Related papers: Approximating Continuous Motions of Geometric Cons…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…
We present a new method for motion planning for control systems. The method aims to provide a natural computational framework in which a broad class of motion planning problems can be cast; including problems with holonomic and…
Geometric computing with chain complexes allows for the computation of the whole chain of linear spaces and (co)boundary operators generated by a space decomposition into a cell complex. The space decomposition is stored and handled with…
We propose a general framework for geometric approximation of circular arcs by parametric polynomial curves. The approach is based on constrained uniform approximation of an error function by scalar polynomials. The system of nonlinear…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
In this paper, we propose a framework for designing sliding mode controllers for a class of mechanical systems with symmetry, both unconstrained and constrained, that evolve on principal fiber bundles. Control laws are developed based on…
Motion planning in high-dimensional space is a challenging task. In order to perform dexterous manipulation in an unstructured environment, a robot with many degrees of freedom is usually necessary, which also complicates its motion…
We propose a novel method for motion planning and illustrate its implementation on several canonical examples. The core novel idea underlying the method is to define a metric for which a path of minimal length is an admissible path, that is…
This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a…
Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians. We discuss the phenomena of oscillations and overlapping which occur for certain choices…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
Inertia-dominated mechanical systems can achieve net displacement by 1) periodically changing their shape (known as kinematic gait) and 2) adjusting their inertia distribution to utilize the existing nonzero net momentum (known as momentum…
An underactuated nonholonomic Dubins-vehicle-like robot with a lower-limited turning radius travels with a constant speed in a plane, which hosts unknown complex objects. The robot has to approach and then circumnavigate all objects, with…
Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to compute numerically by homotopy continuation methods. A…
Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few…
The generation of energy-efficient and dynamic-aware robot motions that satisfy constraints such as joint limits, self-collisions, and collisions with the environment remains a challenge. In this context, Riemannian geometry offers…
We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained…