Section: New Results

Uniprocessor Mixed-Criticality Real-Time Scheduling

In the context of the FUI CEOS project 8.1.1.1, last two years we transformed the free software program PX4, which performs the autopilot of the CEOS drone, in a graph of hard real-time tasks. This transformation was intended to achieve a schedulability analysis guaranteeing the autopilot is able to perform safety critical missions since its behaviour is deemed to be hard real-time, i.e., all deadlines of all tasks are satisfied. It is worth noting that the autopilot is one of the most important programs of the drone since it maintains its stability not only during hover phases but also during automatic flight missions from one GPS point to another. This transformation resulted in a "real-time autopilot" that we called PX4-RT.

For the first version of PX4-RT we chose, as periods, the periods used in the original version of PX4 which was not hard real-time as we shown last year. Then, since these periods was inherited from an automatic control analysis achieved by initial designers of PX4 in a non hard real-time context, we had to determine the right combination of periods of tasks, allowing on the one hand to correctly control the drone, and on the other hand, using a schedulabilty analysis, to satify all the deadlines. In order to achieve this goal, we used a hardware in the loop simulation (HitL) which simulates only the sensors and the actuators, whereas the PX4-RT program runs on the Pixhawk board based on an ARM Cortex-M4 uniprocessor. Eventually, we determined some period combinations that fit our needs, other combinations did not allow the drone to follow correctly the given mission or resulted in a crash. Moreover, we verified that all the right combinations led to a schedulable set of tasks, meaning that corresponding versions of PX4-RT were hard real-time. Finally, we used with success the best combination of periods to run PX4-RT on the real drone of CEOS during a simple flight. Of course, we plan to achieve numerous realistic flights planned in the three industrial use cases of the CEOS project.

In addition to this study intended to determine the right combination of periods, we addressed two other issues. In the first one we tried to decrease the worst case execution times (WCET) of tasks in order to increase the schedulability ratio. Such decrease allows to add on the same processor new tasks presently executed on other processors, e.g., mission planning, fault tolerance, etc. Since we found out that the Kalman filter had the largest measured execution time of all the tasks, we studied the Kalman filter algorithm implemented in PX4 to decrease its WCET. We suppressed the two states of the Kalman Filter corresponding to the wind speed estimation since our drone do not have a sensor measuring this speed. Then, we suppressed the three states of the Kalman filter corresponding to the accelerometer bias whose standard deviation was close to zero. Each of these modifications brought an improvement of 15 percent in term of largest measured execution time without decreasing the performances of the drone. In the second issue we started a theoretical study about relations between the stability of a set of automatic control laws and the schedulability of the corresponding set of real-time tasks. In the literature some results exist about one control law corresponding to one real-time task. To the best of our knowledge there is no result for a set of control laws that exchange data.

Finally, we deeply studied NuttX the real-time operating system used presently to support PX4 and PX4-RT autopilot programs. Indeed, we plan to modify the scheduler of this operating system in order to manage real-time tasks more safely. In order to do that we will draw inspiration from the technique proposed in our time triggered offline scheduler that accounts for the preemption and scheduler cost [14].