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1. Learning Reactive and Predictive Differentiable Controllers for Switching Linear Dynamical Models

   Saxena, S.; LaGrassa, A.; Kroemer, O. (April 2021, IEEE International Conference on Robotics and Automation)

   null (Ed.)

   Humans leverage the dynamics of the environment and their own bodies to accomplish challenging tasks such as grasping an object while walking past it or pushing off a wall to turn a corner. Such tasks often involve switching dynamics as the robot makes and breaks contact. Learning these dynamics is a challenging problem and prone to model inaccuracies, especially near contact regions. In this work, we present a framework for learning composite dynamical behaviors from expert demonstrations. We learn a switching linear dynamical model with contacts encoded in switching conditions as a close approximation of our system dynamics. We then use discrete-time LQR as the differentiable policy class for data-efficient learning of control to develop a control strategy that operates over multiple dynamical modes and takes into account discontinuities due to contact. In addition to predicting interactions with the environment, our policy effectively reacts to inaccurate predictions such as unanticipated contacts. Through simulation and real world experiments, we demonstrate generalization of learned behaviors to different scenarios and robustness to model inaccuracies during execution. 

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2. A continuum membrane model can predict curvature sensing by helix insertion

   https://doi.org/10.1039/d1sm01333e  

   Fu, Yiben; Zeno, Wade F.; Stachowiak, Jeanne C.; Johnson, Margaret E. (December 2021, Soft Matter)

   Protein domains, such as ENTH (epsin N-terminal homology) and BAR (bin/amphiphysin/rvs), contain amphipathic helices that drive preferential binding to curved membranes. However, predicting how the physical parameters of these domains control this ‘curvature sensing’ behavior is challenging due to the local membrane deformations generated by the nanoscopic helix on the surface of a large sphere. We here use a deformable continuum model that accounts for the physical properties of the membrane and the helix insertion to predict curvature sensing behavior, with direct validation against multiple experimental datasets. We show that the insertion can be modeled as a local change to the membrane's spontaneous curvature, c ins0, producing excellent agreement with the energetics extracted from experiments on ENTH binding to vesicles and cylinders, and of ArfGAP helices to vesicles. For small vesicles with high curvature, the insertion lowers the membrane energy by relieving strain on a membrane that is far from its preferred curvature of zero. For larger vesicles, however, the insertion has the inverse effect, de-stabilizing the membrane by introducing more strain. We formulate here an empirical expression that accurately captures numerically calculated membrane energies as a function of both basic membrane properties (bending modulus κ and radius R ) as well as stresses applied by the inserted helix ( c ins0 and area A ins ). We therefore predict how these physical parameters will alter the energetics of helix binding to curved vesicles, which is an essential step in understanding their localization dynamics during membrane remodeling processes. 

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3. Dynamic Inference on Graphs using Structured Transition Models

   Saxena, Saumya; Kroemer, Oliver (January 2022, International Conference on Intelligent Robots and Systems (IROS))

   Modelling and learning the dynamics of intricate dynamic interactions prevalent in common tasks such as push- ing a heavy door or picking up an object in one sweeping motion is a challenging problem. One needs to consider both the dynamics of the individual objects and of the interactions among objects. In this work, we present a method that enables efficient learning of the dynamics of interacting systems by simultaneously learning a dynamic graph structure and a stable and locally linear forward dynamic model of the system. The dynamic graph structure encodes evolving contact modes along a trajectory by making probabilistic predictions over the edge activations. Introducing a temporal dependence in the learned graph structure enables incorporating contact measurement updates which allows for more accurate forward predictions. The learned stable and locally linear dynamics enable the use of optimal control algorithms such as iLQR for long-horizon planning and control for complex interactive tasks. Through experiments in simulation and in the real world, we evaluate the performance of our method by using the learned inter- action dynamics for control and demonstrate generalization to more objects and interactions not seen during training. We also introduce a control scheme that takes advantage of contact measurement updates and hence is robust to prediction inaccuracies during execution. 

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4. Lubricated soft normal elastic contact of a sphere: a new numerical method and experiment

   https://doi.org/10.1039/D1SM01654G  

   Liu, Zezhou; Dong, Hao; Jagota, Anand; Hui, Chung-Yuen (February 2022, Soft Matter)

   An important problem in lubrication is the squeezing of a thin liquid film between a rigid sphere and an elastic substrate under normal contact. Numerical solution of this problem typically uses iteration techniques. A difficulty with iteration schemes is that convergence becomes increasingly difficult under increasingly heavy loads. Here we devise a numerical scheme that does not involve iteration. Instead, a linear problem is solved at every time step. The scheme is fully automatic, stable and efficient. We illustrate this technique by solving a relaxation test in which a rigid spherical indenter is brought rapidly into normal contact with a thick elastic substrate lubricated by a liquid film. The sphere is then fixed in position as the pressure relaxes. We also carried out relaxation experiments on a lubricated soft PDMS (polydimethysiloxane) substrate under different conditions. These experiments are in excellent agreement with the numerical solution. 

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5. Microstructure‐based modeling of primary cilia mechanics

   https://doi.org/10.1002/cm.21860  

   Mostafazadeh, Nima; Resnick, Andrew; Young, Y‐N; Peng, Zhangli (April 2024, Cytoskeleton)

   Abstract A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load‐bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure‐based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets and simulating the tip‐anchored optical tweezer experiment on our computational model, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium‐length‐dependent, we found the mechanical properties of the cilium are also highly deformation‐dependent. More important, we found that the cilium membrane near the base is not under pure in‐plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure‐based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging‐informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base. 

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