Drake: Add Support for Prescribed Motion Constraints
One way to simulate position-controlled robots is to use constraints that achieve a prescribed motion. Such constraints can also be used for kinematic simulations of vehicles. This issue tracks the implementation of these constraints.
@RussTedrake, can you point us to the appropriate reference materials for this?
This might be relevant: http://dl.acm.org/citation.cfm?id=37428
liangfok
All 7 comments
How could we gain access to that paper?
amcastro-tri
on 23 Jun 2016
We'll need to join ACM. I believe it costs $99/yr for access to their digital library.
liangfok
on 23 Jun 2016
I'm a member and can find that paper if you want it (email me). Prescribed motion is a very simple constraint in internal coordinates since we can just write q(t)=func(t) and differentiate twice (func(t) is some analytically known, twice differentiable, function of time, e.g. sin(t)). As a holonomic constraint this is just g(t,q)=q(t)-func(t) and we enforce g(t)=0. But that is not the best way to do prescribed motion because it unnecessarily turns the ODE into a DAE. Prescribed motion is actually localized inverse dynamics so can be solved without constraints using a mixed forward-inverse recursion. Featherstone calls that "hybrid dynamics" and you can read about it ch 9 of his 2008 book. Abhi Jain calls it "generalized articulated body dynamics"; see ch 16 and algorithm 16.2. Simbody implements prescribed motion that way.
sherm1
on 23 Jun 2016
It sounds like Featherstone's book is perhaps a better reference. _Looking for a copy now..._
liangfok
on 23 Jun 2016
Chapter 7.5.2, page 126 of my older copy. It's on top of my desk for those interested.
amcastro-tri
on 23 Jun 2016
Agreed with @sherm1 and we already have them implemented (eg with the loop constraints).
The reason we might want to use an explicit inverse dynamics call instead of prescribed motion is if we want to worry about torque or speed limits.
RussTedrake
on 23 Jun 2016
Defer until later.
jwnimmer-tri
on 22 Dec 2016
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Most helpful comment
I'm a member and can find that paper if you want it (email me). Prescribed motion is a very simple constraint in internal coordinates since we can just write
q(t)=func(t)and differentiate twice (func(t) is some analytically known, twice differentiable, function of time, e.g. sin(t)). As a holonomic constraint this is justg(t,q)=q(t)-func(t)and we enforceg(t)=0. But that is not the best way to do prescribed motion because it unnecessarily turns the ODE into a DAE. Prescribed motion is actually localized inverse dynamics so can be solved without constraints using a mixed forward-inverse recursion. Featherstone calls that "hybrid dynamics" and you can read about it ch 9 of his 2008 book. Abhi Jain calls it "generalized articulated body dynamics"; see ch 16 and algorithm 16.2. Simbody implements prescribed motion that way.