To simplify the inverse kinematics most robots have a spherical wrist, a particular mechanical wrist design. For robots where the inverse kinematics is too hard to figure out we can solve the problem numerically, treating it as an optimisation problem.
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The orientation of a body in 3D can also be described by two vectors, often called the approach and orientation vectors.
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)).
How is an image formed? The real world has three dimensions but an image has only two. We can use linear algebra and homogeneous coordinates to understand what’s going on. This more general approach allows us to model the positions of pixels in the sensor array and to derive relationships between points on the image […]
Another non-linear operation on the pixels in the box around the input pixel is to test whether they match a reference shape. This is a very powerful and useful approach to cleaning up noisy binary images known as mathematical morphology and objects in the image are treated according to their compatibility with a structuring element. […]
It is common to think about an assembly task being specified in terms of coordinates in the 3D world. An alternative approach is to consider the task in terms of the relative position of objects in one or more views of the task — visual servoing.
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.
To move a robot smoothly from one pose to another we need smooth and coordinated motion of all the joints. The simplest approach is called joint interpolated motion but it has some limitations.
For a redundant robot the inverse kinematics can be easily solved using a numerical approach.
Let’s look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations.