Trajectory_optimization

Legged robot research has been an active area of study since the late nineties. Let’s take a look at how we can generate walking trajectories for bipedal robots, using some of these ideas. The Objective: Implement a quick and dirty way of generating walking trajectories Constraints: Do it quickly. Minimize sophistication. Anything goes! What this post will cover: Overview of the minimal set of ideas required to develop walking algorithms Computation of bipedal joint trajectories for a simple walking gait What will not be covered: [Read More]

TrajOpt $[1]$ is an optimization based approach for motion planning. More specifically, it uses a sequential convex optimization procedure along with a formulation of collision constraints to find locally optimal planning trajectories, even for robotic systems that have a large number of degrees of freedom. This post will go into the details of the optimization part, and give an outline of how it can be implemented. My implementation can be found here [Read More]

In this post, we take a look at this $[1]$ paper, which introduces a simple, yet interesting approach to solving a multi-vehicle path planning problem. My implementation of the algorithm that was used to evaluate its performance and generate all the results in this post can be found here $\newcommand{\ith}{i^{th}}$ $\newcommand{\pth}{p^{th}}$ $\newcommand{\qth}{q^{th}}$ $\newcommand{\lth}{l^{th}}$ $\newcommand{\MR}{\mathbb{R}}$ $\newcommand{\xpi}{x_{pi}}$ $\newcommand{\ypi}{y_{pi}}$ $\newcommand{\xqi}{x_{qi}}$ $\newcommand{\yqi}{y_{qi}}$ $\newcommand{\xmin}{x_{min}}$ $\newcommand{\xmax}{x_{max}}$ $\newcommand{\ymin}{y_{min}}$ $\newcommand{\ymax}{y_{max}}$ $\newcommand{\xlmin}{x_{l,min}}$ $\newcommand{\xlmax}{x_{l,max}}$ $\newcommand{\ylmin}{y_{l,min}}$ $\newcommand{\ylmax}{y_{l,max}}$ $\newcommand{\xlimin}{x_{li,min}}$ $\newcommand{\xlimax}{x_{li,max}}$ $\newcommand{\ylimin}{y_{li,min}}$ $\newcommand{\ylimax}{y_{li,max}}$ $\newcommand{\cplx}{c_{pl,x}}$ $\newcommand{\cply}{c_{pl,y}}$ $\newcommand{\dpqx}{d_{pq,x}}$ $\newcommand{\dpqy}{d_{pq,y}}$ $\newcommand{\tpli}{t_{pli}}$ $\newcommand{\spi}{s_{pi}}$ $\newcommand{\spij}{s_{pij}}$ $\newcommand{\spinext}{s_{p,i+1}}$ $\newcommand{\spn}{s_{pN}}$ $\newcommand{\spf}{s_{pf}}$ $\newcommand{\wpi}{w_{pi}}$ $\newcommand{\wpij}{w_{pij}}$ $\newcommand{\wpn}{w_{pN}}$ $\newcommand{\upi}{u_{pi}}$ $\newcommand{\upik}{u_{pik}}$ $\newcommand{\vpi}{v_{pi}}$ $\newcommand{\vpik}{v_{pik}}$ $\newcommand{\Ap}{A_{p}}$ $\newcommand{\Bp}{B_{p}}$ $\newcommand{\qp}{q_{p}}$ $\newcommand{\rp}{r_{p}}$ $\newcommand{\pp}{p_{p}}$ [Read More]