3630-08-lec5

3630-08-lec5 - Intro Coords Models Maneuverability...

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Unformatted text preview: Intro Coords Models Maneuverability Workspace Beyond Basics Wrapup Robot Kinematics Henrik I Christensen Robotics & Intelligent Machines @ GT Georgia Institute of Technology, Atlanta, GA 30332-0760 [email protected] Henrik I Christensen ([email protected]) Robot Locomotion 1 / 46 Intro Coords Models Maneuverability Workspace Beyond Basics Wrapup Outline 1 Introduction 2 Coordinate Systems 3 Kinematic Models and Constraints 4 Mobile Robot Maneuverability 5 Mobile Robot Workspace 6 Beyond Basic Kinematics 7 Wrapup Henrik I Christensen ([email protected]) Robot Locomotion 2 / 46 Intro Coords Models Maneuverability Workspace Beyond Basics Wrapup Motion Control Requirements Kinematic / dynamic model of the robot Model of ground/wheel interaction Definition of required motion → velocity / position control Design of control law to satisfy constriants Henrik I Christensen ([email protected]) Robot Locomotion 3 / 46 Intro Coords Models Maneuverability Workspace Beyond Basics Wrapup Mobile Robot Kinematics Model of mechanical behaviour of robot for design and control Models can be used both for mobile systems and manipulators Manipulators allow “direct” estimation of position, which is rarely true for mobile systems Position to be derived from integration over time Motion is not free. There are constraints to be considered in design and control generation. Henrik I Christensen ([email protected]) Robot Locomotion 4 / 46 Intro Coords Models Maneuverability Workspace Beyond Basics Wrapup Outline 1 Introduction 2 Coordinate Systems 3 Kinematic Models and Constraints 4 Mobile Robot Maneuverability 5 Mobile Robot Workspace 6 Beyond Basic Kinematics 7 Wrapup Henrik I Christensen ([email protected]) Robot Locomotion 5 / 46 Intro Coords Models Maneuverability Workspace Beyond Basics Wrapup Coordinate Systems Points in space can be described by their position ~ p ~ p = x y z For structures the orientation is also of interest ( α, φ, θ ) Coordinate transformations are essential to modelling of robots The basis for the coordinate system decides on the simplicity of the model and control. Henrik I Christensen ([email protected]) Robot Locomotion 6 / 46 Intro Coords Models Maneuverability Workspace Beyond Basics Wrapup Transformations Translation is easy: ~ p r = ~ p + ~ p t Rotation can modelled through a rotation matrix ~ p 1 = R ~ p Rotation α around X axis R x ,α = 1 0 cos α- sin α sin α cos α and similarly for Y and Z rotations Rotations are commutative R xy = R x R y Henrik I Christensen ([email protected]) Robot Locomotion 7 / 46 Intro Coords Models Maneuverability Workspace Beyond Basics Wrapup Homogeneous Coordinates Helpful for integration of scaling, translation and rotation into a single representation!...
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3630-08-lec5 - Intro Coords Models Maneuverability...

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