Summary of paths and Trajectories
In Robotics | No commentThis video gives summary of paths and trajectories.
14 Jul
14 Jul
Interpolating pose in 3D
In Robotics | No commentWe combine what we’ve learnt about smoothly varying position and orientation to create smoothly varying pose, often called Cartesian interpolation.
14 Jul
Interpolating rotation in 3D
In Robotics | No commentWe learn how to create smoothly varying orientation in 3D by interpolating Euler angles and Quaternions.
14 Jul
Multi-dimensional trajectory
In Robotics | No commentWe learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.
14 Jul
1D trajectory with via points
In Robotics | No commentFrequently we want a trajectory that moves smoothly through a series of points without stopping.
14 Jul
1D polynomial trajectory
In Robotics | No commentThe simplest smooth trajectory is a polynomial with boundary conditions on position, velocity and acceleration.
14 Jul
Paths and Trajectories
In Robotics | No commentTime varying coordinate frames are required to describe how the end-effector of a robot should move to grab an object, or to describe objects that are moving in the world. We make an important distinction between a path and a trajectory.
14 Jul
Introduction to Paths and Trajectories
In Robotics | No commentWe will learn how to create coordinate frames that have smoothly changing position and orientation over time.
14 Jul
Summary of 3D geometry and pose
In Robotics | No commentThis video gives summary of 3D geometry and pose.
14 Jul
Describing rotation and translation in 3D
In Robotics | No commentWe learn how to describe the 3D pose of an object by a 4×4 homogeneous transformation matrix which has a special structure.
14 Jul
Quaternions representation of rotation in 3D
In Robotics | No commentThe orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object.
14 Jul
Angle-axis representation of rotation in 3D
In Robotics | No commentThe orientation of a body in 3D can also be described by a single rotation about a particular axis in space.
14 Jul
2-vector representation of rotation in 3D
In Robotics | No commentThe orientation of a body in 3D can also be described by two vectors, often called the approach and orientation vectors.
14 Jul
Singularity in 3D rotation angle sequences
In Robotics | No commentA problem arises when using three-angle sequences and particular values of the middle angle leads to a condition called a singularity. This mathematical phenomena is related to a problem that occurs in the physical world with mechanical gimbal systems.
14 Jul
Rotation angle sequences in 3D
In Robotics | No commentThe orientation of a body in 3D can be described by three angles, examples of which are Euler angles and roll-pitch-yaw angles.
14 Jul
Rotations are non commutative in 3D
In Robotics | No commentIf we apply a sequence of 3D rotations to an objects we see that the order in which they are applied affects the final result.
14 Jul
Describing rotation in 3D
In Robotics | No commentWe learn how to describe the orientation of an object by a 3×3 rotation matrix which has some special properties.
14 Jul
Relative pose in 3D
In Robotics | No commentWe consider multiple objects each with their own 3D 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 previous 2D algebraic notation to 3D and look again at pose graphs.
14 Jul
Pose in 3D
In Robotics | No commentWe extend the idea of relative pose, introduced in the last lecture, to 3D. We learn another right-hand rule that indicates the direction of rotation about an axis, and we see how we can attach 3D coordinate frames to objects to determine their pose in 3D space.
14 Jul
Build your own 3D coordinate frame
In Robotics | No commentThis is an exercise in which you can build a 3D coordinate frame by printing, cutting, folding and stapling.
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