Gabriel Dimonde

I’m Gabriel Dimonde, a mechanical engineer and PhD student researching a higher-order extension of Gauss’s Principle of Least Constraint.

Most physical systems are described by second-order ODEs, so Gauss’s Principle of Least Constraint handles them cleanly. I’m generalizing it for systems whose dynamics are expressed linearly in their higher-order derivative coordinates: systems that include coupling between the orders of their coordinates. A quadrotor exhibits exactly that: angular acceleration in roll and pitch is coupled to positional jerk in its translation. This principle accounts for that coupling without linearization. In addition, we are allowing constraints that, when differentiated to match the order of the dynamics, don’t have to be linearly consistent. When they aren’t, the designer gets to choose the norm that best fits the problem at hand.

That robustness matters because I’m aiming to use it as a “plug-in” for state-space trajectory optimization. A trajectory through state-space is a tight orbit through state-space, so the constraints themselves can be planned through time as surfaces or points in state-space that yield stable transitional orbits, which transition all the way to a specified terminal orbit, in the spirit of a Model Predictive Control trajectory. Doing this expands applicability to systems that are underactuated, or that may become underactuated through damage. The exact extent of underactuation allowed is to be discovered!

I’m drawn to industries where engineering moves the needle: agricultural automation, energy conversion, space exploration, and environmental conservation. After all this experience, i.e., when I’m old and start making mistakes again, I want to teach. I want to be the kind of old dude who inspires his students to work with a higher capacity to care.

Outside of engineering: powerlifting, learning about myself, and spending time with family.