Related papers: Hybrid dynamical type theories for navigation
In this paper we solve the problem of finding a trajectory that shows that a given hybrid dynamical system with deterministic evolution leaves a given set of states considered to be safe. The algorithm combines local with global search for…
This paper addresses the trajectory planning for multiple autonomous underwater vehicles (AUVs) in strong waves that can disturb the AUVs' trajectory tracking ability and cause obstacle and inter-vehicle collisions. A novel approach based…
Synchronization of actively oscillating organelles such as cilia and flagella facilitates self-propulsion of cells and pumping fluid in low Reynolds number environments. To understand the key mechanism behind synchronization induced by…
This paper considers the integration of gap-based local navigation methods with artificial potential field (APF) methods to derive a local planning module for hierarchical navigation systems that has provable collision-free properties.…
We develop an autonomous navigation algorithm for a robot operating in two-dimensional environments containing obstacles, with arbitrary non-convex shapes, which can be in close proximity with each other, as long as there exists at least…
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
We present a new formulation of non-dissipative relativistic spin hydrodynamics that incorporates spin degrees of freedom into the divergence-type theory framework. Due to the divergence-type structure, it is straightforward to enforce…
Tracked vehicles distribute their weight continuously over a large surface area (the tracks). This distinctive feature makes them the preferred choice for vehicles required to traverse soft and uneven terrain. From a robotics perspective,…
In this paper, we propose a new control design scheme for solving the obstacle avoidance problem for nonlinear driftless control-affine systems. The class of systems under consideration satisfies controllability conditions with iterated Lie…
As it stands, a robust mathematical framework to analyse and study various topics in deep learning is yet to come to the fore. Nonetheless, viewing deep learning as a dynamical system allows the use of established theories to investigate…
This paper addresses the problem of navigation control of a general class of 2nd order uncertain nonlinear multi-agent systems in a bounded workspace, which is a subset of $R^3$ , with static obstacles. In particular, we propose a…
We propose foundations for a synthetic theory of $(\infty,1)$-categories within homotopy type theory. We axiomatize a directed interval type, then define higher simplices from it and use them to probe the internal categorical structures of…
This paper presents a novel control strategy for the coordination of a multi-agent system subject to high-level goals expressed as linear temporal logic formulas. In particular, each agent, which is modeled as a sphere with 2nd order…
Dense, dynamic crowds pose a persistent challenge for autonomous mobile robots. Purely reactive planning methods, such as Model Predictive Path Integral (MPPI) control, often fail to escape local minima in complex scenarios due to their…
We present a type system that combines, in a controlled way, first-order polymorphism with intersectiontypes, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that issound and terminating.…
Contact-rich robot dynamics are hybrid: a single observation can match several latent states and contact regimes (free, impact, stick--slip). A standard amortized filter that places no probability on a feasible contact transition will…
We consider synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems are coupled through the connections of two or more distinct networks (each…
This paper presents a three-dimensional, hydrodynamics-inspired collision avoidance framework for uncrewed aerial vehicle (UAV) formations operating in dynamic environments. When moving obstacles enter a UAV's sensing region, they are…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…