Time 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.
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We summarise the important points from this lecture.
We will learn how to create coordinate frames that have smoothly changing position and orientation over time.
We will introduce resolved-rate motion control which is a classical Jacobian-based scheme for moving the end-effector at a specified velocity without having to compute inverse kinematics.
Frequently we want a trajectory that moves smoothly through a series of points without stopping.
The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.
We learn how to describe the orientation of an object by a 3×3 rotation matrix which has some special properties.
A characteristic of inverse kinematics is that there is often more than one solution, that is, more than one set of joint angles gives exactly the same end-effector pose.
We learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.
A 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. Note that in Robotics, Vision & Control (second edition) and RTB10.x the default definition of roll-pitch-yaw […]