Related papers: Designing robust trajectories by lobe dynamics in …
We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then…
This study proposes a new automated strategy for designing and optimizing three-dimensional interplanetary low-thrust (LT) trajectories. The method formulates the design as a hybrid optimal control problem and solves it using a two-step…
We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinc, homoclinic and chaotic…
Driving a quantum system periodically in time can profoundly alter its long-time dynamics and trigger topological order. Such schemes are particularly promising for generating non-trivial energy bands and gauge structures in quantum-matter…
Predictive Feedback Control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive Feedback Control is severely limited because asymptotic convergence speed decreases with…
We present a technique to control chaos in Hamiltonian systems which are close to integrable. By adding a small and simple control term to the perturbation, the system becomes more regular than the original one. We apply this technique to a…
To improve safety and energy efficiency, autonomous vehicles are expected to drive smoothly in most situations, while maintaining their velocity below a predetermined speed limit. However, some scenarios such as low road adherence or…
The deployment of robotic systems in real world environments requires the ability to quickly produce paths through cluttered, non-convex spaces. These planned trajectories must be both kinematically feasible (i.e., collision free) and…
Chaotic dynamics are ubiquitous in nature and useful in engineering, but their geometric design can be challenging. Here, we propose a method using reservoir computing to generate chaos with a desired shape by providing a periodic orbit as…
We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy.…
Performing trajectory design for humanoid robots with high degrees of freedom is computationally challenging. The trajectory design process also often involves carefully selecting various hyperparameters and requires a good initial guess…
As low-thrust space missions increase in prevalence, it is becoming increasingly important to design robust trajectories against unforeseen thruster outages or missed thrust events. Accounting for such events is particularly important in…
Deployment of robotic systems in the real world requires a certain level of robustness in order to deal with uncertainty factors, such as mismatches in the dynamics model, noise in sensor readings, and communication delays. Some approaches…
Safe UAV navigation is challenging due to the complex environment structures, dynamic obstacles, and uncertainties from measurement noises and unpredictable moving obstacle behaviors. Although plenty of recent works achieve safe navigation…
Robotic systems, particularly in demanding environments like narrow corridors or disaster zones, often grapple with imperfect state estimation. Addressing this challenge requires a trajectory plan that not only navigates these restrictive…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
Efficient performance of a number of engineering systems is achieved through different modes of operation - yielding systems described as "hybrid", containing both real-valued and discrete decision variables. Prominent examples of such…
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201…
Chaotic itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors. Several studies have revealed that chaotic…
This paper proposes a systematic method for generating practical and robust low-thrust spacecraft trajectories. One contribution is to consider the change in mass of the spacecraft at two levels: a) the propulsive acceleration and b) the…