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The Schools of Public Engagement ​I okay thank you thank you and this is a work that is mainly developed by Mustafa mamadi a PhD student in my lab he was not able to attend and with my postdoc Davide Bocelli and our friends and collaborator Antonio Frankie from last year s ok so the contribution of this work is here summarized so the idea is to have let me say flying fingers that are attached to quadrotors and they cooperatively go towards an object to realize a flying and that moves an object this this kind of cooperation comes from also from the fact that Antonio is mainly in the quadrotor aerial vehicle control my expertise was mainly on a grasping and deliberation so we found proper competence to develop this kind of research well so what's the context the context is the context of a area of manipulation ok so the area of manipulation are on the left you can see one of the flying helicopter that is a small with a small gripper that takes a small object developed by dollar on the other side here you see a bigger helicopter developed by a group of alero with an arm and a hand because if you want to bring heavy objects heavier objects you have to have a larger vehicles of course you can scale this problem and you can still use smoke quadrotors to to move a larger object by using a team of quadrats the problem of the team of quadrotors here especially in this work by kumar is in this case that they are using the cables the cables have two problems one is that they are flexible so it's difficult to go while flying to grasp at object and the other one is that it's a bilateral constraint so it's not easy to detach at what touch so in some sense requires some maneuver that is not easy to do while while flying so we want to deal with this to program we want to remove the flexible cables and we don't want not to use the bilateral contact constraints so our contact mechanisms is basically one contact point so like while I'm grasping this object with my finger exactly in this way okay so it just is one only lateral contact between the the aerial finger and the object but is in some sense reinforced by the magnet here so the magnet has an adhesive fourths that helps in some sense to have this this contact buys exactly the same equations of friction friction constraints so this is the structure to realize the contact here on one side and the other side you see that we substituted the flexible in with the rigid link okay so this is a design that has been developed during this this work the other thing is that of course it's if everything is rigidly is difficult when I touch a surface so I need to have some degrees of freedom so inspired by the work of Don Judy last year I rose we used a spherical joint this is spherical joint is completely passive so the finger can move freely okay but it is locked during the free motion it becomes free only when it is in contact with the object okay so you will see now a movie when you see the rigid link attached to the quadrotor how it is detached automatically you see here there is a microswitch and these micro switch as soon as I touch the the surface activate a servomotor here on the on the joint that frees the degrees of freedom and then does the spherical joint is free to move okay so this is the idea then the other contribution of this work comes from the literature of grasping and object manipulation so the literature of grasping and optimal pollution is proper for this work because they are I mean in our community we were working a lot we do need lateral constraints you don't need this kind of literature if you have be lateral constraints so if you are attached in some sense of the object may if you can touch and attach you need the knowledge grass pick exactly as we are doing with our manipulating hands okay so we took literature and we okay just briefly when you manipulate an object what you do you basically want to control with your hand or with these flying fingers you're flying and you want to control the motion of the object the trajectory of the object and now you do you do through contact forces so what is your in your hand actually is to control the contact forces between your fingers and the object but unfortunately the contact constraints are constrained so they have to satisfy friction constraints magnetic addition force constraints detachment constraints and another kind of thing so there should be for sure an optimization problem that we have to do to work on okay so a little look at the constraints so the constraints are of course the simplest is on the so you have constraints on the on the ideal vehicle and on the cut on the contact geometry so this is a zoom of the contact here this is the ideal vehicle you can control these forts and you just make the force in the torque on the object here so let's go with the the spherical a spherical joint and sorry that the trust the trust constraints so the transit constraints so you can apply a certain maximum force that depends on the power of your trust okay and also a minimum so it should be greater than a minimum otherwise you you you have a ul problem so the force of the of the aerial vehicle is limited by a minimum and the maximum the other point is that you have a spherical joint limited the spherical joint is a passive joint as some limits so you cannot freely move so your force should say within this cone and this is due to mechanical limited sphere achill join it's like a friction Coney so your force should stay in this friction cone and this is the mathematics that explain this friction sorry this is spherical joint limit cone that comes from the from the mechanical

structure then you have the object fragility the object fragility of course means that if you apply a force here then this force is just missed it onto the object and you don't want to apply too much force otherwise you break the object and on the other side you don't want to detach the object then if there is no magnet this limit is 0 because as soon as the fourth inverted the direction you detach I mean there is no contact anymore this is a little bit more easy because there is a minus km- value that depends on the magnet force okay the magnet had a d adhesive force so this is the friction sorry the cop the contact constraints limit augmented with the with the with magnet then you don't have to break the contents of course because if you have this is just just is not glued of course if you apply a force you can you can detach with the torque okay so this is some constraints on the torques that these forts are applying to this surface and you don't want to detach and these are counterbalancing balanced again by the magnetic magnetic force then you have the friction force that is exactly like the friction cone forts but again is augmented by the addition force so the normal force that is the standard force that you need to evaluate the maximum tangential force that you can apply is augmented by the magnetic bynum magnetic force this tourniquet if k is equal to zero is exactly one finger without any magnets so the mathematics is ready to go for k is equal to 0 to 0 okay and again you can transmit both forces here the contact and also rotational torques so also the rotational courses should torque moment is transmitted contact should not sleep like this way and this is some constraint here okay so we have all these constraints okay and we have to satisfy while we control the object motion all these constraints so go back to the problem of controlling the manipulation of these objects so you want to have a certain a certain controller certain trajectory of the object so you want to move your object I don't know along a circle or some other kind of trajectory and you want to find now the forces that you have to apply with your aerial vehicles that then thrust is to the contact okay so the first equations is very simple it's so you have the dynamics of the object here and B and G the gravity force here this ball G ok so this is just simple dynamics this is interesting this is the grasping force so the F vector are the forces that I applied through the trust's at the aerial vehicle and then they are mapped onto the object and they generate a net force effect on the on the on the object so it basically this is a famous matrix in grasp it's called in fact grass matrix is basically when you apply contact forces at your contact points compute the net effect of these forces onto the object ok so it's basically the control in the center of mass of the of the object ok so you have in this case we have F is a 9 vector because you have three forces in the first ideal vehicle two three four three components of the fourth in the secondary or vehicle and the three components offload in the third aerial vehicle so this is nine then there is a theorem in grasping of course it's not so much difficult that says if you have three not three points that do not belong to two a plane then you can always apply any branch to the object ok so also while you do some grass planning you have to be sure that you have not to be close to the singularity in order to apply any force this is important for unilateral et because if it is be lateral there is no dis constraints ok if it is attached ok then it's easily Nielsen too ok ok then the realities of course this is trajectory control what we have to do is to try to distribute these forts onto the onto the trust of the single motor if we do this with the grasping force distribution the blasting force distribution consists of basically an equality is computed according to the constraints so you want that your 40 sequel to the one that you plan to move the object then you have to satisfy all the constraints that I described it before and then there is an optimization so you want to find another old contact force that satisfy as mod faults in order to have the energy low and also some first orders mooting during the motion if you realize and you saw sorry if you stayed and solve this convex optimization problem you find the solution and you are able to find this force vector here they then they are moved to do the attitude and trust control that is the classical literature in aerial vehicle control we use this reference but basically we just computed the trust given the total force we want to apply we orient basically the play so this is that ok so this is the slave part then go we go to the optic part the optic part I will try to go very quick so the optic part is a so there is a lot of literature also Paolo and Antonia work the encima Christian together with the Christian circus a key and boot off on the haptic coordination and control of team of robots and there is evidence the tactics is very good in control in this kind of a robot this is the optic interface I don't want to go into these details what they want to say just is that the force feedback is done by using an obstacle repulsive force that comes from the literature on the the aerial vehicle plus two components that are viscoelastic forts one is the force that brings the the end point of the omega at the center of the workspace because we are controlling in velocity so a displacement of the optic this display is a velocity ok and then there is also a viscoelastic forts here I'm sorry where is it yes it's here the viscoelastic force here that smooths that get closer to the to the side the trajectory if we are far away from the trajectory tracking let me show a video so it's almost experimental so we have a real robot in my lab running with the rigid this is the rigid link this is the the contact point with the badness this is there is a spherical point you can see we are controlling everything is not ready yet to do the grasping we did the simulation everything has been simulated the quad rotor dynamics the motor data the trust dynamics this is the simulation with the with human in the loop which means that we simulated this contact interaction

and all the dynamics are here simulated it's very very realistic we are really ready to go in the scenario we are tracking the d-pad rotors with the Vikon system and these using the optic interface and moving the object from here to the go you see that the inequality the upper bound and the lower bound or Devine equality constraints are all of them are negative the Equality constraints that means then really applying the force is this and then this is trajectory that is very close to the one that we desire these are the forces and also in terms of optics we have an improvement we tested thanks objects and we saw that without optics the performance so all the subjects have the visual feedback but when you have optics there is a lot of it I mean there is improvement conclusions so we want to go in a real experiments by adding also the passivity layer in the end real experiments then we want to evaluate also other haptic policy and to improve the content mechanism to remove the magnet part and they wish to thank Mustafa who did the most of the job my postdoc Davide and the cooperation with Antonia Frank thank you so in this case since we have freakin trick 3 trika the contact we don't have any limit in terms of geometry but just as constraints like you said but so we have we didn't perceive problem with the with the constraints yet because the friction was I one of the reason of use the plate is that the plate is really high friction and we have the magnet so the constraint is there but we were not able to perceive what you are saying is there to do some analysis to to see what happens if you go if you ever come the constraints and what happens for the apt except the optimization always satisfy the constraints so if you don't have the constraint satisfied you don't get the results in some sense the master feels it yeah exactly and because of the constraints for days for example I expected user fees sanitation yeah Wiley is asking for yes this is true but this is also limit of this is a force device now we are in my lab we have a sigma that has also torques and also the long-term goal is to apply my free and technologists there so you should be able to see what happens in terms of rotation because yeah you had more information on the display on the uptick display you Cayuga Community College.