Detect higher-order rigidity #35

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opened 2025-01-25 20:38:17 +00:00 by Vectornaut · 0 comments

Vectornaut commented

2025-01-25 20:38:17 +00:00

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The tangent space of the solution variety parameterizes the assembly's first-order degrees of freedom. In other words, it describes the first-order motions that preserve the constraints to first order. That means we can give feedback when a manipulation fails to move the assembly because the assembly is rigid against that motion to first order. This is discussed in #31.

An assembly might look flexible along a certain direction to first order, but actually be rigid along that direction when you examine the constraints at higher order. In other words, not every first-order motion that preserves the constraints to first order extends to a continuous motion that preserves the constraints. It might be useful to detect higher-order rigidity so that we can give feedback in more situations where a manipulation fails to move the assembly.

As of #29, the engine approximates the tangent space of the solution variety. The approximate tangent space usually matches the actual tangent space, and it should tend to contain the actual tangent space when it doesn't match. The tangent space of the solution variety parameterizes the assembly's first-order degrees of freedom. In other words, it describes the first-order motions that preserve the constraints to first order. That means we can give feedback when a manipulation fails to move the assembly because the assembly is rigid against that motion to first order. This is discussed in #31. An assembly might look flexible along a certain direction to first order, but actually be rigid along that direction when you examine the constraints at higher order. In other words, not every first-order motion that preserves the constraints to first order extends to a continuous motion that preserves the constraints. It might be useful to detect higher-order rigidity so that we can give feedback in more situations where a manipulation fails to move the assembly.