russtedrake PRO
Roboticist at MIT and TRI
(should we use analytical gradients?)
Russ Tedrake
Slides available at https://slides.com/russtedrake/iros-contact
Frictional contact \(\Rightarrow\) (Measure) differential inclusions
Frictional contact \(\Rightarrow\) (Measure) differential inclusions
OpenAI - Learning Dexterity
People like me went through a series of reactions:
A key question for the success of gradient-based optimization
Use initial conditions here as a surrogate for dependence on policy parameters, etc.
For the mathematical model... (ignoring numerical issues)
we do expect \(q(t_f) = F\left(q(t_0)\right)\) to be continuous.
point contact on half-plane
We have "real" discontinuities at the corner cases
Soft/compliant contact can replace discontinuities with stiff approximations
\[ \min_x f(x) \]
For gradient descent, discontinuities / non-smoothness can
J. Burke, F. E. Curtis, A. Lewis, M. Overton, and L. Simoes, Gradient Sampling Methods for Nonsmooth Optimization, 02 2020, pp. 201–225.
But \(\frac{\partial f(x)}{\partial x} = 0\) almost everywhere! So \( \frac{1}{K} \sum_{i=1}^K \frac{\partial f(\mu + w_i)}{\partial \mu} = 0 \not\approx \frac{\partial}{\partial \mu} E_\mu [f(x)] \)
Big question: Why use zero-order (black-box) optimizations instead of first-order (analytical gradients)?
now available on arxiv
Can we reduce sample complexity? (with sampling strategies targeting the non-smoothness of contact?)
The cartoon from walking is not rich enough for manipulation...
My claim: Subtle interactions between the collision and physics engines can cause artificial discontinuities
(sometimes with dramatic results)
Understanding this requires a few steps
Green arrow is the force on the red box due to the overlap with the blue box.
Many heuristics for using multiple points...
major contributions from Damrong Guoy, Sean Curtis, Rick Cory, Alejandro Castro, ...
Red box is rigid, blue box is soft.
Both boxes are soft.
Point contact (discontinuous)
Hydroelastic
(continuous)
vs
Compliant ball vs. compliant box. Rigid ball vs. compliant box Compliant ball vs. rigid box
Hydroelastic is
State-space (for simulation, planning, control) is the original rigid-body state.
Point contact and multi-point contact can produce qualitatively wrong behavior.
Hydroelastic often resolves it.
Manually-curated point contacts
Hydroelastic contact surfaces
Stable and symmetrical hydroelastic forces
Before
Now
Text
Point contact
Hydroelastic contact
the frictionless case
Point contact (no friction)
Hydroelastic
(no friction)
Tobia Marcucci, Jack Umenberger, Pablo Parrilo, Russ Tedrake. Shortest Paths in Graphs of Convex Sets. Available on arxiv.
Previous best formulations | New formulation | |
---|---|---|
Lower Bound (from convex relaxation) |
7% of MICP | 80% of MICP |
http://manipulation.mit.edu
By russtedrake
IROS keynote, 2021