Related papers: Lie Group Formulation and Sensitivity Analysis for…
Soft robots achieve functionality through tight coupling among geometry, material composition, and actuation. As a result, effective design optimization requires these three aspects to be considered jointly rather than in isolation. This…
Model-based control usually relies on an accurate model, which is often obtained from CAD and actuator models. The more accurate the model the better the control performance. However, in bipedal robots that demonstrate high agility actions,…
The loop variable approach is a proposal for a gauge invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space-time gauge invariance…
Tensorial curvature measures are tensor-valued generalizations of the curvature measures of convex bodies. We prove a complete set of kinematic formulae for such tensorial curvature measures on convex bodies and for their (nonsmooth)…
We develop the theory of left-invariant generalized pseudo-Riemannian metrics on Lie groups. Such a metric accompanied by a choice of left-invariant divergence operator gives rise to a Ricci curvature tensor and we study the corresponding…
Tendon-driven continuum robots offer intrinsically safe and contact-rich interactions owing to their kinematic redundancy and structural compliance. However, their perception often depends on external sensors, which increase hardware…
Mechanical control systems such as aerial, marine, space, and terrestrial robots often naturally admit a state-space that has the structure of a Lie group. The kinetic energy of such systems is commonly invariant to the induced action by…
Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data,…
An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out…
The robotic manipulation of deformable linear objects has shown great potential in a wide range of real-world applications. However, it presents many challenges due to the objects' complex nonlinearity and high-dimensional configuration. In…
We generalize classical kinematic formulas for convex bodies in a real vector space $V$ to the setting of non-compact Lie groups admitting a Cartan decomposition. Specifically, let $G$ be a closed linear group with Cartan decomposition $G…
This paper introduces a learning-based modeling framework for a magnetically steerable soft suction device designed for endoscopic endonasal brain tumor resection. The device is miniaturized (4 mm outer diameter, 2 mm inner diameter, 40 mm…
We construct an explicit renormalization group (RG) transformation for Levin and Wen's string-net models on a hexagonal lattice. The transformation leaves invariant the ground-state "fixed-point" wave function of the string-net condensed…
This paper proposes a model-based approach to control the shape of a tensegrity system by driving its node position locations. The nonlinear dynamics of the tensegrity system is used to regulate position, velocity, and acceleration to the…
Reductive Lie Groups, such as the orthogonal groups, the Lorentz group, or the unitary groups, play essential roles across scientific fields as diverse as high energy physics, quantum mechanics, quantum chromodynamics, molecular dynamics,…
Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been…
In this paper, we propose a novel variable-length estimation approach for shape sensing of extensible soft robots utilizing fiber Bragg gratings (FBGs). Shape reconstruction from FBG sensors has been increasingly developed for soft robots,…
Obtaining dynamic models of continuum soft robots is central to the analysis and control of soft robots, and researchers have devoted much attention to the challenge of proposing both data-driven and first-principle solutions. Both avenues…
We present a parallel robot mechanism and the constitutive laws that govern the deformation of its constituent soft actuators. Our ultimate goal is the real-time motion-correction of a patient's head deviation from a target pose where the…
We view disentanglement learning as discovering an underlying structure that equivariantly reflects the factorized variations shown in data. Traditionally, such a structure is fixed to be a vector space with data variations represented by…