Category: robotics

Key Control Strategies Emerge in Spring Loaded Inverted Pendulum Traversal of Slippery Terrain
Last week I returned from the Dynamic Walking 2017 conference, where I had a poster and five minute talk on some of the numerical trajectory optimization work I’ve been doing for spring loaded inverted pendulums. More specifically, I was trying to determine what kinds of strategies the optimizer discovers when recovering from landing unexpectedly on…

Legged Helicopter Landing Gear
One of my biggest projects to date is a legged landing gear that allows helicopters to land on uneven terrain with large touchdown velocity. For a quick overview, please see the following video. Inspiration Traditional helicopter landing gears generally consist of two tubular skids, or three wheels for larger helicopters. These designs require a very…

Optimizing Trajectories for the Spring Loaded Inverted Pendulum over Slippery Terrain
Previously, I’ve written short introductions to numerical trajectory optimization here and here—if you’re unfamiliar with the basics, I recommend you check those out first. This write up expands upon a section of my research paper (which I hope to finish soon) and is meant to be a walkthrough of how to apply numerical trajectory optimization to realworld scenarios. The Problem…

Tutorial: Direct Collocation Trajectory Optimization with Matlab
In the previous tutorial, we focused on single shooting trajectory optimization, which involved timediscretizing the control input and simply integrating the dynamics. The desired end state was then added as a constraint to fmincon. Here, we focus on a different trajectory optimization technique, known as direct collocation. Simultaneous Optimization The core difference between shooting methods…

Tutorial: Single Shooting Trajectory Optimization with Matlab
Numerical methods for trajectory optimization have become increasingly popular for analyzing the motion of bipedal springmass walkers, whose complex nonlinear dynamics make analytical solutions often infeasible. When I began looking into trajectory optimization, the number of different methods often obscured some of the basic ideas in the field. This tutorial is meant to provide a simple introduction to trajectory optimization with some example…

3D Printing Inaccuracies with the Lulzbot Mini
A few months ago, I bought a LulzBot Mini to print parts for a robotics project. Despite its rather goofy name, the machine itself is great, especially for the price. However, it does suffer from the same inaccuracies that are fairly common among typical 3D printers. Since many of my parts had to be precisely…

Optimizing Retraction Reflexes Using Reinforcement Learning based on Particle Filtering
As part of my development of a legged helicopter landing gear (more on this later), I started studying ways to minimize landing impact using a combination of leg retraction (active impedance) and elastic elements (passive impedance). This lead me to the paper “Can Active Impedance Protect Robots from Landing Impact?” by Houman Dallali et. al. Although…

Relationships Between Current, Angular Velocity, and Torque in PositionControlled Servos
TL;DR I did some experimentation on whether or not it is possible to estimate the shaft torque on a cheap, positioncontrolled hobby servo using current and angular velocity. A paper documenting the findings along with the complete data is available is available on GitHub (direct link to paper: paper.pdf). Background At Darien High School, I’m part of…