Related papers: An Eikonal Approach for Globally Optimal Free Flig…
Due to their energy-efficient flight characteristics, fixed-wing type UAVs are useful robotic tools for long-range and duration flight applications in large-scale environments. However, flying fixed-wing UAV in confined environments, such…
We present a fast convolution-based technique for computing an approximate, signed Euclidean distance function $S$ on a set of 2D and 3D grid locations. Instead of solving the non-linear, static Hamilton-Jacobi equation ($\|\nabla S\|=1$),…
This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport…
In many mobile robotics scenarios, such as drone racing, the goal is to generate a trajectory that passes through multiple waypoints in minimal time. This problem is referred to as time-optimal planning. State-of-the-art approaches either…
We present an analytical solution for the projectile coplanar motion under constant drag parametrised by the velocity angle. We found the locus formed by the apices of the projectile trajectories. The range and time of flight are obtained…
This paper propose a new frame work for finding global minima which we call optimization by cut. In each iteration, it takes some samples from the feasible region and evaluates the objective function at these points. Based on the…
The time dependent Eikonal equation is a Hamilton-Jacobi equation with Hamiltonian $H(P)=|P|$, which is not strictly convex nor smooth. The regularizing effect of Hamiltonian for the Eikonal equation is much weaker than that of strictly…
Wide parameter space searches for long lived continuous gravitational wave signals are computationally limited. It is therefore critically important that available computational resources are used rationally. In this paper we consider…
We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique…
In this paper, we present a novel approach to efficiently generate collision-free optimal trajectories for multiple non-holonomic mobile robots in obstacle-rich environments. Our approach first employs a graph-based multi-agent path planner…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
In this paper we consider an optimal control problem in large time horizon and solve it numerically. More precisely, we are interested in an aerial vehicle guidance problem: launched from a ground platform, the vehicle aims at reaching a…
Space missions that use low-thrust propulsion technology are becoming increasingly popular since they utilize propellant more efficiently and thus reduce mission costs. However, optimizing continuous-thrust trajectories is complex,…
In this work, we solve a discrete optimal transport problem in a nonuniform environment. To solve the optimal transport problem, we build the cost matrix and then use classical solvers for discrete optimal transport. The challenge is to…
We consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A new formulation…
Ground robots navigating in complex, dynamic environments must compute collision-free trajectories to avoid obstacles safely and efficiently. Nonconvex optimization is a popular method to compute a trajectory in real-time. However, these…
We present a data-driven optimization framework that aims to address online adaptation of the flight path shape for an airborne wind energy system (AWE) that follows a repetitive path to generate power. Specifically, Bayesian optimization,…
This paper examines the question of finding feasible points to discrete-time optimal control problems. The optimization problem of finding a feasible trajectory is transcribed to an unconstrained optimal control problem. An efficient…
In this paper, we present a motion planning strategy for UAVs that generates a time-optimal trajectory to survey a given target area. There are several situations where completing an aerial survey is time sensitive, such as gaining…
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…