scale Robot

A Blade Element Approach to Modeling Aerodynamic Flight of an Insect-scale Robot A Blade Element Approach to Modeling Aerodynamic Flight of an Insect-scale Robot Taylor S. Clawson, Sawyer B. Fuller Robert J. Wood, Silvia Ferrari American Control Conference Seattle, WA May 25, 2016

More information

Multibody simulation

Multibody simulation Multibody simulation Dynamics of a multibody system (Euler-Lagrange formulation) Dimitar Dimitrov Örebro University June 16, 2012 Main points covered Euler-Lagrange formulation manipulator inertia matrix

More information

ARTISAN ( ) ARTISAN ( ) Human-Friendly Robot Design

ARTISAN ( ) ARTISAN ( ) Human-Friendly Robot Design Human-Friendly Robot Design Torque Control: a basic capability dynamic performance compliance, force control safety, interactivity manipulation cooperation ARTISAN (1990-95) ARTISAN (1990-95) 1 intelligence

More information

Robotics I Kinematics, Dynamics and Control of Robotic Manipulators. Velocity Kinematics

Robotics I Kinematics, Dynamics and Control of Robotic Manipulators. Velocity Kinematics Robotics I Kinematics, Dynamics and Control of Robotic Manipulators Velocity Kinematics Dr. Christopher Kitts Director Robotic Systems Laboratory Santa Clara University Velocity Kinematics So far, we ve

More information

2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity

2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity 2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity Energy 7 4 Kinematics Free fall Collisions 3 5 Dynamics

More information

Mechanics. In the Science Program, Mechanics contributes to the following program goals described in the Exit Profile:

Mechanics. In the Science Program, Mechanics contributes to the following program goals described in the Exit Profile: Mechanics Objectives: 00UR Discipline: Physics Ponderation: 3-2-3 Course Code: 203-NYA-05 Prerequisite: Sec. V Physics 534, Mathematics 536 (or equivalent) Course Credit: 2 2/3 Corequisite: 00UP (Calculus

More information

Screw Theory and its Applications in Robotics

Screw Theory and its Applications in Robotics Screw Theory and its Applications in Robotics Marco Carricato Group of Robotics, Automation and Biomechanics University of Bologna Italy IFAC 2017 World Congress, Toulouse, France Table of Contents 1.

More information

Models and Anthropometry

Models and Anthropometry Learning Objectives Models and Anthropometry Readings: some of Chapter 8 [in text] some of Chapter 11 [in text] By the end of this lecture, you should be able to: Describe common anthropometric measurements

More information

Center of Gravity. The location of the center of gravity is defined by: n mgx. APSC 111 Review Page 7

Center of Gravity. The location of the center of gravity is defined by: n mgx. APSC 111 Review Page 7 Center of Gravity We have said that for rigid bodies, all of the forces act at the centre of mass. This is a normally a very good approximation, but strictly speaking, the forces act at the centre of gravity,

More information

DYNAMICS OF SERIAL ROBOTIC MANIPULATORS

DYNAMICS OF SERIAL ROBOTIC MANIPULATORS DYNAMICS OF SERIAL ROBOTIC MANIPULATORS NOMENCLATURE AND BASIC DEFINITION We consider here a mechanical system composed of r rigid bodies and denote: M i 6x6 inertia dyads of the ith body. Wi 6 x 6 angular-velocity

More information

, respectively to the inverse and the inverse differential problem. Check the correctness of the obtained results. Exercise 2 y P 2 P 1.

, respectively to the inverse and the inverse differential problem. Check the correctness of the obtained results. Exercise 2 y P 2 P 1. Robotics I July 8 Exercise Define the orientation of a rigid body in the 3D space through three rotations by the angles α β and γ around three fixed axes in the sequence Y X and Z and determine the associated

More information

Introduction to Haptic Systems

Introduction to Haptic Systems Introduction to Haptic Systems Félix Monasterio-Huelin & Álvaro Gutiérrez & Blanca Larraga October 8, 2018 Contents Contents 1 List of Figures 1 1 Introduction 2 2 DC Motor 3 3 1 DOF DC motor model with

More information

ME451 Kinematics and Dynamics of Machine Systems

ME451 Kinematics and Dynamics of Machine Systems ME451 Kinematics and Dynamics of Machine Systems Introduction to Dynamics 6.1 October 30, 2014 Dan Negrut ME451, Fall 2014 University of Wisconsin-Madison Quote of the day: Computer science education cannot

More information

557. Radial correction controllers of gyroscopic stabilizer

557. Radial correction controllers of gyroscopic stabilizer 557. Radial correction controllers of gyroscopic stabilizer M. Sivčák 1, J. Škoda, Technical University in Liberec, Studentská, Liberec, Czech Republic e-mail: 1 michal.sivcak@tul.cz; jan.skoda@pevnosti.cz

More information

Robust Control of Robot Manipulator by Model Based Disturbance Attenuation

Robust Control of Robot Manipulator by Model Based Disturbance Attenuation IEEE/ASME Trans. Mechatronics, vol. 8, no. 4, pp. 511-513, Nov./Dec. 2003 obust Control of obot Manipulator by Model Based Disturbance Attenuation Keywords : obot manipulators, MBDA, position control,

More information