I previously asked about modeling a 2-finger gripper as a 1-DOF system in Drake:
How to make a gripper with two fingers (2DOF) have 1 DOF making one finger symmetric to the other.
My gripper had two fingers (each with a prismatic joint) and I wanted to represent it as a 1-DOF system in Drake. The answer provided indicated to use the <mimic> tag in an SDF file to achieve this. However, this approach does not reduce the num_positions() in the plant, meaning both finger joints are still considered in the configuration space.
Now, I am working with C-IRIS to generate convex polytopes and need to ensure that the gripper fingers are treated as having only 1 DOF in configuration space while still considering collisions correctly.
The right finger is not an independent variable and should move symmetrically to the left finger. C-IRIS should account for collisions involving the right finger, even though it is not explicitly controlled.
How can I make C-IRIS ignore the redundant DOF when computing convex polytopes?
At the same time:
How can I ensure that collisions involving the right finger are still considered, even though it follows the left finger's motion?
Any guidance on handling this in Drake would be greatly appreciated!
I am using the python bindings with Pydrake version 1.35.0
It is doable inside C-IRIS (well, not out-of-the-box).
What C-IRIS does is that it certifies the following problem
∀s ∈ {s | C*s <= d}, ∃ a(s), b(s), such that the separating plane a(s) * x + b(s) = 0 separates the geometries A and B in the Cartesian space.
Normally we search for the parameter C and d in the polytope {s | C*s <= d}. In your case, you want to say that your s variable also live in a subspace (specifically, to enforce symmetry of the joints, you probably want s_left + s_right = 0, which are two additional rows in the constraint C * s <= d). And then you can ask whether this polytope {s | C*s <= d} (which includes the constraint s_left + s_right = 0 ) is collision free (for example, using FindSeparationCertificateGivenPolytope ). So given a polytope C * s <= d (which lives in the subspace s_left+s_right=0 ), you can query the no-collision certificate.
Searching for C and d is harder, as now you need to impose the additional constraint on C and d, such that it includes s_left + s_right <= 0 and -s_left - s_right <= 0. You could call InitializePolytopeSearchProgram and then impose additional constraints on C and d (for example, some entries in C needs to be 1 or -1, some corresponding entries in d need to be 0). And then solve the returned optimization problem with the right objective function. You can refer to FindPolytopeGivenLagrangian function in cspace_free_polytope.cc for an implementation.