Related papers: Computing Minimum Time Paths With Bounded Accelera…
We consider trajectory optimal control problems in which parameter uncertainty limits the applicability of control trajectories computed prior to travel. Hence, efficient trajectory adjustment is needed to ensure successful travel. However,…
In this paper, we present an optimization based method for path planning of a mobile robot subject to time bounded temporal constraints, in a dynamic environment. Temporal logic (TL) can address very complex task specification such as…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to…
We consider the problem of generating a time-optimal quadrotor trajectory that attains a set of prescribed waypoints. This problem is challenging since the optimal trajectory is located on the boundary of the set of dynamically feasible…
We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some…
We consider how to use the Bellman residual of the dynamic programming operator to compute suboptimality bounds for solutions to stochastic shortest path problems. Such bounds have been previously established only in the special case that…
We revisit the linear search problem where a robot, initially placed at the origin on an infinite line, tries to locate a stationary target placed at an unknown position on the line. Unlike previous studies, in which the robot travels along…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a…
This paper considers the problem of computing an optimal trajectory for an autonomous system that is subject to a set of potentially conflicting rules. First, we introduce the concept of prioritized safety specifications, where each rule is…
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…
Agile quadrotor flight relies on rapidly planning and accurately tracking time-optimal trajectories, a technology critical to their application in the wild. However, the computational burden of computing time-optimal trajectories based on…
An effective method for optimizing path planning for a specific model of a 6-degree-of-freedom (6-DOF) robot manipulator is presented as part of the motion planning of the manipulator using computer algebra. We assume that we are given a…
This paper proposes a two-stage approach to formulate the time-optimal point-to-point motion planning problem, involving a first stage with a fixed time grid and a second stage with a variable time grid. The proposed approach brings…
We tackle the problem of planning a minimum-time trajectory for a quadrotor over a sequence of specified waypoints in the presence of obstacles while exploiting the full quadrotor dynamics. This problem is crucial for autonomous search and…
In this paper we present a method for automatically planning robust optimal paths for a group of robots that satisfy a common high level mission specification. Each robot's motion in the environment is modeled as a weighted transition…
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimum-weight subset of the obstacles separating the two points.…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…