Algorithms in the age of the quaternion

Pedro Castil­lo, CNRS research-sci­en­tist at UTC’s Heudi­asyc Lab­o­ra­to­ry, is co-leader of the Robot­ic Inter­ac­tion Sys­tems (SyRI) team. Spe­cial­ized in auto­mat­ic con­trol applied to robot­ics, he is also in charge of the unit’s «drones» activities.

Pedro Castil­lo and drones go back a long way, since he start­ed his the­sis at UTC in 2000, focussing on the auto­mat­ic con­trol of drones. In ear­ly 2004, this the­sis won him the nation­al prize for the best the­sis in auto­mat­ic con­trol. In 2005, he joined the CNRS at the Heudi­asyc UTC joint research unit, where he con­tin­ued his research into minia­ture drone con­trol. The ASER team, lat­er renamed SyRI, was one of the first to work on the sub­ject and was one of the first to devel­op an autonomous four rotor drone.

At the time, this research was car­ried out using very con­ven­tion­al meth­ods, based in par­tic­u­lar on one of the New­ton-Euler the­o­ries. Since then, the team has changed its approach to one based on the so-called quaternion.

In con­crete terms? «The quater­nion is a math­e­mat­i­cal approach that can rep­re­sent the rota­tions of a body in three dimen­sions. Applied to UAVs (unmanned aer­i­al vehi­cles), it enables us to devel­op more robust and pow­er­ful algo­rithms to pre­cise­ly con­trol the ori­en­ta­tion and speed of a giv­en UAV or object. It also enables us to design con­trol and pre­dic­tion schemes, par­tic­u­lar­ly in the event of an attack on the drone. In this sit­u­a­tion, we can make it fly at very high speed, decel­er­ate very quick­ly or change its tra­jec­to­ry», explains Pedro Castillo.

Up to now, where­as drones nav­i­gat­ed with incli­na­tions of less than 10°, SyRI’s researchers have suc­ceed­ed, thanks to their new approach, in mak­ing them do pirou­ettes too. It may sound triv­ial, but the poten­tial appli­ca­tions are real. «Imag­ine a mad­man hold­ing a fam­i­ly in a house with a slight­ly open win­dow. The drone can sneak in and give the police the topog­ra­phy of the scene, the loca­tion of the hostages and the intrud­er, etc., with min­i­mal risk of being shot down, since it can accel­er­ate or change tra­jec­to­ry very quick­ly. We’re also work­ing on a drone that can be launched like a boomerang, and which, even though its motors are not switched on, will sta­bi­lize itself in flight autonomous­ly. It will then fol­low the instruc­tions giv­en to it by the oper­a­tor, such as chas­ing a tar­get, tak­ing pho­tos, etc. This will be very use­ful for our work in the field. This will be very use­ful for fire­fight­ers, for exam­ple,» he assures us.

The quater­nion approach has enabled them to extend their research to het­ero­ge­neous coop­er­a­tion, i.e., inter­ac­tion between an aer­i­al vehi­cle and an autonomous ground vehi­cle and to move from work­ing on a sin­gle agent to mul­ti­a­gent UAVs. In oth­er words, sev­er­al drones cooperating.

In the first case, the aim is to ensure that the exchange of infor­ma­tion between the two vehi­cles is as pre­cise as pos­si­ble. «Take a phe­nom­e­non like an earth­quake. The drone can go where the ground vehi­cle can­not, and vice ver­sa. In this sce­nario, co-oper­a­tion between the two and the exchange of pre­cise infor­ma­tion between the two can be vital for sur­vivors,» he says.

In the sec­ond case, their work focuss­es on the drone/an­ti-drone issue, in response to a call for projects from the French Nation­al Research Agency (ANR). The call for projects was prompt­ed by the explo­sion in the num­ber of drones pos­sessed and flown by indi­vid­u­als and the mul­ti­ple over­flights of sen­si­tive areas such as nuclear pow­er plants and air­ports. «The idea is to mobi­lize a fleet of drones to neu­tral­ize the unwant­ed intrud­ers. Even though we didn’t receive ANR fund­ing, we con­tin­ued to work on this prob­lem. Today, we are propos­ing ener­gy-based con­trol approach­es to stu­dents for the pur­pose of track­ing the dynam­ic tar­get encir­cling and neu­tral­iz­ing it. These con­trols turn the intrud­er into an «attrac­tor» for the drones assigned this task, viz., neu­tral­iz­ing it, while avoid­ing the risk of col­li­sion. The lat­ter can adapt both their speed and tra­jec­to­ry to the target’s move­ments», explains Pedro Castillo.

Oth­er drone-relat­ed research projects? «We are also work­ing with Jean-Daniel Cha­zot de Rober­val on acoustic drones. This involves equip­ping drones with acoustic anten­nae to detect a par­tic­u­lar sound and adapt their tra­jec­to­ry to the source of that sound. Take the case of an earth­quake. Peo­ple may still be alive but buried under rub­ble. A drone equipped with a cam­era won’t be of much use, but one with acoustic anten­nae can detect the cries of these peo­ple, enabling res­cuers to get to their pre­cise loca­tions. This could also be use­ful for neu­tral­iz­ing Asian hor­net nests, for exam­ple, which are often nes­tled high up in trees or under roofs, by track­ing a hor­net. A CIFRE the­sis with CETIM is cur­rent­ly under­way on this sub­ject and anoth­er is due to start in the autumn,» he concludes.

MSD

Le magazine

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