Category: trajectory optimization
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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…
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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 real-world scenarios. The Problem…
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Tutorial: Direct Collocation Trajectory Optimization with Matlab
In the previous tutorial, we focused on single shooting trajectory optimization, which involved time-discretizing 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…
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Tutorial: Single Shooting Trajectory Optimization with Matlab
Numerical methods for trajectory optimization have become increasingly popular for analyzing the motion of bipedal spring-mass 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…