Related papers: Asymptotic Optimality of Rapidly Exploring Random …
An underlying structure in several sampling-based methods for continuous multi-robot motion planning (MRMP) is the tensor roadmap (TR), which emerges from combining multiple PRM graphs constructed for the individual robots via a tensor…
Path planning in robotics often involves solving continuously valued, high-dimensional problems. Popular informed approaches include graph-based searches, such as A*, and sampling-based methods, such as Informed RRT*, which utilize informed…
A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or…
Rapidly exploring random trees (RRTs) have proven effective in quickly finding feasible solutions to complex motion planning problems. RRT* is an extension of the RRT algorithm that provides probabilistic asymptotic optimality guarantees…
We provide asymptotics for the range R(n) of a random walk on the d-dimensional lattice indexed by a random tree with n vertices. Using Kingman's subadditive ergodic theorem, we prove under general assumptions that R(n)/n converges to a…
We present a motion planner for planning through space-time with dynamic obstacles, velocity constraints, and unknown arrival time. Our algorithm, Space-Time RRT* (ST-RRT*), is a probabilistically complete, bidirectional motion planning…
Robots operating in changing environments either predict obstacle changes and/or plan quickly enough to react to them. Predictive approaches require a strong prior about the position and motion of obstacles. Reactive approaches require no…
We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the…
With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion…
Motivated by what is required for real-time path planning, the paper starts out by presenting sRMPD, a new recursive "local" planner founded on the key notion that, unless made necessary by an obstacle, there must be no deviation from the…
The random forest (RF) algorithm has become a very popular prediction method for its great flexibility and promising accuracy. In RF, it is conventional to put equal weights on all the base learners (trees) to aggregate their predictions.…
This paper proposes a new optimal control synthesis algorithm for multi-robot systems under global temporal logic tasks. Existing planning approaches under global temporal goals rely on graph search techniques applied to a product automaton…
Current motion planning approaches rely on binary collision checking to evaluate the validity of a state and thereby dictate where the robot is allowed to move. This approach leaves little room for robots to engage in contact with an…
We study the asymptotic optimal control of multi-class restless bandits. A restless bandit is a controllable stochastic process whose state evolution depends on whether or not the bandit is made active. Since finding the optimal control is…
We consider a one dimensional ballistic random walk evolving in a parametric independent and identically distributed random environment. We study the asymptotic properties of the maximum likelihood estimator of the parameter based on a…
We study the asymptotic behavior of the maximum degree in the evolving tree model with a choice based on both degree and fitness of a vertex. The tree is constructed in the following recursive way. Each vertex is assigned a parameter to it…
RRT* is an efficient sampling-based motion planning algorithm. However, without taking advantages of accessible environment information, sampling-based algorithms usually result in sampling failures, generate useless nodes, and/or fail in…
Current theoretical results on optimization trajectories of neural networks trained by gradient descent typically have the form of rigorous but potentially loose bounds on the loss values. In the present work we take a different approach…
An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions and is ideally suited for empirical Bayes applications. This…
Robots are increasingly deployed in dynamic and crowded environments, such as urban areas and shopping malls, where efficient and robust navigation is crucial. Traditional risk-based motion planning algorithms face challenges in such…