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Optimizing over trajectories -> calculus of variations?


What are some of these algorithms that can help determine a realistic method of movement? I feel like while this may be something necessary to help pipeline the coding process, I'm not sure how exactly we determine whether a way of moving is realistic or not.


I thought inverse kinematics predetermines the position of the in between joints?


Are there particular methods of representing the problem which allows us to find a better motion (like what we did for Euler angles vs exponential matrices for rotations)?