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A new approach is presented for the problem of optimal impulsive rendezvous of a spacecraft in an inertial frame near a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a…
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic…
We consider the problem of finding minimum-link rectilinear paths in rectilinear polygonal domains in the plane. A path or a polygon is rectilinear if all its edges are axis-parallel. Given a set $\mathcal{P}$ of $h$ pairwise-disjoint…
Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising…
Time-optimal trajectories drive quadrotors to their dynamic limits, but computing such trajectories involves solving non-convex problems via iterative nonlinear optimization, making them prohibitively costly for real-time applications. In…
Motion planning for urban environments with numerous moving agents can be viewed as a combinatorial problem. With passing an obstacle before, after, right or left, there are multiple options an autonomous vehicle could choose to execute.…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…
Widespread development of driverless vehicles has led to the formation of autonomous racing, where technological development is accelerated by the high speeds and competitive environment of motorsport. A particular challenge for an…
In this paper, we propose a trajectory optimization for computing smooth collision free trajectories for nonholonomic curvature bounded vehicles among static and dynamic obstacles. One of the key novelties of our formulation is a hierarchal…
The paper addresses the problem of computing maximal expected time to termination of probabilistic timed automata (PTA) models, under the condition that the system will, eventually, terminate. This problem can exhibit high computational…
Consider a general path planning problem of a robot on a graph with edge costs, and where each node has a Boolean value of success or failure (with respect to some task) with a given probability. The objective is to plan a path for the…
We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a…
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…
Many path-finding algorithms on graphs such as A* are sped up by using a heuristic function that gives lower bounds on the cost to reach the goal. Aiming to apply similar techniques to speed up sampling-based motion-planning algorithms, we…
This paper studies bandit convex optimization in non-stationary environments with two-point feedback, using dynamic regret as the performance measure. We propose an algorithm based on bandit mirror descent that extends naturally to…
Computing shortest paths is one of the most researched topics in algorithm engineering. Currently available algorithms compute shortest paths in mere fractions of a second on continental sized road networks. In the presence of…
Trajectory planning for autonomous cars can be addressed by primitive-based methods, which encode nonlinear dynamical system behavior into automata. In this paper, we focus on optimal trajectory planning. Since, typically, multiple criteria…
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 centralized algorithmic framework for solving multi-robot path planning problems in general, two-dimensional, continuous environments while minimizing globally the task completion time. The framework obtains high levels of…
Many real-world problems require to optimise trajectories under constraints. Classical approaches are based on optimal control methods but require an exact knowledge of the underlying dynamics, which could be challenging or even out of…