MEAM Ph.D. Thesis Defense: “Addressing Stiffness-induced Challenges In Modeling and Identification of Rigid Body Systems with Frictional Impact”

Imperfect but useful dynamical models have enabled significant progress in planning and controlling robotic locomotion and manipulation. Traditionally, these models have been physics-based, with accuracy relying upon manual calibration only feasible in laboratory environments. As robotics expands into complex real-world applications, models must instead be automatically fit to limited data. One major challenge is modeling frictional contact, especially during collisions involved in common robotics tasks. Rapid deformation under impact manifests as extreme sensitivity to initial conditions and material properties. Thus, even slight errors in state estimation and system identification can lead to significant prediction errors. Consequently, model inaccuracy or the sim-to-real gap often hinders the development of performant robotics algorithms.

When only a few parameters are unknown, physical models can be optimized using advanced techniques to overcome these challenges. However, even with accurately identified parameters, roboticists must make inaccurate rigid-body approximations to reduce the computational burdens of physical simulation to meet faster-than-real-time requirements. An alternative black-box approach has attempted to address these issues, in which dynamical models are learned from scratch, for instance using deep neural networks (DNN’s). While DNNs in theory can capture any dynamical behavior, they have empirically struggled with the stiff behaviors associated with contact.

The dissertation instead focuses on scaling physical model identification to the high-dimensional setting and quantifying the limited accuracy of low-fidelity physics models. We consider rigid bodies undergoing rigid contact, for which infinite stiffness is represented as constrained optimization inside the dynamics. By careful treatment of these constraints, we demonstrate that infinitely-stiff dynamics can be identified by optimizing a non-stiff objective. In conjunction, we use DNN’s in a white-box setting to model purely physical quantities, specifically reconstructing geometries from scratch. We then consider how the simplified rigid-body view of collisions lacks fidelity to correctly predict the outcomes of nearly-simultaneous collisions—such as heel and toe strikes during a foot step. We develop a theoretical basis to capture partial knowledge of such events as uncertain set-valued outcomes, and again use numerical optimization to compute approximations of such sets.