Guidance: Convex hull, null space and convex basis etc

[Inner_Peace]

Hi friends!
I am getting started with a research paper that discusses the closure properties of a robotic grasp. There are of lot of mathematical terms that confuse me like 'convex hull' , convex basis, convex combination of vectors, a free subset, nullspace etc. I might have studied some of them in University mathematics but that seems a long ago. Could you please suggest me places where should I start looking for concept building ? Any good tutorials or books?

Thank you ! :)

 

[mathman]

Have you tried to google these terms?

 

[HallsofIvy]

I don't see this as having much to do with vectors. A "convex set" in $R^n$ is a set such that for any two points p and q in the set the line segment between p and q is in the set also.

The "convex hull" of a set, A, is the smallest convex set that has A as a subset. One way to construct the convex hull of a set is to add all line segments between any two points in the set.

I don't recognize the terms "convex basis", "convex combination", or "free space".

The "null space" of a linear Transformation, T, from one vector space to another, is the set of all vectors, v, such that T(v)= 0. One can show that the null space is a subspace of the domain vector space.

 

[FactChecker]

Amazon.com has several books on the subject. You will need to look at the reviews to see what fits your needs.
A convex basis is a set of vectors that can be added together with positive weights (all weights 0<=w<=1 that sum to 1). Those weighted sums are the convex combinations.

 

[blue_raver22]

Hello! It's great that you are diving into a research paper on robotic grasping. The terms you mentioned, such as convex hull, null space, and convex basis, are all important mathematical concepts in the field of robotics and specifically in grasp planning.

To start building your understanding of these concepts, I recommend looking into linear algebra and optimization theory. These subjects will provide the foundation for understanding convex hulls, null spaces, and convex bases. In particular, understanding convex optimization will be crucial for grasping research as it deals with finding optimal solutions for problems with convex constraints.

Some good resources for learning about these topics include textbooks such as "Convex Optimization" by Stephen Boyd and Lieven Vandenberghe, "Linear Algebra and Its Applications" by David C. Lay, and "Robotics: Modelling, Planning and Control" by Bruno Siciliano and Oussama Khatib.

Additionally, there are many online tutorials and lectures available on these topics, such as those on YouTube or through online learning platforms like Coursera or edX.

I also recommend reaching out to experts in the field of robotics and grasp planning for guidance and further resources. They may also be able to provide valuable insights and explanations on these concepts.

Overall, building a strong understanding of these mathematical concepts will greatly benefit your research and allow you to effectively analyze and develop solutions for robotic grasping problems. Best of luck with your research paper!