Related papers: A Simple Proof that Ricochet Robots is PSPACE-Comp…
We study reinforcement learning (RL) with linear function approximation. Existing algorithms for this problem only have high-probability regret and/or Probably Approximately Correct (PAC) sample complexity guarantees, which cannot guarantee…
Snakes are a remarkable evolutionary success story. Many snake-inspired robots have been proposed over the years. Soft robotic snakes (SRS) with their continuous and smooth bending capability better mimic their biological counterparts'…
Legged robots are promising candidates for exploring challenging areas on low-gravity bodies such as the Moon, Mars, or asteroids, thanks to their advanced mobility on unstructured terrain. However, as planetary robots' power and thermal…
The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled…
We investigate the intersection problem for finite monoids, which asks for a given set of regular languages, represented by recognizing morphisms to finite monoids from a variety V, whether there exists a word contained in their…
We analyze affine reachability problems in dimensions 1 and 2. We show that the reachability problem for 1-register machines over the integers with affine updates is PSPACE-hard, hence PSPACE-complete, strengthening a result by Finkel et…
We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then,…
We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod that is able to control its spontaneous curvature. Using a Cosserat model we derive, through variational principles, the…
We prove that the problem of deciding the consequence relation of the full Lambek calculus with weakening is complete for the class HAck of hyper-Ackermannian problems (i.e., level F_{\omega}^{\omega} of the ordinal-indexed hierarchy of…
While modular robots offer versatility, excessive joint torque during locomotion poses a significant risk of mechanical failure, especially for detachable joints. To address this, we propose an optimization framework using the NSGA-III…
Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bounded subgradients, we establish finite termination for several…
An optimization problem that naturally arises in the study of swarm robotics is the Freeze-Tag Problem (FTP) of how to awaken a set of ``asleep'' robots, by having an awakened robot move to their locations. Once a robot is awake, it can…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…
The high probability of hardware failures prevents many advanced robots (e.g., legged robots) from being confidently deployed in real-world situations (e.g., post-disaster rescue). Instead of attempting to diagnose the failures, robots…
Parkour poses a significant challenge for legged robots, requiring navigation through complex environments with agility and precision based on limited sensory inputs. In this work, we introduce a novel method for training end-to-end visual…
A recent result of Haase et al. has shown that reachability in two-clock timed automata is log-space equivalent to reachability in bounded one-counter automata. We show that reachability in bounded one-counter automata is PSPACE-complete.
Constraint automata are an adaptation of B\"uchi-automata that process data words where the data comes from some relational structure S. Every transition of such an automaton comes with constraints in terms of the relations of S. A…
This work proposes a robot task planning framework for retrieving a target object in a confined workspace among multiple stacked objects that obstruct the target. The robot can use prehensile picking and in-workspace placing actions. The…
A closed convex conic subset $\mathcal{S}$ of the positive semidefinite (PSD) cone is rank-one generated (ROG) if all of its extreme rays are generated by rank-one matrices. The ROG property of $\mathcal{S}$ is closely related to the…
Reallocation scheduling is one of the most fundamental problems in various areas such as supply chain management, logistics, and transportation science. In this paper, we introduce the reallocation problem that models the scheduling in…