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Introduction to 3D Geometry

We learn how to describe the position and orientation of objects in the 3-dimensional space that we live in. This builds on our understanding of describing position and orientation in two dimensions.  

Relative pose in 2D

We consider multiple objects each with its own coordinate frame. Now we can describe the relationships between the frames and find a vector describing a point with respect to any of these frames. We extend our algebraic notation to ease the manipulation of relative poses.  

Relative Positions in 2D

We introduce the idea of attaching a coordinate frame to an object. We can describe points on the object by constant vectors with respect to the object’s coordinate frame, and then relate those to the points described with respect to a world coordinate frame. We introduce a simple algebraic notation to describe this.  

Position and Pose in 2D

To fully describe an object on the plane we need to not only describe its position, but also which direction it is pointing. This combination is referred to as pose.  

2D Geometry Refresher

We revisit the fundamentals of geometry that you would have learned at school: Euclidean geometry, Cartesian or analytic geometry, coordinate frames, points and vectors.  

Introduction to 2D Geometry

We learn how to describe the position and orientation of objects on a 2-dimensional plane. We introduce the notion of reference frames as a basis for describing the position of objects in two dimensions.  

Robots in History

Humans have long been fascinated by machines that mimic people and animals. These and several other technologies are the precursors of modern robots.  

Playing Catch and Juggling with a Humanoid Robot

Robots in entertainment environments typically do not allow for physical interaction and contact with people. However, catching and throwing back objects is one form of physical engagement that still maintains a safe distance between the robot and participants. Using an animatronic humanoid robot, we developed a test bed for a throwing and catching game scenario. We use an external camera system (ASUS Xtion PRO LIVE) to locate balls and a Kalman filter to predict ball destination and timing. The robot’s hand and joint-space are calibrated to the vision coordinate system using a least-squares technique, such that the hand can be…

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