The use of unmanned aerial vehicles (UAV), so-called drones, has been growingrapidly in the last decade. Today, they are used for, among other things, monitoring missions and inspections of places that are difficult for people to access. Toefficiently and robustly execute these types of missions, a swarm of drones maybe used, i.e., a collection of drones that coordinate together. However, this introduces new requirements on what solutions are used for control and navigation. Two important aspects of autonomous navigation of drone swarms are formationcontrol and collision avoidance. To manage these problems, we propose four different solution algorithms. Two of them use leader-follower control to keep formation, Artificial PotentialField (APF) for path planning and Control Barrier Function (CBF)/ExponentialControl Barrier Function (ECBF) to guarantee that the control signal is safe i.e.the drones keep the desired safety distance. The other two solutions use an optimal control problem formulation of a motion planning problem to either generate open-loop or closed-loop trajectories with a linear quadratic regulator (LQR)controller for trajectory following. The trajectories are optimized in terms of timeand formation keeping. Two different controllers are used in the solutions. Oneof which uses cascade PID control, and the other uses a combination of cascadePID control and LQR control. As a way to test our solutions, a scenario is created that can show the utilityof the presented algorithms. The scenario consists of two drone swarms that willtake on different missions executed in the same environment, where the droneswarms will be on a direct collision course with each other. The implementedsolutions should keep the desired formation while smoothly avoiding collisionsand deadlocks. The tests are conducted on real UAVs, using the open sourceflying development platform Crazyflie 2.1 from Bitcraze AB. The resulting trajectories are evaluated in terms of time, path length, formation error, smoothnessand safety.  The obtained results show that generating trajectories from an optimal control problem is superior compared to using APF+leader-follower+CBF/ECBF. However, one major advantage of the last-mentioned algorithms is that decision making is done at every time step making these solutions more robust to disturbancesand changes in the environment.