Related papers: Computing Feasible Trajectories for an Articulated…
Learning-based approaches for controlling safety-critical systems are rapidly growing in popularity; thus, it is important to assure their performance and safety. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification…
Considering uncertainties and disturbances is an important, yet challenging, step in successful decision making. The problem becomes more challenging in safety-constrained environments. In this paper, we propose a robust and safe trajectory…
Fix a point in a finite-dimensional complex vector space and consider the sequence of iterates of this point under the composition of a unitary map with the orthogonal projection on the hyperplane orthogonal to the starting point. We prove…
We study the linearizability monitoring problem, which asks whether a given concurrent history of a data structure is equivalent to some sequential execution of the same data structure. In general, this problem is $\textsf{NP}$-hard, even…
Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…
We study a trajectory analysis problem we call the Trajectory Capture Problem (TCP), in which, for a given input set ${\cal T}$ of trajectories in the plane, and an integer $k\geq 2$, we seek to compute a set of $k$ points (``portals'') to…
The problem of multi-armed bandits (MAB) asks to make sequential decisions while balancing between exploitation and exploration, and have been successfully applied to a wide range of practical scenarios. Various algorithms have been…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the…
Trajectory clustering is an important operation of knowledge discovery from mobility data. Especially nowadays, the need for performing advanced analytic operations over massively produced data, such as mobility traces, in efficient and…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of…
A turn sequence of left and right turns is realized as a simple rectilinear chain of integral segments whose turns at its bends are the same as the turn sequence. The chain starts from the origin and ends at some point which we call a…
Autonomous mobile robots must maintain safety, but should not sacrifice performance, leading to the classical reach-avoid problem: find a trajectory that is guaranteed to reach a goal and avoid obstacles. This paper addresses the near…
We present a scalable and effective multi-agent safe motion planner that enables a group of agents to move to their desired locations while avoiding collisions with obstacles and other agents, with the presence of rich obstacles,…
In this paper, we consider convex feasibility problems where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal…
What is the minimal information that a robot must retain to achieve its task? To design economical robots, the literature dealing with reduction of combinatorial filters approaches this problem algorithmically. As lossless state compression…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
This paper attacks the following problem. We are given a large number $N$ of rectangles in the plane, each with horizontal and vertical sides, and also a number $r<N$. The given list of $N$ rectangles may contain duplicates. The problem is…
Continuous formulations of trajectory planning problems have two main benefits. First, constraints are guaranteed to be satisfied at all times. Secondly, dynamic obstacles can be naturally considered with time. This paper introduces a novel…