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Can you set up the problem so that the quantities you care about (e.g. power) are more explicitly represented? Reasoning physically, where could the power go? Accelerating masses, including rotation Pushing against gravity, electromagnetics, other potentials Stretching springs and whatever Dissipation through friction You say "optimize power ...

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First, you need to get rid of the damping matrix C as it transforms kinetic energy into heat. Second, you should make the mass matrix as small as possible. (lightweight construction). After that you can think about the best way to distribute the mass that you cant get rid off by taking the desired movements into account.

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The code is computing the gradient of the cost, which is jerk squared, not the gradient of the jerk. The comment there is misleading! As written, it seems the code is implementing the chain rule of $$c = j^\top j$$ $$\frac{\partial c}{\partial q} = 2j\frac{\partial j}{\partial q}$$ $2j$ is set to temp_j and you can see how the partial of jerk w.r.t q is ...

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The word is exactly as it sounds. It is a submap of a larger map. Essentially a large map is broken up into smaller submaps in order to improve the computational complexity. In the reference you give the map is the accumulated pointcloud. This giant pointcloud is then broken up into smaller pointclouds(the submaps*). These submaps are then used to ...

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Try looking to Linear Integer Programming LIP where you are doing optimization by maximizing task allocation or Utility function at the same time minimizing distance and energy constraints. You will have to formulate the set of equations and use available LIP solvers.

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From the Appendix section of the ORB SLAM paper: ... In pose optimization, or motion-only BA, (see section V) all points are fixed and only the camera pose is optimized. So yes, they are the same, I assume it's only the context that makes the use of one term preferable over the other.

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I think there is information missing to analyze the problem. If that's an rpm-torque graph the fast answer is to search the largest combination of torque*rpm... And for the reduction ratio, 1:1 is the most efficient if you don't have any constraints 😅. But optimal will always depend on the application. And if you want motor efficiency you need to look at ...

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See https://www.cis.upenn.edu/~cjtaylor/PUBLICATIONS/pdfs/TaylorTR94b.pdf. You can absolutely use "flat" Euclidean space based optimizers while also optimizing on the manifold, but I agree the default scipy solvers don't give you an easy way to do that. Perhaps you can use pymanopt? See https://www.pymanopt.org/. Although I wouldn't be scared of ...

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This seems like a mTSP (multi traveling salesman problem). Summary: The Multiple Traveling Salesman Problem (mTSP) is a generalization of the Traveling Salesman Problem (TSP) in which more than one salesman is allowed. Given a set of cities, one depot where m salesmen are located, and a cost metric, the objective of the mTSP is to determine a tour for ...

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First thing to do is pick your World frame. This is your main frame where the 3D coordinates of your points and poses of your cameras will be. Typically the origin of this world frame is the pose of your first camera. You then triangulate every point with all of the cameras that see it. A rough guess can be computed with an algorithm like DLT, and then ...

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