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Why is RRT efficient?

less than 1 minute read


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

3 minute read


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 forms and Convexity

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.

Simulated Annealing

less than 1 minute read


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.


  • 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]

Trajectory planning for bertha—a local, continuous method


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.




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.