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For a real 6-link robot our previous approach to computing the Jacobian becomes unwieldy so we will instead compute a numerical approximation to the forward kinematic function.

We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.

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.

For real robots such as those with 6 joints that move in 3D space the inverse kinematics is quite complex, but for many of these robots the solutions have been helpfully derived by others and published. Let’s explore the inverse kinematics of the classical Puma 560 robot.

A body moving in 3D space has a translational velocity and a rotational velocity. The combination is called spatial velocity and is described by a 6-element vector.

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.

The linear algebra approach we’ve discussed is very well suited to MATLAB implementation. Let’s look at some toolbox functions that can simulate what cameras do. If you are using a more recent version of MVTB, ie. MVTB 4.x then please change>> cam.project(PW ‘Tcam’, transl(0.1, 0, 0)) to >> cam.project(PW ‘pose’, transl(0.1, 0, 0)).

Let’s look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations. For RTB10.x please note that the mask value must be explicitly preceded by the ‘mask’ keyword. For example: >> q = p2.ikine(T, [-1 -1], ‘mask’, [1 1 0 0 0 0])

We learn a method for succinctly describing the structure of a serial-link manipulator in terms of its Denavit-Hartenberg parameters, a widely used notation in robotics.

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 […]