Related papers: Two-Impulse Trajectory Design in Two-Body Systems …
We address the challenge of real-time planning of minimum-time trajectories over multiple waypoints, onboard multirotor UAVs. Previous works demonstrated that achieving a truly time-optimal trajectory is computationally too demanding to…
The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due…
By using optimal transport theory, we establish a sharp Alexandroff--Bakelman--Pucci (ABP) type estimate on metric measure spaces with synthetic Riemannian Ricci curvature lower bounds, and prove some geometric and functional inequalities…
In one dimensional transport problems the scattering matrix $S$ is decomposed into a block structure corresponding to reflection and transmission matrices at the two ends. For $S$ a random unitary matrix, the singular value probability…
A computational approach is developed for the design of continuous low thrust transfers in the planar circular restricted three-body problem. The transfer design method of invariant manifolds is extended with the addition of continuous low…
Trajectory optimization is an essential tool for generating efficient, dynamically consistent gaits in legged locomotion. This paper explores the indirect method of trajectory optimization, emphasizing its application in creating optimal…
A novel trajectory design methodology is proposed in the current work to minimize the state uncertainty in the crucial mission of spacecraft rendezvous. The trajectory is shaped under constraints utilizing a multiple-impulse approach. State…
Optimization under the symplecticity constraint is an approach for solving various problems in quantum physics and scientific computing. Building on the results that this optimization problem can be transformed into an unconstrained problem…
It is shown that the free motion of massive particles moving in static spacetimes are given by the geodesics of an energy-dependent Riemannian metric on the spatial sections analogous to Jacobi's metric in classical dynamics. In the…
We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To…
This paper extends the RRT* algorithm, a recently developed but widely-used sampling-based optimal motion planner, in order to effectively handle nonlinear kinodynamic constraints. Nonlinearity in kinodynamic differential constraints often…
A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for…
In this paper, we discuss a mathematical model for inverse freeform design of an optical system with two reflectors in which light transfers from a point source to a point target. In this model, the angular light intensity emitted from the…
Fix two points $x,\bar{x}\in S^2$ and two directions (without orientation) $\eta,\bar\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\gamma]=\int_0^T…
Motion planning for multi-jointed robots is challenging. Due to the inherent complexity of the problem, most existing works decompose motion planning as easier subproblems. However, because of the inconsistent performance metrics, only…
In this paper a direct method based on a transcription by finite elements in time has been used to design optimal interplanetary trajectories, exploiting a combination of gravity assist maneuvers and low-thrust propulsion. A multiphase…
We consider the space of probability measures on a discrete set $X$, endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset $Y \subseteq X$, it is natural to ask whether they can be connected…
This paper introduces a novel methodology that leverages the Hamilton-Jacobi solution to enhance non-linear model predictive control (MPC) in scenarios affected by navigational uncertainty. Using Hamilton-Jacobi-Theoretic approach, a…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…
We propose a fast, simple and robust algorithm for computing shortest paths and distances on Riemannian manifolds learned from data. This amounts to solving a system of ordinary differential equations (ODEs) subject to boundary conditions.…