*1.2. Reluctance Coil Guns: A Ball Launcher That Can Be Optimized*

Even if reluctance coil guns are a relevant solution for kicking soccer balls efficiently, it is important to note that they are not very efficient in terms of energy conversion. In [11], electrical energy for the coil gun is stored in a capacitor having a capacitance value *C* = 4700 μF under 425 V. Stored electrical energy is equal to:

$$E\_{\mathbb{C}} = \frac{1}{2} C \mathcal{U}\_{\mathbb{C}}^2 = 424 \text{ J}$$

Consequently, the ratio of ball kinetic energy to the input electrical one is only 7%, and the ratio of the overall mechanical transmitted energy (including the kinetic energies of the iron rod, the lever and the ball as explained later) to the input electrical one is 12%. However, the energy necessary for kicking like human soccer players is already stored in the capacitor. This means that if a robot's kick is 10 times less powerful than a human one, it is not an issue related to available energy, but it is a problem of inefficiency of energy transfer in reluctance coil guns.

Optimizing this energy transfer can be done in two main ways without changing the size and the weight of the launcher. The first one is to adjust the initial position of the plunger, and the length of its non-magnetic extension. [12] shows that energy transmission can be increased by 70% using this technique compared to the reference case presented in [11]. This optimization is interesting because nothing is changed on the coil gun structure and size; it is only an optimization of initial conditions and a plunger parameter adjustment.

A second way of improving the energy transfer of a coil gun is to modify its inner structure by splitting the coil and the energy storage capacitor into several ones [7,13], without changing the overall quantity of coil copper and the overall capacitance value. Instead of sending an energy pulse to a single coil, a sequence of smaller energy pulses will be sent to the different coils propagating the magnetic force along the coil as the plunger enters it. The number of coils and the triggering sequence are the parameters to be optimized.

This paper focuses on this second method for optimizing the energy transfer in a reluctance coil gun. It is divided into three sections:

