arXiv subjects

Marius Kloetzer

Publications and source records attributed to Marius Kloetzer.

5 recordsLinked to original sources

arXiv2025

Smooth path planning with safety margins using Piece-Wise Bezier curves

In this paper, we propose a computationally efficient quadratic programming (QP) approach for generating smooth, $C^1$ continuous paths for mobile robots using piece-wise quadratic Bezier (PWB) curves. Our method explicitly incorporates safety margins within a structured optimization framework, balancing trajectory smoothness and robustness with manageable numerical complexity suitable for real-time and embedded applications. Comparative simulations demonstrate clear advantages over traditional piece-wise linear (PWL) path planning methods, showing reduced trajectory deviations, enhanced robustness, and improved overall path quality. These benefits are validated through simulations using a Pure-Pursuit controller in representative scenarios, highlighting the practical effectiveness and scalability of our approach for safe navigation.

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arXiv2025

Structural Integrality in Task Assignment and Path Finding via Total Unimodularity of Petri Net Models

Task Assignment and Path Finding (TAPF) concerns computing collision-free motions for multiple robots while jointly selecting goal locations. In this paper, safety is enforced by requiring unit-capacity traversal between successive intermediate markings, yielding coordination strategies that are valid independently of any specific time interpretation. Existing optimization-based approaches typically rely on time-expanded network-flow models, which result in large mixed-integer programs and limited scalability. We instead develop a Petri net (PN)-based optimization framework that exploits structural properties of the motion model to improve computational efficiency without explicit time expansion. When robot motion is modeled by strongly connected state-machine PNs, we show that, once the congestion level (equivalently, the synchronization depth) is fixed to an integer value, the resulting motion-planning constraint matrix is totally unimodular. Consequently, the corresponding LP relaxation admits integral optimal solutions for the motion variables. When the estimated congestion exceeds one, we introduce a synchronization-on-demand mechanism based on intermediate markings; for a fixed number of synchronization stages, the associated constraint matrices remain totally unimodular, thereby preserving integrality of the motion variables. Finally, we extend TAPF to Boolean specifications over regions of interest and propose a two-stage LP/mixed-integer linear programming (MILP) scheme in which integrality is confined to task-selection variables. Simulations on large benchmarks demonstrate substantial scalability improvements over time-expanded optimization baselines.

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arXiv2023

Multi-robot Motion Planning based on Nets-within-Nets Modeling and Simulation

This paper focuses on designing motion plans for a heterogeneous team of robots that must cooperate to fulfill a global mission. Robots move in an environment that contains some regions of interest, while the specification for the entire team can include avoidance, visits, or sequencing of these regions of interest. The mission is expressed in terms of a Petri net corresponding to an automaton, while each robot is also modeled by a state machine Petri net. The current work brings about the following contributions with respect to existing solutions for related problems. First, we propose a novel model, denoted High-Level robot team Petri Net (HLrtPN) system, to incorporate the specification and robot models into the Nets-within-Nets paradigm. A guard function, named Global Enabling Function, is designed to synchronize the firing of transitions so that robot motions do not violate the specification. Then, the solution is found by simulating the HLrtPN system in a specific software tool that accommodates Nets-within-Nets. Illustrative examples based on Linear Temporal Logic missions support the computational feasibility of the proposed framework.

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arXiv2022

On Multi-Robot Path Planning Based on Petri Net Models and LTL specifications

This work considers the path planning problem for a team of identical robots evolving in a known environment. The robots should satisfy a global specification given as a Linear Temporal Logic (LTL) formula over a set of regions of interest. The proposed method exploits the advantages of Petri net models for the team of robots and Büchi automata modeling the specification. The approach in this paper consists in combining the two models into one, denoted Composed Petri net and use it to find a sequence of action movements for the mobile robots, providing collision free trajectories to fulfill the specification. The solution results from a set of Mixed Integer Linear Programming (MILP) problems. The main advantage of the proposed solution is the completeness of the algorithm, meaning that a solution is found when exists, this representing the key difference with our previous work in [1]. The simulations illustrate comparison results between current and previous approaches, focusing on the computational complexity.

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arXiv2011

Multi-robot Deployment From LTL Specifications with Reduced Communication

In this paper, we develop a computational framework for fully automatic deployment of a team of unicycles from a global specification given as an LTL formula over some regions of interest. Our hierarchical approach consists of four steps: (i) the construction of finite abstractions for the motions of each robot, (ii) the parallel composition of the abstractions, (iii) the generation of a satisfying motion of the team; (iv) mapping this motion to individual robot control and communication strategies. The main result of the paper is an algorithm to reduce the amount of inter-robot communication during the fourth step of the procedure.

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