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The accelerated deployment of service robots have spawned a number of algorithm variations to better handle real-world conditions. Many local trajectory planning techniques have been deployed on practical robot systems successfully. While most formulations of Dynamic Window Approach and Model Predictive Control can progress along paths and optimize for additional criteria, the use of pure path tracking algorithms is still commonplace. Decades later, Pure Pursuit and its variants continues to be one of the most commonly utilized classes of local trajectory planners. However, few Pure Pursuit variants have been proposed with schema for variable linear velocities - they either assume a constant velocity or fails to address the point at all. This paper presents a variant of Pure Pursuit designed with additional heuristics to regulate linear velocities, built atop the existing Adaptive variant. The Regulated Pure Pursuit algorithm makes incremental improvements on state of the art by adjusting linear velocities with particular focus on safety in constrained and partially observable spaces commonly negotiated by deployed robots. We present experiments with the Regulated Pure Pursuit algorithm on industrial-grade service robots. We also provide a high-quality reference implementation that is freely included ROS 2 Nav2 framework at https://github.com/ros-planning/navigation2 for fast evaluation.

Self-localization is a fundamental capability that mobile robot navigation systems integrate to move from one point to another using a map. Thus, any enhancement in localization accuracy is crucial to perform delicate dexterity tasks. This paper describes a new location that maintains several populations of particles using the Monte Carlo Localization (MCL) algorithm, always choosing the best one as the sytems's output. As novelties, our work includes a multi-scale match matching algorithm to create new MCL populations and a metric to determine the most reliable. It also contributes the state-of-the-art implementations, enhancing recovery times from erroneous estimates or unknown initial positions. The proposed method is evaluated in ROS2 in a module fully integrated with Nav2 and compared with the current state-of-the-art Adaptive ACML solution, obtaining good accuracy and recovery times., Comment: Submission for ICRA 2023

We study translating solitons for the mean curvature flow, $\Sigma^2\subseteq\mathbb{R}^3$ which are contained in slabs, and are of finite genus and finite entropy. As a first consequence of our results, we can enumerate connected components of slices to define asymptotic invariants $\omega^\pm(\Sigma)\in\mathbb{N}$, which count the numbers of "wings''. Analyzing these, we give a method for computing the entropies $\lambda(\Sigma)$ via a simple formula involving the wing numbers, which in particular shows that for this class of solitons the entropy is quantized into integer steps. Finally, combining the concept of wing numbers with Morse theory for minimal surfaces, we prove the uniqueness theorem that if $\Sigma$ is a complete embedded simply connected translating soliton contained in a slab with entropy $\lambda(\Sigma)=3$ and containing a vertical line, then $\Sigma$ is one of the translating pitchforks of Hoffman-Mart\'in-White, Comment: 42 pages, 4 figures. Theorem 1.5 has been corrected. New material has been added

The intelligent robotics community usually organizes knowledge into symbolic and sub-symbolic levels. These two levels establish the set of symbols and rules for manipulating knowledge based on their (symbol system - dictionary). Thus, the correspondences -- Grounding or knowledge representation -- require specific software techniques for anchoring continuous and discrete state variables between these two levels. This paper presents the design and evaluation of an Open Source tool called KANT(Knowledge mAnagemeNT) to let different components of the system architecture controlling the robot query, save, edit, and delete the data from the Knowledge Base without having to worry about the type and the implementation of the source data. Using KANT, components managing subsymbolic information can smoothly interact with symbolic components. Besides, implementation mechanisms used in KANT, such as the use of in-memory and non-SQL databases, improve the performance of the knowledge management systems in ROS middleware, as shown by the evaluations presented in this work.

For a class of functions (called minimal Rad\'o functions) that arise naturally in minimal surface theory, we bound the number of interior critical points (counting multiplicity) in terms of the boundary data and the Euler characteristic of the domain of the function., Comment: 33 pages. 2 Figures. Final version to appear in the Journal of the LMS

Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation $\rho:\underline{G}_{R}\rightarrow \underline{\textrm{Aut}}_{\textrm{Mod}(R)}(M)$. For the graded $T$-algebra $A$, defined as $ A := \left( S_{T}^{\bullet} (M^{\vee} \otimes_{R}N )\right)^{G}, $ we determine the conditions under which the graded $T$-algebra $A$ is finitely generated, finitely presented, or flat. Furthermore, we establish the conditions under which a closed embedding of $\textrm{Proj} \ A$ into a projective space exists. Since we do not impose any Noetherian hypotheses, our results generalize those in the literature, providing new powerful tools regarding moduli problems., Comment: Most of the results have been generalized. For instance, $\Bbbk$ is now a commutative ring instead of a field of characteristic zero. The title and the abstract have changed as well

Autonomous robots need to plan the tasks they carry out to fulfill their missions. The missions' increasing complexity does not let human designers anticipate all the possible situations, so traditional control systems based on state machines are not enough. This paper contains a description of the ROS2 Planning System (PlanSys2 in short), a framework for symbolic planning that incorporates novel approaches for execution on robots working in demanding environments. PlanSys2 aims to be the reference task planning framework in ROS2, the latest version of the {\em de facto} standard in robotics software development. Among its main features, it can be highlighted the optimized execution, based on Behavior Trees, of plans through a new actions auction protocol and its multi-robot planning capabilities. It already has a small but growing community of users and developers, and this document is a summary of the design and capabilities of this project., Comment: Preprint of the accepted paper at 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2021)

Robots need task planning to sequence and execute actions toward achieving their goals. On the other hand, Behavior Trees provide a mathematical model for specifying plan execution in an intrinsically composable, reactive, and robust way. PDDL (Planning Domain Definition Language) has become the standard description language for most planners. In this paper, we present a novel algorithm to systematically create behavior trees from PDDL plans to execute them. This approach uses the execution graph of the plan to generate a behavior tree. The most remarkable contribution of this approach is the algorithm to build a Behavior Tree that optimizes its execution by paralyzing actions, applicable to any plan, taking into account the actions' causal relationships. We demonstrate the improvement in the execution of plans in mobile robots using the ROS2 Planning System framework., Comment: Technical Report of the official paper published at AAMAS 2021