Special Propeller Protractor

A special protractor was designed and built with a view towards supplying a simple, inexpensive, practical, portable instrument for making measurements to detect propeller warpage under practically all conditions, without the use of auxiliary equipment, and without having to remove the propeller from the airplane. A detailed description is given of the protractor. Techniques for measuring are described. Directions are given on how to use the protractor to set detachable blade-type propellers on an airplane

Alternative sets of hyperspherical harmonics: Satisfying cusp conditions through frame transformations

By extending the concept of Euler-angle rotations to more than three dimensions, we develop the systematics under rotations in higher-dimensional space for a novel set of hyperspherical harmonics. Applying this formalism, we determine all pairwise Coulomb interactions in a few-body system without recourse to multipole expansions. Our approach combines the advantages of relative coordinates with those of the hyperspherical description. In the present method, each Coulomb matrix element reduces to the ``1/r'' form familiar from the two-body problem. Consequently, our calculation accounts for all the cusps in the wave function whenever an interparticle separation vanishes. Unlike a truncated multipole expansion, the calculation presented here is exact. Following the systematic development of the procedure for an arbitrary number of particles, we demonstrate it explicitly with the simplest nontrivial example, the three-body system.Comment: 19 pages, no figure

Shaping in Practice: Training Wheels to Learn Fast Hopping Directly in Hardware

Learning instead of designing robot controllers can greatly reduce engineering effort required, while also emphasizing robustness. Despite considerable progress in simulation, applying learning directly in hardware is still challenging, in part due to the necessity to explore potentially unstable parameters. We explore the concept of shaping the reward landscape with training wheels: temporary modifications of the physical hardware that facilitate learning. We demonstrate the concept with a robot leg mounted on a boom learning to hop fast. This proof of concept embodies typical challenges such as instability and contact, while being simple enough to empirically map out and visualize the reward landscape. Based on our results we propose three criteria for designing effective training wheels for learning in robotics. A video synopsis can be found at https://youtu.be/6iH5E3LrYh8.Comment: Accepted to the IEEE International Conference on Robotics and Automation (ICRA) 2018, 6 pages, 6 figure