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## Markdown

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## Why is RRT efficient?

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Trajectory optimization is a local method, it only explores the neighborhood of an initial seed, besides, in the direct transcription, we discretize along the trajectory instead of every dimension of the C-space, thus it scales well in high dimensional space. But RRT is a global method, what makes it efficient in exploring a collision-free path in high dimensional space?

## Convex optimization, QP, SQP

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### Definition of convex function

For all ${ 0\leq t \leq 1}$ and all ${ x_{1},x_{2}\in X,}$ ${ f\left(tx_{1}+(1-t)x_{2}\right)~\leq ~tf\left(x_{1}\right)+(1-t)f\left(x_{2}\right).}$

Quadratic form in variables ${ x_1,x_2…, x_n}$ is a polynomial function $Q$, where all the terms in $Q(x_1, x_2,…, x_n)$ have order two. Quadratic functions $\neq$ convex functions.

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## Simulated Annealing

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Simulated Annealing is a probabilistic method for approximating the global optimum of a given function. It is helpful especially in the case of large search space.

• Make use of randomness, random walk on a search graph.
• Transition probabilities..
• Higher probability of accepting worse solutions in the begining (high temperature).

## Motion planning and control Misc.

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• The notion of configuration space is the key insight to Lagrangian mechanics of rigid bodies, as it allows dynamics to be expressed using the precise degrees of freedom of a body. [1]

## Modern Robotics: Mechanics, Planning, and Control (Chapter 13)

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Wheeled mobile robots may be classified in two major categories, omnidirectional and nonholonomic. We focus on nonholonomic mobile robots in the rest of the note.

## TRAC-IK: An open-source library for improved solving of generic inverse kinematics

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• SQP: $arg \underset{q \in \bf{R}^n}{\text{min}} (q_{seed}-q)^T(q_{seed}-q)$ subject to $f_i(q) \leq b_i, i=1,\dots,m$
• SQP-DQ: the objective is the task space pose error.
• KDL-RR: KDL ik with random restarts

## Trajectory planning for bertha—a local, continuous method

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The solution trajectory is the constrained extremum of an objective function that is designed to express dynamic feasibility and comfort. Static and dynamic obstacle constraints are incorporated in the form of polygons. The constraints are carefully designed to ensure that the solution converges to a single, global optimum.

## Sampling-based methods for motion planning with constraints

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This paper considers geometrical constraints that reduce the number of degrees of freedom.

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TODO

## Paper Title Number 1

Published in Journal 1, 2009

This paper is about the number 1. The number 2 is left for future work.

Recommended citation: Your Name, You. (2009). "Paper Title Number 1." Journal 1. 1(1). http://academicpages.github.io/files/paper1.pdf

## Paper Title Number 2

Published in Journal 1, 2010

This paper is about the number 2. The number 3 is left for future work.

Recommended citation: Your Name, You. (2010). "Paper Title Number 2." Journal 1. 1(2). http://academicpages.github.io/files/paper2.pdf

## Paper Title Number 3

Published in Journal 1, 2015

This paper is about the number 3. The number 4 is left for future work.

Recommended citation: Your Name, You. (2015). "Paper Title Number 3." Journal 1. 1(3). http://academicpages.github.io/files/paper3.pdf

## Talk 1 on Relevant Topic in Your Field

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This is a description of your talk, which is a markdown files that can be all markdown-ified like any other post. Yay markdown!

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## Conference Proceeding talk 3 on Relevant Topic in Your Field

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This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.

## Teaching experience 1

Undergraduate course, University 1, Department, 2014

This is a description of a teaching experience. You can use markdown like any other post.

## Teaching experience 2

Workshop, University 1, Department, 2015

This is a description of a teaching experience. You can use markdown like any other post.