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Simple Trajectory Optimization Algorithms #142

@Gregory119

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@Gregory119

I am currently learning about and implementing some trajectory optimization algorithms as part of my capstone project for a master's in robotics at WPI. I am interested in integrating the algorithms I end up implementing into RoboPlan as I progress. I am currently unfamiliar with RoboPlan, but I expect to learn more about it in order to achieve this integration. I'll likely need some guidance on this. However, I can elaborate more on the work I plan on doing outside of RoboPlan as a starting point for further discussion.

The first two algorithms I am currently implementing are trapezoidal and Hermite-Simpson direct collocation in C++. I'll be applying these to some simple motions using the SO101 robot arm in simulation, using Mujoco, and on physical hardware. The general flow will be to generate a trajectory and then sample the state trajectory over time for the position controlled servos to track. The main software dependencies will be ifopt, ipopt, and pinnochio. It looks like pinnochio is already used by RoboPlan, which is helpful. Out of interest I am tracking this work at https://github.com/Gregory119/traj-opt-arm.

I think that once I have these two algorithms producing a trajectory that the arm can follow in simulation with plotted results, then I can share that here and start the integration into RoboPlan. Up until then, it would probably be helpful for me to start getting a bit more familiar with RoboPlan. I'll likely follow any documentation and examples, and then poke around some of the source code. I'm open to any suggestions.

Ideally I'd like to use this initial work as a base for integrating any other algorithms I end up implementing.

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