The force is equal to minus gradient of the potential, therefore, minus gradient of the potential is equal to the acceleration.
Keywords: mobile robot, path planning, artificial potential fields method
No, it can’t. How to numerically integrate the equations of motion is well-known and doesn’t rely on decomposing the forces into ``attractive" and ``repulsive". The total potential energy only matters.
Stam Nicolis Thank you for your answer.
In the literature, several researchers have used the gradient descent method.
Stam Nicolis My objective is to apply the potential field method to determine the trajectory of a mobile robot, avoiding obstacles and reaching a target.
If you want to determine the trajectory, you solve Newton's equations; the gradient descent method doesn't have anything to do with this, however.
The gradient descent method-as the name indicates-is a method that finds the local minimum of the potential, by solving
dx/dt = -grad V(x)
These aren't Newton's equations, that read
dx/dt = v
mdv/dt = -grad V(x)
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