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You do not neceserily create an explicit C-Space representation which you sample. You have to choose, if you want to create your path in axis space or operational space (Cartesian space). This is a design choice and has some influence on the final shape of the trajectory. I am going to assume, that you plan in operational space (Cartesian-like). You sample ...


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The role of the gradient here is to get vector information from the potential functions and not just a value. You are right in assuming, that you work separately on the X and Y axes, in the sense that the equations are vector and not scalar equations. The potential function is a differentiable scalar function. Adding the gradient to the scalar function will ...


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