When objects collide, small changes in initial conditions can lead to dramatically different outcomes (imagine a pool break). Rigid models capture this via non-uniqueness. Typically, model-based controllers optimistically ignore these possibilities, sometimes leading to poor behavior around impact events. Using differential inclusions and complementarity problems, we describe and compute the set of possible outcomes for multiple, frictional impacts and provide guarantees of existence and completeness.
Differentiable physics models enable learning contact dynamics for robotic systems, but at what cost? The underlying stiffness of contact poses a fundamental challenge to deep learning methods. Via numerical experiments learning ODEs for contact dynamics, we find that stiffness severely impacts (1) training error, (2) generalization error, and (3) data efficiency.
The theoretical underpinnings of these results are perhaps well known, arising from the high Lipschitz constants due to contact stiffness. However, given the rise of deep learning applied to differentiable physics models of contact, it’s important to keep in mind the limitations of these approximations. There’s a resulting fundamental trade-off between physical accuracy (for stiff robotic contact) and amenability to learning methods.
Learning on artificially soft contact models may not transfer to stiffer, real systems!
When a robot impacts its environment, it undergoes a large and rapid (though not quite instantaneous) change in velocity. Mode detection and state estimation in these brief periods are incredibly difficult, so it makes very little sense to apply feedback on these varying and imprecise velocity estimates. However, this uncertainty only applies to a subspace of velocities. In a new preprint, Impact Invariant Control with Applications to Bipedal Locomotion, we project velocities onto an impact invariant subspace, preserving control authority in this subspace without spuriously reacting to impact-driven uncertainty.
ReLU activated neural networks have a lot in common with non-smooth dynamical systems! Building off our prior work on frictional robotic systems, we analyze the stability of learned neural network control policies using convex optimization, specifically Linear Matrix Inequalities (LMIs). This efficient approach is made possible by drawing a clear connection between these neural networks and Linear Complementarity Systems. Feedback is welcome! The paper is below, with code to come shortly.
We’re excited to share a new preprint where we learn the dynamics of multi-contact interaction. Contact dynamics are notoriously difficult to model and identify, owing largely to the discontinuous nature of impacts and friction.
Common methods for learning implicitly assume motion is continuous, causing unrealistic predictions (e.g. penetration or floating). We resolve this conflict by learning a smooth, implicit encoding of contact-induced discontinuities, leading to data-efficient identification. Our method can predict realistic impact, non-penetration, and stiction when trained on 60 seconds of real-world data
How should force (tactile) sensors be used within reactive feedback loops? We have a new preprint available (an extended version of a 2020 ICRA publication), where we use bilinear matrix inequalities to synthesize provably stabilizing controllers for multi-contact systems, without combinatorial mode enumeration.
Next week, it’s #icra2020! In “Optimal Reduced-order Modeling of Bipedal Locomotion” by Yu-Ming Chen and Michael Posa, we try to find the best low-dimensional model that captures high-performance walking. The solution combines trajectory optimization and stochastic gradient descient, as a bilevel optimization directly over potential models. Check out the paper or virtual talk.
We’re excited to present our work at #icra2020! In “Contact-Aware Controller Design for Complementarity Systems” by Alp Aydinoglu, Victor Preciado, and Michael Posa, we use bilinear matrix inequalities to synthesize controllers that use tactile feedback to stabilize systems through nearby contact events. Check out the paper or the virtual talk.