update docs

docs/functional-areas/sensor-to-control/controllers.md

@@ -6,10 +6,12 @@ page_id: controllers
 
 Once the [state estimator](/docs/functional-areas/sensor-to-control/state_estimators.md) have outputed the current (estimated) situation of the crazyflie in position velocity and attitude, it is time for the controllers to keep it that way or to move the crazyflie into a new position based on a setpoint. This is an important part of the stabilization system in the crazyflie.
 
- * [Overview of Control](#overview-of-control)
- * [Cascaded PID controller](#cascaded-pid-controller)
- * Mellinger Controller (TO DO)
- * INDI Controller (TO DO)
+- [Overview of control](#overview-of-control)
+- [Cascaded PID controller](#cascaded-pid-controller)
+- [Mellinger Controller](#mellinger-controller)
+- [INDI Controller](#indi-controller)
+- [Brescianini Controller](#brescianini-controller)
+- [Lee Controller](#lee-controller)
 
 ## Overview of control
 There are four levels to control in the Crazyflie:
@@ -55,3 +57,51 @@ Check the implementation details in `attitude_pid_controller.c` in `attitudeCont
 The most outer-loop of the cascaded PID controller is the position and velocity controller. It receives position or velocity input from a commander which are handled, since it is possible to set in the variable `setpoint_t` which  stabilization mode to use `stab_mode_t` (either position:  `modeAbs` or `modeVelocity`). These can be found in `stabilizer_types.h`. The control loop runs at 100 Hz.
 
 Check the implementation details in `position_controller_pid.c` in `positionController()` and  `velocityController()`.
+
+## Mellinger Controller
+
+Conceptually the Mellinger controller is similar to the cascaded PID controller, i.e. there is an attitude controller (running at 250 Hz) and a position controller (running at 100 Hz). The main difference to the cascaded PID controller is how errors are defined and how the position error is translated into desired attitude setpoints. Like the cascaded PID, this is a reactive geometric controller that uses the mathematical property of differential flatness. Details are given in the following scientific publication:
+
+```
+Daniel Mellinger, and Vijay Kumar
+Minimum snap trajectory generation and control for quadrotors
+IEEE International Conference on Robotics and Automation (ICRA), 2011
+https://doi.org/10.1109/ICRA.2011.5980409
+```
+
+The implementation follows the paper, also for the names of the variables. The main difference is the addition of I-gains and a D-term for the angular velocity.
+
+## INDI Controller
+
+This control algorithm is the Incremental Nonlinear Dynamic Inversion (INDI) controller. Details are given in the following scientific publication:
+
+```
+Ewoud J. J. Smeur, Qiping Chu, and Guido C. H. E. de Croon
+Adaptive Incremental Nonlinear Dynamic Inversion for Attitude Control of Micro Air Vehicles
+JCGD 2015
+https://doi.org/10.2514/1.G001490
+```
+
+## Brescianini Controller
+
+Details of this controller are in the following scientific publication:
+
+```
+Dario Brescianini, Markus Hehn, and Raffaello D'Andrea
+Nonlinear quadrocopter attitude control
+Technical Report ETHZ, 2013
+https://doi.org/10.3929/ethz-a-009970340
+```
+
+## Lee Controller
+
+Conceptually the Lee controller is similar to the cascaded PID controller, i.e. there is an attitude controller (running at 250 Hz) and a position controller (running at 100 Hz). The main difference to the cascaded PID controller is how errors are defined and how the position error is translated into desired attitude setpoints. Like the cascaded PID, this is a reactive geometric controller that uses the mathematical property of differential flatness. Compared to the Mellinger controller, a different angular velocity error and higher-order terms in the attitude controller are used. Details including a stability proof are given in the following scientific publication:
+
+```
+Taeyoung Lee, Melvin Leok, and N. Harris McClamroch
+Geometric Tracking Control of a Quadrotor UAV on SE(3)
+CDC 2010
+https://doi.org/10.1109/CDC.2010.5717652
+```
+
+The implementation follows the paper, also for the names of the variables. The main difference is the addition of I-gains, which are not needed for the theoretical proof, but helpful on the practical system.