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H Geyer Image

16-711 Kinematics, Dynamics and Control


Recommended Books

[MLS]  A Mathematical Introduction to Robotic Manipulation
R Murray, Z Li and S Sastry, CRC 1994.

[SSVO]  Robotics: Modeling, Planning and Control
B Siciliano, L Sciavicco, L Villani and G Oriolo, Springer 2009.

[M] Applied Dynamics
F Moon, Wiley-VCH 1998.

[AM]  Feedback Systems: An Introduction for Scientists and Engineers
K Astrom and R Murray, Princeton 2010.

[E] Control System Design Guide
G Ellis, Elsevier 2004.

[F]  Control System Design: An Introduction to State-Space Methods
B Friedland, Dover 2005.

Assignments and Projects

Assignments will determine 70% of your grade. They will be handed out every two weeks and consist of mixed problems in theory and implementation. Implementations should be done in Matlab (C,C++ is fine too). The deadline for submission is at midnight on the due date. Please submit your assignments as pdf and commented code.  Assignments can be downloaded and uploaded through CMU Blackboard.

Projects will determine 30% of your grade. The projects ideally help you with your research. Teams of up to three students are encouraged. Projects include a presentation talk during the last week of lectures and a final technical report that is due one week later.

Syllabus and Resources


KINEMATICS

Chapter 1: Rigid Body Motions [MLS]

Fundamentals
Euclidean Space
Inertial Frame
Rigid Body
Body Frame

Tracking Rigid Bodies
Rotation Matrix
Rotational Transformations
Euler Angles, Quaternions
Exponential Coordinates
Homogeneous Transformation
Twists (Generalized 6d Motion)
Screw Coordinates

Differential Kinematics
Rotational Velocity
Generalized Rigid Body Velocity
Adjoint Transformation
Wrenches (Generalized 6d Forces)
Screw Coordinates


Chapter 2: Kinematic Chains [MLS,SSVO]

Forward Kinematics (FK)
Basic Conventions
Product of Exponentials
Parametrization, Comparison to Denavit-Hartenberg
Manipulator Workspace

Inverse Kinematics (IK)
Multiplicity of Inverse Solutions
Classical Solution Techniques
Paden-Kahen Subproblems

Differential Manipulator Kinematics
Jacobian Matrix
Manipulator Jacobian
Inverse Kinematics Algorithm
Kineto-Statics Duality
Redundant Manipulator
Singular Configurations
Manipulability Measures
Structure Equation of Closed Chains


DYNAMICS

Chapter 3: Rigid Body Dynamics [MLS,M]

Dynamics of Constrained Particles
Newton's Laws
d'Alembert's Principle
Lagrange Equations
Hamilton's Principle

Dynamics of a Rigid Body
Center of Mass and Linear Momentum
Angular Momentum and Inertia Matrix
Newton-Euler Equations
Lagrangian of a Rigid Body


Chapter 4: Manipulator Dynamics [MLS,SSVO]

Dynamics of Serial Manipulators
Manipulator Lagrangian
Equations of Motion
Dynamic Parameter Identification
Manipulator Dynamics based on Twists
Joint Friction Models
Geared Actuators

Manipulator Dynamics with Constraints
Contact Models
Grasp and Ground Contact Constraints
Lagrangian Multipliers
Robotic Applications
Redundant Manipulators


CONTROL

Chapter 5: Fundamentals of Control [AM,E,F]

Linear Time Invariant Systems with Single In- and Output
LTI Systems in State Space
Characteristic Solutions
Transfer Functions
Laplace Transform
Composition Rules

Feedback Control and Stability
Reachability
Loop Transfer Function
Root Locus Plot and Method
Nyquist Plot and Criterion
Stability Margins and Bode Plots

PID Controller
PID Components
Integral Windup
Gain Scheduling

State Estimation in Feedback Systems
Observability
Luenberger Observer
Kalman Filter
Bayes Filters and Algorithm
Extended Kalman and Particle Filters


Chapter 6: Manipulator Control [MLS,SSVO]

Local vs Centralized Motion Control Strategies
Independent Joint Control
Computed Torque Feedforward Action
Lyapunov Stability Analysis of MIMO Controls
Feedback Linearization
Operational Space Control

Indirect vs Direct Force Control Strategies
Impedance Control
Direct Force Control
Cascade Controllers

© H. Geyer, 2 May 2012