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The deformable and continuum nature of soft robots promises versatility and adaptability. However, control of modular, multi-limbed soft robots for terrestrial locomotion is challenging due to the complex robot structure, actuator mechanics…
Autonomy in robotic surgery is very challenging in unstructured environments, especially when interacting with deformable soft tissues. The main difficulty is to generate model-based control methods that account for deformation dynamics…
This paper presents a method for optimal motion planning of continuum robots by employing Bernstein surfaces to approximate the system's dynamics and impose complex constraints, including collision avoidance. The main contribution is the…
In this paper we describe a methodology for the identification of symmetric quadrature rules inside of quadrilaterals, triangles, tetrahedra, prisms, pyramids, and hexahedra. The methodology is free from manual intervention and is capable…
According to flexure theory of plate, on the premise of plane deformation assumption, an analytic model of U-free bend theory is proposed in this paper, which considered the harden, anisotropy and elastic deformation of material. Then the…
A complex ruled surface admits an iterated blow-up encoded by a parabolic structure with rational weights. Under a condition of parabolic stability, one can construct a Kaehler metric of constant scalar curvature on the blow-up according to…
The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear…
The robotic shape control of deformable linear objects has garnered increasing interest within the robotics community. Despite recent progress, the majority of shape control approaches can be classified into two main groups: open-loop…
With the field of rigid-body robotics having matured in the last fifty years, routing, planning, and manipulation of deformable objects have recently emerged as a more untouched research area in many fields ranging from surgical robotics to…
In this paper we study the dimension of bivariate polynomial splines of mixed smoothness on polygonal meshes. Here, "mixed smoothness" refers to the choice of different orders of smoothness across different edges of the mesh. To study the…
Research on control using models based on machine-learning methods has now shifted to the practical engineering stage. Achieving high performance and theoretically guaranteeing the safety of the system is critical for such applications. In…
The Boundary representation (B-rep) format is the de-facto shape representation in computer-aided design (CAD) to model solid and sheet objects. Recent approaches to generating CAD models have focused on learning sketch-and-extrude modeling…
A method is proposed for constructing a spline curve of the Bezier type, which is continuous along with its first derivative by a piecewise polynomial function. Conditions for its existence and uniqueness are given. The constructed curve…
We study a class of mechanisms known as Kokotsakis polyhedra with a quadrangular base. These are $3\times3$ quadrilateral meshes whose faces are rigid bodies and joined by hinges at the common edges. In contrast to existing work, the…
In this paper we study robust output tracking and disturbance rejection of linear partial differential equation (PDE) models. We focus on demonstrating how the abstract internal model based controller design methods developed for "regular…
In this paper, we investigate rigid-ruling folding motions of crease-rule patterns, that is, conjugacy-preserving isometries of developable semi-discrete conjugate nets. We derive two conditions for the rigid-ruling foldability of pairs of…
Deformable robots are notoriously difficult to model or control due to its high-dimensional configuration spaces. Direct trajectory optimization suffers from the curse-of-dimensionality and incurs a high computational cost, while…
Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline…
Real-time proprioception is a challenging problem for soft robots, which have almost infinite degrees-of-freedom in body deformation. When multiple actuators are used, it becomes more difficult as deformation can also occur on actuators…