Relationships Between Current, Angular Velocity, and Torque in Position-Controlled Servos

TL;DR

I did some experimentation on whether or not it is possible to estimate the shaft torque on a cheap, position-controlled 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 the ASR (Authentic Scientific Research) program. This three-year course is a mixture of class time—mostly spent presenting papers, or presenting our own research—and independent time learning about a chosen field. Every ASR student is welcome to research whatever topic they wish, and going into my first year of ASR as a sophomore I decided to study legged robotics.

Part of the ASR experience is competing in science fairs against other regional schools. Last February, I, along with the rest of my sophomore classmates and a few juniors, participated in the Southern Connecticut Science & Engineering Fair (SCSEF). As most sophomores don’t complete research during their first year, I was entered into the “research proposal” category for physical science (a broad category including anything not behavioral, environmental, or health/medical).

After some heavy consideration, I picked hobby servos as my poster topic. In the past, I had read a number of papers on bipedal robot balancing that gave a set of torques as the output of some proposed control algorithm. In simulation, these algorithms worked beautifully; however, when attempting to implement them with hardware I ran into the limitation that the HJ S3315D servos I had available did not allow for torque control like higher-end Dynamixels. Hobby servos such as the HJ S3315D only allow you to set the position, and will use as much or as little torque as needed to reach that position.

The vast majority SCSEF research proposals are never actually implemented. Originally, I hadn’t intended on doing more than a cursory follow-up of my servo idea; however, I eventually began to grow curious about the feasibility of some of my more grandiose visions of the project’s implications. Winning first place for the physical science proposals category also compelled me to look more into my topic. Fueled by an egregious underestimation of how much work would be involved, I began the painstaking process of devising and running experiments. Having put in the effort for that, I was averse to letting some of my more interesting findings stay unknown and wrote a much more time-consuming paper documenting my results. I hope anyone reading this finds it useful. The paper (paper.pdf) and the complete data are available on GitHub.

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