Robot Control Interface

Hi,

I still not agree with your decision. This is just a bad modelling / understanding what a torque and rotation are !

Rotation are member of the SO space. SO is not R^3 It is a group in linear algebra term using the the composition operator. It means you do not add elements of this group (the mathematical addition of element of SO does not give you an element of SO ) . You can only combine them using composition. Now if you represent the element of SO using unit quaternion, it means that the only valid operation you can do on them is multiplication. Basically quaternions are just a mathematical artefact to help you numerically use element of SO. Here you could use angle axis, Rotation matrices as you wish. I agree quaternion is a valid choice to represent rotation, even if always (and will always be) questionnable. Providing simple interface to go from / to angle axis and matrices is a really wise decision, as you will never make everybody agree that quaternion are the best.

Now lets go again to torque. A torque is an element of R^3. YOu cannot mathematically compose torque. This is a clear non-sense. They lie in the euclidian space R^3. Therefore you cannot multiply them (there is no multiuply operation for a torque. you can use the cross product, but it does not mean anything physically to do the cross product of two torque). Representing them as quaternion and multiply these object, is in fact doing a composition of the two forces. BAsically it does not mean anything at all. because you do not appply torque 1, and apply torque 2 on the result of the application of torque 1. These are jsu additive elements. The only mathematically valid operation you can do on torque, that still give you a torque are multiplication by a scalar and addition with another torque.

Furthermore torque are quite complex object. Indeed in french they are called "couple" like beeing in couple. Why because the only way practical way to produce a pure torque at a given point is to appply a couple of linar counter-acting forces at two different poinst. In the middle of the two application point they will produce a pure couple, with no linear forces. Basically torque does not exist and are just mathematical object that tool to illustrate Archimede's cantilever effect. What I want to illustrate here is that a torque could not be not tied to a linear forces. They are always tied to such force. We always speak of the torque of a given (linear) force. Only in teh special case of a net torque (when the sum of the (linear) forces are zero), this torque will be invariant in space. otherwise we have to use the transport law ( http://en.wikipedia.org/wiki/Torque see net versus torque section). Therefore they does not share the same algebra at all.

I still think using quaternion as opposed to just raw vector for torque is a huge mistake and a misunderstanding of kinematic and dynamic. You should definitively change this. Or at least I will for myself not use RCI anymore if such mistake want to be actively and knowingly kept in the code base.

Alexandre Tuleu wrote:

Hi,

I still not agree with your decision. This is just a bad modelling / understanding what a torque and rotation are !

Rotation are member of the SO (3) space. SO (3) is not R^3 It is a group in linear algebra term using the the composition operator. It means you do not add elements of this group (the mathematical addition of element of SO does not give you an element of SO ) . You can only combine them using composition. Now if you represent the element of SO (3) using unit quaternion, it means that the only valid operation you can do on them is multiplication. Basically quaternions are just a mathematical artefact to help you numerically use element of SO. Here you could use angle axis, Rotation matrices as you wish. I agree quaternion is a valid choice to represent rotation, even if always (and will always be) questionnable. Providing simple interface to go from / to angle axis and matrices is a really wise decision, as you will never make everybody agree that quaternion are the best.

Now lets go again to torque. A torque is an element of R^3. YOu cannot mathematically compose torque. This is a clear non-sense. They lie in the euclidian space R^3. Therefore you cannot multiply them (there is no multiuply operation for a torque. you can use the cross product, but it does not mean anything physically to do the cross product of two torque). Representing them as quaternion and multiply these object, is in fact doing a composition of the two forces. BAsically it does not mean anything at all. because you do not appply torque 1, and apply torque 2 on the result of the application of torque 1. These are jsu additive elements. The only mathematically valid operation you can do on torque, that still give you a torque are multiplication by a scalar and addition with another torque.

Furthermore torque are quite complex object. Indeed in french they are called "couple" like beeing in couple. Why because the only way practical way to produce a pure torque at a given point is to appply a couple of linar counter-acting forces at two different poinst. In the middle of the two application point they will produce a pure couple, with no linear forces. Basically torque does not exist and are just mathematical object that tool to illustrate Archimede's cantilever effect. What I want to illustrate here is that a torque could not be not tied to a linear forces. They are always tied to such force. We always speak of the torque of a given (linear) force. Only in teh special case of a net torque (when the sum of the (linear) forces are zero), this torque will be invariant in space. otherwise we have to use the transport law ( http://en.wikipedia.org/wiki/Torque see net versus torque section). Therefore they does not share the same algebra at all.

I still think using quaternion as opposed to just raw vector for torque is a huge mistake and a misunderstanding of kinematic and dynamic. You should definitively change this. Or at least I will for myself not use RCI anymore if such mistake want to be actively and knowingly kept in the code base.

Sorry I tried to edit my message. PLease read SO - parenthesis- 3 parenthesis instead of SO

Alexandre Tuleu wrote:

Hi,

I still not agree with your decision. This is just a bad modelling / understanding what a torque and rotation are !

Rotation are member of the SO space. SO is not R^3 It is a group in linear algebra term using the the composition operator. It means you do not add elements of this group (the mathematical addition of element of SO does not give you an element of SO ) . You can only combine them using composition. Now if you represent the element of SO using unit quaternion, it means that the only valid operation you can do on them is multiplication. Basically quaternions are just a mathematical artefact to help you numerically use element of SO. Here you could use angle axis, Rotation matrices as you wish. I agree quaternion is a valid choice to represent rotation, even if always (and will always be) questionnable. Providing simple interface to go from / to angle axis and matrices is a really wise decision, as you will never make everybody agree that quaternion are the best.

Now lets go again to torque. A torque is an element of R^3. YOu cannot mathematically compose torque. This is a clear non-sense. They lie in the euclidian space R^3. Therefore you cannot multiply them (there is no multiuply operation for a torque. you can use the cross product, but it does not mean anything physically to do the cross product of two torque). Representing them as quaternion and multiply these object, is in fact doing a composition of the two forces. BAsically it does not mean anything at all. because you do not appply torque 1, and apply torque 2 on the result of the application of torque 1. These are jsu additive elements. The only mathematically valid operation you can do on torque, that still give you a torque are multiplication by a scalar and addition with another torque.

Furthermore torque are quite complex object. Indeed in french they are called "couple" like beeing in couple. Why because the only way practical way to produce a pure torque at a given point is to appply a couple of linar counter-acting forces at two different poinst. In the middle of the two application point they will produce a pure couple, with no linear forces. Basically torque does not exist and are just mathematical object that tool to illustrate Archimede's cantilever effect. What I want to illustrate here is that a torque could not be not tied to a linear forces. They are always tied to such force. We always speak of the torque of a given (linear) force. Only in teh special case of a net torque (when the sum of the (linear) forces are zero), this torque will be invariant in space. otherwise we have to use the transport law ( http://en.wikipedia.org/wiki/Torque see net versus torque section). Therefore they does not share the same algebra at all.

I still think using quaternion as opposed to just raw vector for torque is a huge mistake and a misunderstanding of kinematic and dynamic. You should definitively change this. Or at least I will for myself not use RCI anymore if such mistake want to be actively and knowingly kept in the code base.